Номер 512, страница 70, часть 1 - гдз по физике 10-11 класс сборник задач Парфентьева

Авторы: Парфентьева Н. А.

Тип: Сборник задач

Серия: классический курс

Издательство: Просвещение

Год издания: 2007 - 2026

Часть: 1

Цвет обложки: фиолетовый

ISBN: 978-5-09-092936-3

Часть 1. 10 класс. Молекулярная физика. Тепловые явления. Основы термодинамики. Второй закон термодинамики - номер 512, страница 70.

App\Models\Task {#1030 // resources/views/models/task/default.blade.php
  #connection: "mysql"
  #table: "tasks"
  #primaryKey: "id"
  #keyType: "int"
  +incrementing: true
  #with: []
  #withCount: []
  +preventsLazyLoading: false
  #perPage: 15
  +exists: true
  +wasRecentlyCreated: false
  #escapeWhenCastingToString: false
  #attributes: array:24 [
    "id" => 1320515
    "created_at" => "2026-04-10 13:58:26"
    "updated_at" => null
    "field_page_start" => "70"
    "field_page_end" => null
    "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach/1-512"
    "field_display_title" => "512"
    "field_outside_task" => null
    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037
      #items: array:1 [
        0 => App\Models\Term {#1036
          #connection: "mysql"
          #table: "terms"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: false
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:6 [
            "id" => 26
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "name" => "номер"
            "field_cases" => array:6 [
              "field_accusative_case" => "номер"
              "field_creative_case" => "номером"
              "field_dative_case" => "номеру"
              "field_genitive_case" => "номера"
              "field_nominative_case" => "номер"
              "field_prepositional_case" => "номере"
            ]
            "field_short_name" => ""
          ]
          #original: array:6 [
            "id" => 26
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "name" => "номер"
            "field_cases" => array:6 [
              "field_accusative_case" => "номер"
              "field_creative_case" => "номером"
              "field_dative_case" => "номеру"
              "field_genitive_case" => "номера"
              "field_nominative_case" => "номер"
              "field_prepositional_case" => "номере"
            ]
            "field_short_name" => ""
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "field_metatags_title" => null
    "field_metatags_description" => null
    "field_h1" => null
    "field_description_top" => null
    "field_description_bottom" => null
    "field_match" => null
    "breadcrumbs" => []
    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035
      #items: []
      #escapeWhenCastingToString: false
    }
    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1075
      #items: array:1 [
        0 => App\Models\Branch {#1034
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1319883
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "1"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039
              #items: array:1 [
                0 => App\Models\Term {#1038
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 31
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Часть"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => "1"
                    "field_short_name" => "ч."
                  ]
                  #original: array:7 [
                    "id" => 31
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Часть"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => "1"
                    "field_short_name" => "ч."
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "5"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1040
              #items: array:1 [
                0 => App\Models\Book {#1041
                  #connection: "mysql"
                  #table: "books"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:50 [
                    "id" => 3751
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1042 …2}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1047 …2}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1049 …2}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 …2}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 …2}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1054 …2}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1056 …2}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1058 …2}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 …2}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 …2}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2}
                    "field_publication_number" => "13"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064 …2}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1066 …2}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2007"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное пособие"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "1110"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_10/parfenteva-sz/"
                    "field_isbn" => "978-5-09-092936-3"
                    "field_cover" => array:1 [ …1]
                    "field_cover_alts" => array:1 [ …1]
                    "field_covers" => array:1 [ …1]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1067 …2}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1068 …2}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1069 …2}
                    "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1070 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [ …3]
                  ]
                  #original: array:50 [
                    "id" => 3751
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1042 …2}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1047 …2}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1049 …2}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 …2}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 …2}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1054 …2}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1056 …2}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1058 …2}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 …2}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 …2}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2}
                    "field_publication_number" => "13"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064 …2}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1066 …2}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2007"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное пособие"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "1110"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_10/parfenteva-sz/"
                    "field_isbn" => "978-5-09-092936-3"
                    "field_cover" => array:1 [ …1]
                    "field_cover_alts" => array:1 [ …1]
                    "field_covers" => array:1 [ …1]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1067 …2}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1068 …2}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1069 …2}
                    "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1070 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [ …3]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1072
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1319883
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "1"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039}
            "field_page_start" => "5"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1040}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1072}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1226
      #items: array:5 [
        0 => App\Models\Branch {#1238
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1319883
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "1"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1242
              #items: array:1 [
                0 => App\Models\Term {#1239
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 31
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Часть"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => "1"
                    "field_short_name" => "ч."
                  ]
                  #original: array:7 [
                    "id" => 31
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Часть"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => "1"
                    "field_short_name" => "ч."
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "5"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1274
              #items: array:1 [
                0 => App\Models\Book {#1241
                  #connection: "mysql"
                  #table: "books"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:50 [
                    "id" => 3751
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1243
                      #items: array:1 [
                        0 => App\Models\Term {#1240
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6493
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Физика"
                            "field_abbreviated_name" => null
                            "field_cases" => array:6 [ …6]
                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "fizika"
                          ]
                          #original: array:10 [
                            "id" => 6493
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Физика"
                            "field_abbreviated_name" => null
                            "field_cases" => array:6 [ …6]
                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "fizika"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1244
                      #items: array:2 [
                        0 => App\Models\Term {#1245
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 5459
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "10"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "desjatyj"
                          ]
                          #original: array:6 [
                            "id" => 5459
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "10"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "desjatyj"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        1 => App\Models\Term {#1246
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 5460
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "11"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "odinadcatyj"
                          ]
                          #original: array:6 [
                            "id" => 5460
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "11"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "odinadcatyj"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1247
                      #items: array:1 [
                        0 => App\Models\Term {#1248
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 5153
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Просвещение"
                            "field_cases" => null
                            "field_translit" => "prosveschenie"
                          ]
                          #original: array:6 [
                            "id" => 5153
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Просвещение"
                            "field_cases" => null
                            "field_translit" => "prosveschenie"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1249
                      #items: array:1 [
                        0 => App\Models\Term {#1250
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 5418
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Парфентьева"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Наталия"
                            "field_patronymic" => "Андреевна"
                            "field_surname_rp" => "Парфентьевой"
                          ]
                          #original: array:12 [
                            "id" => 5418
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Парфентьева"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Наталия"
                            "field_patronymic" => "Андреевна"
                            "field_surname_rp" => "Парфентьевой"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1251
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1252
                      #items: array:1 [
                        0 => App\Models\Term {#1253
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6598
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Сборник задач"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [ …6]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "sbornik zadach"
                          ]
                          #original: array:10 [
                            "id" => 6598
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Сборник задач"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [ …6]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "sbornik zadach"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1254
                      #items: array:1 [
                        0 => App\Models\Term {#1255
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "rossiya"
                          ]
                          #original: array:6 [
                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "rossiya"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1256
                      #items: array:1 [
                        0 => App\Models\Term {#1257
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "moskva"
                          ]
                          #original: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "moskva"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1258
                      #items: array:1 [
                        0 => App\Models\Term {#1259
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:8 [
                            "id" => 4718
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "классический курс"
                            "field_cases" => null
                            "field_foreign_lang_series" => null
                            "field_transcription_eng" => null
                            "field_translit" => "klassicheskiy kurs"
                          ]
                          #original: array:8 [
                            "id" => 4718
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "классический курс"
                            "field_cases" => null
                            "field_foreign_lang_series" => null
                            "field_transcription_eng" => null
                            "field_translit" => "klassicheskiy kurs"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1260
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1261
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1262
                      #items: array:1 [
                        0 => App\Models\Term {#1263
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6706
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (старый)"
                            "field_cases" => array:6 [ …6]
                            "field_color" => null
                            "field_end_year" => "2022"
                            "field_start_year" => "2019"
                            "field_translit" => "fgos-old"
                            "field_type" => null
                          ]
                          #original: array:10 [
                            "id" => 6706
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (старый)"
                            "field_cases" => array:6 [ …6]
                            "field_color" => null
                            "field_end_year" => "2022"
                            "field_start_year" => "2019"
                            "field_translit" => "fgos-old"
                            "field_type" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publication_number" => "13"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1264
                      #items: array:1 [
                        0 => App\Models\Term {#1265
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 33
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "стереотипное"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "stereotipnoe"
                          ]
                          #original: array:6 [
                            "id" => 33
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "стереотипное"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "stereotipnoe"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1266
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2007"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное пособие"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "1110"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_10/parfenteva-sz/"
                    "field_isbn" => "978-5-09-092936-3"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_10/parfenteva-sz/covers/cover1.webp?ts=1756251235"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/fizika_10/parfenteva-sz/covers/cover1.webp?ts=1756251235"
                        "alt" => ""
                        "width" => "1588"
                        "height" => "2426"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1267
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1268
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1269
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1270
                      #items: array:1 [
                        0 => App\Models\Term {#1271
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 48
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "фиолетовый"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "fioletovyy"
                          ]
                          #original: array:6 [
                            "id" => 48
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "фиолетовый"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "fioletovyy"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 381
                      "subject" => 556
                      "class_subject" => 494
                    ]
                  ]
                  #original: array:50 [
                    "id" => 3751
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1243}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1244}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1247}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1249}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1251}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1252}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1254}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1256}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1258}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1260}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1261}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1262}
                    "field_publication_number" => "13"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1264}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1266}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2007"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное пособие"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "1110"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_10/parfenteva-sz/"
                    "field_isbn" => "978-5-09-092936-3"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_10/parfenteva-sz/covers/cover1.webp?ts=1756251235"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/fizika_10/parfenteva-sz/covers/cover1.webp?ts=1756251235"
                        "alt" => ""
                        "width" => "1588"
                        "height" => "2426"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1267}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1268}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1269}
                    "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1270}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 381
                      "subject" => 556
                      "class_subject" => 494
                    ]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1272
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1319883
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "1"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1242}
            "field_page_start" => "5"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1274}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1272}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Branch {#1273
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1319884
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "10 класс"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1275
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "5"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1276
              #items: array:1 [
                0 => App\Models\Book {#1241}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1277
              #items: array:1 [
                0 => App\Models\Branch {#1034}
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1319884
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "10 класс"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1275}
            "field_page_start" => "5"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1276}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1277}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        2 => App\Models\Branch {#1278
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1319925
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Молекулярная физика. Тепловые явления"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1279
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "51"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1280
              #items: array:1 [
                0 => App\Models\Book {#1241}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1323
              #items: array:1 [
                0 => App\Models\Branch {#1281
                  #connection: "mysql"
                  #table: "branches"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 1319884
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "10 класс"
                    "field_branch_order" => null
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1283 …2}
                    "field_page_start" => "5"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
                    "field_display_task_interval" => "0"
                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1282 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1315 …2}
                  ]
                  #original: array:24 [
                    "id" => 1319884
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "10 класс"
                    "field_branch_order" => null
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1283 …2}
                    "field_page_start" => "5"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
                    "field_display_task_interval" => "0"
                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1282 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1315 …2}
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1319925
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Молекулярная физика. Тепловые явления"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1279}
            "field_page_start" => "51"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1280}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1323}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        3 => App\Models\Branch {#1321
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1319934
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Основы термодинамики"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1322
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "64"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1324
              #items: array:1 [
                0 => App\Models\Book {#1241}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1402
              #items: array:1 [
                0 => App\Models\Branch {#1325
                  #connection: "mysql"
                  #table: "branches"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 1319925
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Молекулярная физика. Тепловые явления"
                    "field_branch_order" => null
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1327 …2}
                    "field_page_start" => "51"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
                    "field_display_task_interval" => "0"
                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1326 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1359 …2}
                  ]
                  #original: array:24 [
                    "id" => 1319925
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Молекулярная физика. Тепловые явления"
                    "field_branch_order" => null
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1327 …2}
                    "field_page_start" => "51"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
                    "field_display_task_interval" => "0"
                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1326 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1359 …2}
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1319934
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Основы термодинамики"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1322}
            "field_page_start" => "64"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1324}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1402}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        4 => App\Models\Branch {#1400
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1319938
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Второй закон термодинамики"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1401
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "69"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1403
              #items: array:1 [
                0 => App\Models\Book {#1241}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1412
              #items: array:1 [
                0 => App\Models\Branch {#1411
                  #connection: "mysql"
                  #table: "branches"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 1319934
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Основы термодинамики"
                    "field_branch_order" => null
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1413 …2}
                    "field_page_start" => "64"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
                    "field_display_task_interval" => "0"
                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1414 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1415 …2}
                  ]
                  #original: array:24 [
                    "id" => 1319934
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Основы термодинамики"
                    "field_branch_order" => null
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1413 …2}
                    "field_page_start" => "64"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
                    "field_display_task_interval" => "0"
                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1414 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1415 …2}
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1319938
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Второй закон термодинамики"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1401}
            "field_page_start" => "69"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1403}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1412}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "content" => Illuminate\Database\Eloquent\Collection {#1150
      #items: array:2 [
        0 => App\Models\Element {#1223
          #connection: "mysql"
          #table: "elements"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:7 [
            "id" => 1496673
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1213
              #items: array:1 [
                0 => App\Models\Edition {#1221
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:21 [
                    "id" => 5460
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1219 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text, image"
                    "field_page_content_mode" => "image"
                    "field_content_text_checked" => null
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "stas"
                    "field_edition_type" => "statement"
                    "field_root_dir" => "0-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1218 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1216 …2}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1217 …2}
                    "field_content_source" => null
                  ]
                  #original: array:21 [
                    "id" => 5460
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1219 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text, image"
                    "field_page_content_mode" => "image"
                    "field_content_text_checked" => null
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "stas"
                    "field_edition_type" => "statement"
                    "field_root_dir" => "0-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1218 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1216 …2}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1217 …2}
                    "field_content_source" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "task" => array:2 [
              "refs" => "1320515"
              "type" => "task"
            ]
            "text" => "<p><strong>512.</strong> [433] Определите количество теплоты, переданной одноатомному газу при переходе его из состояния 1 в состояние 2, как показано на рисунке 102, если $p_1 = 500$ кПа, $V_1 = 1$ л, $V_2 = 4$ л.</p><p>Рис. 102</p>"
            "img" => array:2 [
              0 => array:5 [
                "name" => "512-1.jpg"
                "alt" => null
                "width" => "878"
                "height" => 350
                "path" => "/media/fizika_10/parfenteva-sz/0-1/512-1.webp?ts=1756373384"
              ]
              1 => array:5 [
                "name" => "512-2.jpg"
                "alt" => null
                "width" => "491"
                "height" => 437
                "path" => "/media/fizika_10/parfenteva-sz/0-1/512-2.webp?ts=1756373384"
              ]
            ]
          ]
          #original: array:7 [
            "id" => 1496673
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1213}
            "task" => array:2 [
              "refs" => "1320515"
              "type" => "task"
            ]
            "text" => "<p><strong>512.</strong> [433] Определите количество теплоты, переданной одноатомному газу при переходе его из состояния 1 в состояние 2, как показано на рисунке 102, если $p_1 = 500$ кПа, $V_1 = 1$ л, $V_2 = 4$ л.</p><p>Рис. 102</p>"
            "img" => array:2 [
              0 => array:5 [
                "name" => "512-1.jpg"
                "alt" => null
                "width" => "878"
                "height" => 350
                "path" => "/media/fizika_10/parfenteva-sz/0-1/512-1.webp?ts=1756373384"
              ]
              1 => array:5 [
                "name" => "512-2.jpg"
                "alt" => null
                "width" => "491"
                "height" => 437
                "path" => "/media/fizika_10/parfenteva-sz/0-1/512-2.webp?ts=1756373384"
              ]
            ]
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Element {#1214
          #connection: "mysql"
          #table: "elements"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:6 [
            "id" => 1724600
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1204
              #items: array:1 [
                0 => App\Models\Edition {#1215
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:21 [
                    "id" => 6302
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение"
                    "field_order" => "2"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1210 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text"
                    "field_page_content_mode" => ""
                    "field_content_text_checked" => null
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Gemini 2.5 Pro"
                    "field_moderator" => "tolik"
                    "field_edition_type" => "solution"
                    "field_root_dir" => "1-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1211 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1208 …2}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1209 …2}
                    "field_content_source" => null
                  ]
                  #original: array:21 [
                    "id" => 6302
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение"
                    "field_order" => "2"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1210 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text"
                    "field_page_content_mode" => ""
                    "field_content_text_checked" => null
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Gemini 2.5 Pro"
                    "field_moderator" => "tolik"
                    "field_edition_type" => "solution"
                    "field_root_dir" => "1-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1211 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1208 …2}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1209 …2}
                    "field_content_source" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "task" => array:2 [
              "refs" => "1320515"
              "type" => "task"
            ]
            "text" => "<p><strong>Дано:</strong></p><p>Газ - одноатомный</p><p>$p_1 = 500 \text{ кПа} = 500 \cdot 10^3 \text{ Па} = 5 \cdot 10^5 \text{ Па}$</p><p>$V_1 = 1 \text{ л} = 1 \cdot 10^{-3} \text{ м}^3$</p><p>$V_2 = 4 \text{ л} = 4 \cdot 10^{-3} \text{ м}^3$</p><p><strong>Найти:</strong></p><p>$\text{Q}$</p><p><strong>Решение:</strong></p><p>Количество теплоты, переданное газу, найдем по первому закону термодинамики:</p><p>$Q = \Delta U + A$</p><p>где $\Delta U$ — изменение внутренней энергии газа, а $\text{A}$ — работа, совершенная газом.</p><p>Для одноатомного идеального газа изменение внутренней энергии вычисляется по формуле:</p><p>$\Delta U = \frac{3}{2}(p_2V_2 - p_1V_1)$</p><p>Работа газа $\text{A}$ в процессе 1-2 численно равна площади трапеции под графиком на диаграмме $p-V$:</p><p>$A = \frac{p_1 + p_2}{2}(V_2 - V_1)$</p><p>Для вычисления $\Delta U$ и $\text{A}$ необходимо найти конечное давление $p_2$. График процесса представляет собой прямую линию, проходящую через точки $(V_1, p_1)$ и $(V_2, p_2)$. Судя по рисунку, продолжение этой прямой проходит через начало координат $(0,0)$, что означает прямую пропорциональность между давлением и объемом: $p = kV$.</p><p>Из этого соотношения следует:</p><p>$\frac{p_1}{V_1} = \frac{p_2}{V_2}$</p><p>Отсюда выразим и найдем $p_2$:</p><p>$p_2 = p_1 \frac{V_2}{V_1} = 5 \cdot 10^5 \text{ Па} \cdot \frac{4 \cdot 10^{-3} \text{ м}^3}{1 \cdot 10^{-3} \text{ м}^3} = 20 \cdot 10^5 \text{ Па} = 2 \cdot 10^6 \text{ Па}$</p><p>Теперь рассчитаем работу газа $\text{A}$:</p><p>$A = \frac{5 \cdot 10^5 \text{ Па} + 20 \cdot 10^5 \text{ Па}}{2} \cdot (4 \cdot 10^{-3} \text{ м}^3 - 1 \cdot 10^{-3} \text{ м}^3) = \frac{25 \cdot 10^5}{2} \cdot 3 \cdot 10^{-3} = 12.5 \cdot 10^5 \cdot 3 \cdot 10^{-3} = 37.5 \cdot 10^2 \text{ Дж} = 3750 \text{ Дж}$</p><p>Рассчитаем изменение внутренней энергии $\Delta U$:</p><p>$\Delta U = \frac{3}{2}(2 \cdot 10^6 \text{ Па} \cdot 4 \cdot 10^{-3} \text{ м}^3 - 5 \cdot 10^5 \text{ Па} \cdot 1 \cdot 10^{-3} \text{ м}^3) = \frac{3}{2}(8000 \text{ Дж} - 500 \text{ Дж}) = \frac{3}{2} \cdot 7500 \text{ Дж} = 11250 \text{ Дж}$</p><p>Наконец, найдем общее количество переданной теплоты $\text{Q}$:</p><p>$Q = \Delta U + A = 11250 \text{ Дж} + 3750 \text{ Дж} = 15000 \text{ Дж} = 15 \text{ кДж}$</p><p><strong>Ответ:</strong> количество теплоты, переданной газу, равно $15 \text{ кДж}$.</p>"
          ]
          #original: array:6 [
            "id" => 1724600
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1204}
            "task" => array:2 [
              "refs" => "1320515"
              "type" => "task"
            ]
            "text" => "<p><strong>Дано:</strong></p><p>Газ - одноатомный</p><p>$p_1 = 500 \text{ кПа} = 500 \cdot 10^3 \text{ Па} = 5 \cdot 10^5 \text{ Па}$</p><p>$V_1 = 1 \text{ л} = 1 \cdot 10^{-3} \text{ м}^3$</p><p>$V_2 = 4 \text{ л} = 4 \cdot 10^{-3} \text{ м}^3$</p><p><strong>Найти:</strong></p><p>$\text{Q}$</p><p><strong>Решение:</strong></p><p>Количество теплоты, переданное газу, найдем по первому закону термодинамики:</p><p>$Q = \Delta U + A$</p><p>где $\Delta U$ — изменение внутренней энергии газа, а $\text{A}$ — работа, совершенная газом.</p><p>Для одноатомного идеального газа изменение внутренней энергии вычисляется по формуле:</p><p>$\Delta U = \frac{3}{2}(p_2V_2 - p_1V_1)$</p><p>Работа газа $\text{A}$ в процессе 1-2 численно равна площади трапеции под графиком на диаграмме $p-V$:</p><p>$A = \frac{p_1 + p_2}{2}(V_2 - V_1)$</p><p>Для вычисления $\Delta U$ и $\text{A}$ необходимо найти конечное давление $p_2$. График процесса представляет собой прямую линию, проходящую через точки $(V_1, p_1)$ и $(V_2, p_2)$. Судя по рисунку, продолжение этой прямой проходит через начало координат $(0,0)$, что означает прямую пропорциональность между давлением и объемом: $p = kV$.</p><p>Из этого соотношения следует:</p><p>$\frac{p_1}{V_1} = \frac{p_2}{V_2}$</p><p>Отсюда выразим и найдем $p_2$:</p><p>$p_2 = p_1 \frac{V_2}{V_1} = 5 \cdot 10^5 \text{ Па} \cdot \frac{4 \cdot 10^{-3} \text{ м}^3}{1 \cdot 10^{-3} \text{ м}^3} = 20 \cdot 10^5 \text{ Па} = 2 \cdot 10^6 \text{ Па}$</p><p>Теперь рассчитаем работу газа $\text{A}$:</p><p>$A = \frac{5 \cdot 10^5 \text{ Па} + 20 \cdot 10^5 \text{ Па}}{2} \cdot (4 \cdot 10^{-3} \text{ м}^3 - 1 \cdot 10^{-3} \text{ м}^3) = \frac{25 \cdot 10^5}{2} \cdot 3 \cdot 10^{-3} = 12.5 \cdot 10^5 \cdot 3 \cdot 10^{-3} = 37.5 \cdot 10^2 \text{ Дж} = 3750 \text{ Дж}$</p><p>Рассчитаем изменение внутренней энергии $\Delta U$:</p><p>$\Delta U = \frac{3}{2}(2 \cdot 10^6 \text{ Па} \cdot 4 \cdot 10^{-3} \text{ м}^3 - 5 \cdot 10^5 \text{ Па} \cdot 1 \cdot 10^{-3} \text{ м}^3) = \frac{3}{2}(8000 \text{ Дж} - 500 \text{ Дж}) = \frac{3}{2} \cdot 7500 \text{ Дж} = 11250 \text{ Дж}$</p><p>Наконец, найдем общее количество переданной теплоты $\text{Q}$:</p><p>$Q = \Delta U + A = 11250 \text{ Дж} + 3750 \text{ Дж} = 15000 \text{ Дж} = 15 \text{ кДж}$</p><p><strong>Ответ:</strong> количество теплоты, переданной газу, равно $15 \text{ кДж}$.</p>"
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "next" => array:2 [
      "refs" => "1320516"
      "type" => "task"
    ]
    "previous" => array:2 [
      "refs" => "1320514"
      "type" => "task"
    ]
    "book" => Illuminate\Database\Eloquent\Collection {#1192
      #items: array:1 [
        0 => App\Models\Book {#1241}
      ]
      #escapeWhenCastingToString: false
    }
    "page" => Illuminate\Database\Eloquent\Collection {#1188
      #items: array:1 [
        0 => App\Models\BookPage {#1224
          #connection: "mysql"
          #table: "book_pages"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:21 [
            "id" => 1341320
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_page_start" => "70"
            "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach/page-70"
            "field_display_title" => "70"
            "field_folder" => "1"
            "field_image_name" => "70"
            "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1206
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_weight" => "0"
            "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1207
              #items: array:1 [
                0 => App\Models\Book {#1241}
              ]
              #escapeWhenCastingToString: false
            }
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "edition_groups" => Illuminate\Database\Eloquent\Collection {#1205
              #items: []
              #escapeWhenCastingToString: false
            }
            "content" => Illuminate\Database\Eloquent\Collection {#1195
              #items: array:1 [
                0 => App\Models\Element {#1194
                  #connection: "mysql"
                  #table: "elements"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:6 [
                    "id" => 1516535
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "edition" => Illuminate\Database\Eloquent\Collection {#1190 …2}
                    "book_page" => array:2 [ …2]
                    "img" => array:1 [ …1]
                  ]
                  #original: array:6 [
                    "id" => 1516535
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "edition" => Illuminate\Database\Eloquent\Collection {#1190 …2}
                    "book_page" => array:2 [ …2]
                    "img" => array:1 [ …1]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "next" => array:2 [
              "refs" => "1341321"
              "type" => "book_page"
            ]
            "previous" => array:2 [
              "refs" => "1341319"
              "type" => "book_page"
            ]
            "tasks" => Illuminate\Database\Eloquent\Collection {#1514
              #items: array:6 [
                0 => App\Models\Task {#1526
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 1320514
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "70"
                    "field_page_end" => null
                    "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach/1-511"
                    "field_display_title" => "511"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1527 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1528 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1529 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1530 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1532 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1538 …2}
                    "page" => array:2 [ …2]
                  ]
                  #original: array:24 [
                    "id" => 1320514
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "70"
                    "field_page_end" => null
                    "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach/1-511"
                    "field_display_title" => "511"
                    "field_outside_task" => null
                     …16
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
                1 => App\Models\Task {#1533
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [ …24]
                  #original: array:24 [ …24]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
                2 => App\Models\Task {#1545
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [ …24]
                  #original: array:24 [ …24]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
                3 => App\Models\Task {#1765
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [ …24]
                  #original: array:24 [ …24]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
                4 => App\Models\Task {#1836
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [ …24]
                  #original: array:24 [ …24]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
                5 => App\Models\Task {#1825
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [ …24]
                  #original: array:24 [ …24]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:21 [
            "id" => 1341320
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_page_start" => "70"
            "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach/page-70"
            "field_display_title" => "70"
            "field_folder" => "1"
            "field_image_name" => "70"
            "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1206}
            "field_weight" => "0"
            "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1207}
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "edition_groups" => Illuminate\Database\Eloquent\Collection {#1205}
            "content" => Illuminate\Database\Eloquent\Collection {#1195}
            "next" => array:2 [
              "refs" => "1341321"
              "type" => "book_page"
            ]
            "previous" => array:2 [
              "refs" => "1341319"
              "type" => "book_page"
            ]
            "tasks" => Illuminate\Database\Eloquent\Collection {#1514}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
  ]
  #original: array:24 [
    "id" => 1320515
    "created_at" => "2026-04-10 13:58:26"
    "updated_at" => null
    "field_page_start" => "70"
    "field_page_end" => null
    "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach/1-512"
    "field_display_title" => "512"
    "field_outside_task" => null
    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037}
    "field_metatags_title" => null
    "field_metatags_description" => null
    "field_h1" => null
    "field_description_top" => null
    "field_description_bottom" => null
    "field_match" => null
    "breadcrumbs" => []
    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035}
    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1075}
    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1226}
    "content" => Illuminate\Database\Eloquent\Collection {#1150}
    "next" => array:2 [
      "refs" => "1320516"
      "type" => "task"
    ]
    "previous" => array:2 [
      "refs" => "1320514"
      "type" => "task"
    ]
    "book" => Illuminate\Database\Eloquent\Collection {#1192}
    "page" => array:2 [
      "refs" => "1341320"
      "type" => "book_page"
    ]
  ]
  #changes: []
  #casts: []
  #classCastCache: []
  #attributeCastCache: []
  #dateFormat: null
  #appends: []
  #dispatchesEvents: []
  #observables: []
  #relations: []
  #touches: []
  +timestamps: true
  +usesUniqueIds: false
  #hidden: []
  #visible: []
  #fillable: []
  #guarded: array:1 [
    0 => "*"
  ]
}
№512 (с. 70)
Условие. №512 (с. 70)
скриншот условия
Физика, 10-11 класс Сборник задач, автор: Парфентьева Наталия Андреевна, издательство Просвещение, Москва, 2007, Часть 1, страница 70, номер 512, Условие
Физика, 10-11 класс Сборник задач, автор: Парфентьева Наталия Андреевна, издательство Просвещение, Москва, 2007, Часть 1, страница 70, номер 512, Условие (продолжение 2)

512. [433] Определите количество теплоты, переданной одноатомному газу при переходе его из состояния 1 в состояние 2, как показано на рисунке 102, если $p_1 = 500$ кПа, $V_1 = 1$ л, $V_2 = 4$ л.

Рис. 102

Решение. №512 (с. 70)

Дано:

Газ - одноатомный

$p_1 = 500 \text{ кПа} = 500 \cdot 10^3 \text{ Па} = 5 \cdot 10^5 \text{ Па}$

$V_1 = 1 \text{ л} = 1 \cdot 10^{-3} \text{ м}^3$

$V_2 = 4 \text{ л} = 4 \cdot 10^{-3} \text{ м}^3$

Найти:

$\text{Q}$

Решение:

Количество теплоты, переданное газу, найдем по первому закону термодинамики:

$Q = \Delta U + A$

где $\Delta U$ — изменение внутренней энергии газа, а $\text{A}$ — работа, совершенная газом.

Для одноатомного идеального газа изменение внутренней энергии вычисляется по формуле:

$\Delta U = \frac{3}{2}(p_2V_2 - p_1V_1)$

Работа газа $\text{A}$ в процессе 1-2 численно равна площади трапеции под графиком на диаграмме $p-V$:

$A = \frac{p_1 + p_2}{2}(V_2 - V_1)$

Для вычисления $\Delta U$ и $\text{A}$ необходимо найти конечное давление $p_2$. График процесса представляет собой прямую линию, проходящую через точки $(V_1, p_1)$ и $(V_2, p_2)$. Судя по рисунку, продолжение этой прямой проходит через начало координат $(0,0)$, что означает прямую пропорциональность между давлением и объемом: $p = kV$.

Из этого соотношения следует:

$\frac{p_1}{V_1} = \frac{p_2}{V_2}$

Отсюда выразим и найдем $p_2$:

$p_2 = p_1 \frac{V_2}{V_1} = 5 \cdot 10^5 \text{ Па} \cdot \frac{4 \cdot 10^{-3} \text{ м}^3}{1 \cdot 10^{-3} \text{ м}^3} = 20 \cdot 10^5 \text{ Па} = 2 \cdot 10^6 \text{ Па}$

Теперь рассчитаем работу газа $\text{A}$:

$A = \frac{5 \cdot 10^5 \text{ Па} + 20 \cdot 10^5 \text{ Па}}{2} \cdot (4 \cdot 10^{-3} \text{ м}^3 - 1 \cdot 10^{-3} \text{ м}^3) = \frac{25 \cdot 10^5}{2} \cdot 3 \cdot 10^{-3} = 12.5 \cdot 10^5 \cdot 3 \cdot 10^{-3} = 37.5 \cdot 10^2 \text{ Дж} = 3750 \text{ Дж}$

Рассчитаем изменение внутренней энергии $\Delta U$:

$\Delta U = \frac{3}{2}(2 \cdot 10^6 \text{ Па} \cdot 4 \cdot 10^{-3} \text{ м}^3 - 5 \cdot 10^5 \text{ Па} \cdot 1 \cdot 10^{-3} \text{ м}^3) = \frac{3}{2}(8000 \text{ Дж} - 500 \text{ Дж}) = \frac{3}{2} \cdot 7500 \text{ Дж} = 11250 \text{ Дж}$

Наконец, найдем общее количество переданной теплоты $\text{Q}$:

$Q = \Delta U + A = 11250 \text{ Дж} + 3750 \text{ Дж} = 15000 \text{ Дж} = 15 \text{ кДж}$

Ответ: количество теплоты, переданной газу, равно $15 \text{ кДж}$.

Помогло решение? Оставьте отзыв в комментариях ниже.

Присоединяйтесь к Телеграм-группе @top_gdz

Присоединиться

Мы подготовили для вас ответ c подробным объяснением домашего задания по физике за 10-11 класс, для упражнения номер 512 расположенного на странице 70 для 1-й части к сборнику задач серии классический курс 2007 года издания для учащихся школ и гимназий.

Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №512 (с. 70), автора: Парфентьева (Наталия Андреевна), 1-й части ФГОС (старый) учебного пособия издательства Просвещение.