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Номер 511, 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
Популярные ГДЗ в 10 классе
Часть 1. 10 класс. Молекулярная физика. Тепловые явления. Основы термодинамики. Второй закон термодинамики - номер 511, 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" => 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 {#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 {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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 {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #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 {#1058 #items: array:1 [ 0 => App\Models\Book {#1057 #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 {#1062 #items: array:1 [ 0 => App\Models\Term {#1059 #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 {#1060 #items: array:2 [ 0 => App\Models\Term {#1071 #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 {#1072 #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 {#1070 #items: array:1 [ 0 => App\Models\Term {#1068 #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 {#1076 #items: array:1 [ 0 => App\Models\Term {#1075 #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 {#1063 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1066 #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 {#1067 #items: array:1 [ 0 => App\Models\Term {#1065 #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 {#1078 #items: array:1 [ 0 => App\Models\Term {#1073 #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 {#1080 #items: array:1 [ 0 => App\Models\Term {#1077 #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 {#1079 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1084 #items: array:1 [ 0 => App\Models\Term {#1081 #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 {#1086 #items: array:1 [ 0 => App\Models\Term {#1083 #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 {#1085 #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 {#1082 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Term {#1089 #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 {#1062} "field_class" => Illuminate\Database\Eloquent\Collection {#1060} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1070} "field_author" => Illuminate\Database\Eloquent\Collection {#1076} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1063} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1064} "field_country" => Illuminate\Database\Eloquent\Collection {#1067} "field_city" => Illuminate\Database\Eloquent\Collection {#1078} "field_series" => Illuminate\Database\Eloquent\Collection {#1080} "field_umk" => Illuminate\Database\Eloquent\Collection {#1079} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1084} "field_publication_number" => "13" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1086} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1085} "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 {#1082} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1087} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1088} "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1092} "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 {#1048 #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 {#1050} "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 {#1058} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1048} ] #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 {#1115 #items: array:5 [ 0 => App\Models\Branch {#1127 #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 {#1128 #items: array:1 [ 0 => App\Models\Term {#1047} ] #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 {#1129 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130 #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 {#1128} "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 {#1129} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130} ] #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 {#1131 #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 {#1132 #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 {#1133 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #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 {#1132} "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 {#1133} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1134} ] #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 {#1135 #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 {#1136 #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 {#1137 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Branch {#1145 #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 {#1147 …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 {#1148 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1149 …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 {#1147 …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 {#1148 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1149 …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 {#1136} "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 {#1137} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1146} ] #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 {#1139 #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 {#1138 #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 {#1142 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Branch {#1154 #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 {#1156 …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 {#1157 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1158 …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 {#1156 …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 {#1157 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1158 …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 {#1138} "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 {#1142} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155} ] #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 {#1143 #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 {#1140 #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 {#1151 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1164 #items: array:1 [ 0 => App\Models\Branch {#1163 #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 {#1165 …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 {#1166 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1167 …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 {#1165 …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 {#1166 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1167 …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 {#1140} "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 {#1151} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1164} ] #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 {#1038 #items: array:2 [ 0 => App\Models\Element {#1107 #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" => 1496672 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Edition {#1097 #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 {#1095 …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 {#1091 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094 …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 {#1095 …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 {#1091 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094 …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" => "1320514" "type" => "task" ] "text" => "<p><strong>511.</strong> [432] Одноатомный газ переводят из состояния 1 в состояние 2, для чего используют изохорный и изобарный процессы (рис. 101). При этом $V_2 = 2V_1$, $p_2 = 2p_1$. Определите отношение количеств теплоты, необходимой для совершения перехода из состояния 1 в состояние 2 в одном случае через состояние 3, в другом через состояние 4.</p><p>Рис. 101</p>" "img" => array:1 [ 0 => array:5 [ "name" => "511-1.jpg" "alt" => null "width" => "1359" "height" => 605 "path" => "/media/fizika_10/parfenteva-sz/0-1/511-1.webp?ts=1756373384" ] ] ] #original: array:7 [ "id" => 1496672 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098} "task" => array:2 [ "refs" => "1320514" "type" => "task" ] "text" => "<p><strong>511.</strong> [432] Одноатомный газ переводят из состояния 1 в состояние 2, для чего используют изохорный и изобарный процессы (рис. 101). При этом $V_2 = 2V_1$, $p_2 = 2p_1$. Определите отношение количеств теплоты, необходимой для совершения перехода из состояния 1 в состояние 2 в одном случае через состояние 3, в другом через состояние 4.</p><p>Рис. 101</p>" "img" => array:1 [ 0 => array:5 [ "name" => "511-1.jpg" "alt" => null "width" => "1359" "height" => 605 "path" => "/media/fizika_10/parfenteva-sz/0-1/511-1.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 {#1106 #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" => 1724599 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Edition {#1052 #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 {#1124 …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 {#1039 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1055 …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 {#1124 …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 {#1039 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1055 …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" => "1320514" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Газ одноатомный<br>$V_2 = 2V_1$<br>$p_2 = 2p_1$</p><p><strong>Найти:</strong></p><p>$\frac{Q_{1 \t°3 \t°2}}{Q_{1 \t°4 \t°2}}$</p><p><strong>Решение:</strong></p><p>Для решения задачи воспользуемся первым началом термодинамики, согласно которому количество теплоты $\text{Q}$, переданное системе, идет на изменение ее внутренней энергии $\Delta U$ и на совершение системой работы $\text{A}$ над внешними силами:</p><p>$Q = \Delta U + A$</p><p>Для одноатомного идеального газа изменение внутренней энергии определяется формулой:</p><p>$\Delta U = \frac{3}{2}\nu R \Delta T = \frac{3}{2}(p_k V_k - p_н V_н)$, где $p_н, V_н$ — начальные давление и объем, а $p_k, V_k$ — конечные.</p><p>Работа газа $\text{A}$ при изохорном процессе ($V=const$) равна нулю, а при изобарном процессе ($p=const$) вычисляется как $A = p \Delta V$.</p><p>Рассмотрим первый способ перевода газа из состояния 1 в состояние 2: через точку 3 (процесс 1 → 3 → 2).</p><p><strong>1.</strong> Процесс 1 → 3 является изохорным, так как объем не меняется ($V_1 = V_3 = const$).</p><p>Работа газа на этом участке равна нулю: $A_{13} = 0$.</p><p>Изменение внутренней энергии: $\Delta U_{13} = \frac{3}{2}(p_3 V_3 - p_1 V_1) = \frac{3}{2}(p_2 V_1 - p_1 V_1) = \frac{3}{2} V_1 (p_2 - p_1)$.</p><p>Количество теплоты: $Q_{13} = \Delta U_{13} + A_{13} = \frac{3}{2} V_1 (p_2 - p_1)$.</p><p><strong>2.</strong> Процесс 3 → 2 является изобарным, так как давление не меняется ($p_3 = p_2 = const$).</p><p>Работа газа: $A_{32} = p_2 (V_2 - V_3) = p_2 (V_2 - V_1)$.</p><p>Изменение внутренней энергии: $\Delta U_{32} = \frac{3}{2}(p_2 V_2 - p_3 V_3) = \frac{3}{2}(p_2 V_2 - p_2 V_1) = \frac{3}{2} p_2 (V_2 - V_1)$.</p><p>Количество теплоты: $Q_{32} = \Delta U_{32} + A_{32} = \frac{3}{2} p_2 (V_2 - V_1) + p_2 (V_2 - V_1) = \frac{5}{2} p_2 (V_2 - V_1)$.</p><p>Суммарное количество теплоты для процесса 1 → 3 → 2:</p><p>$Q_{1 \t°3 \t°2} = Q_{13} + Q_{32} = \frac{3}{2} V_1 (p_2 - p_1) + \frac{5}{2} p_2 (V_2 - V_1)$.</p><p>Подставим известные соотношения $V_2 = 2V_1$ и $p_2 = 2p_1$:</p><p>$Q_{1 \t°3 \t°2} = \frac{3}{2} V_1 (2p_1 - p_1) + \frac{5}{2} (2p_1) (2V_1 - V_1) = \frac{3}{2} V_1 p_1 + \frac{5}{2} (2p_1) V_1 = \frac{3}{2} p_1 V_1 + 5 p_1 V_1 = \frac{13}{2} p_1 V_1$.</p><p>Рассмотрим второй способ перевода газа из состояния 1 в состояние 2: через точку 4 (процесс 1 → 4 → 2).</p><p><strong>1.</strong> Процесс 1 → 4 является изобарным ($p_1 = p_4 = const$).</p><p>Работа газа: $A_{14} = p_1 (V_4 - V_1) = p_1 (V_2 - V_1)$.</p><p>Изменение внутренней энергии: $\Delta U_{14} = \frac{3}{2}(p_4 V_4 - p_1 V_1) = \frac{3}{2}(p_1 V_2 - p_1 V_1) = \frac{3}{2} p_1 (V_2 - V_1)$.</p><p>Количество теплоты: $Q_{14} = \Delta U_{14} + A_{14} = \frac{3}{2} p_1 (V_2 - V_1) + p_1 (V_2 - V_1) = \frac{5}{2} p_1 (V_2 - V_1)$.</p><p><strong>2.</strong> Процесс 4 → 2 является изохорным ($V_4 = V_2 = const$).</p><p>Работа газа: $A_{42} = 0$.</p><p>Изменение внутренней энергии: $\Delta U_{42} = \frac{3}{2}(p_2 V_2 - p_4 V_4) = \frac{3}{2}(p_2 V_2 - p_1 V_2) = \frac{3}{2} V_2 (p_2 - p_1)$.</p><p>Количество теплоты: $Q_{42} = \Delta U_{42} + A_{42} = \frac{3}{2} V_2 (p_2 - p_1)$.</p><p>Суммарное количество теплоты для процесса 1 → 4 → 2:</p><p>$Q_{1 \t°4 \t°2} = Q_{14} + Q_{42} = \frac{5}{2} p_1 (V_2 - V_1) + \frac{3}{2} V_2 (p_2 - p_1)$.</p><p>Подставим известные соотношения $V_2 = 2V_1$ и $p_2 = 2p_1$:</p><p>$Q_{1 \t°4 \t°2} = \frac{5}{2} p_1 (2V_1 - V_1) + \frac{3}{2} (2V_1) (2p_1 - p_1) = \frac{5}{2} p_1 V_1 + \frac{3}{2} (2V_1) p_1 = \frac{5}{2} p_1 V_1 + 3 p_1 V_1 = \frac{11}{2} p_1 V_1$.</p><p>Теперь найдем искомое отношение количеств теплоты:</p><p>$\frac{Q_{1 \t°3 \t°2}}{Q_{1 \t°4 \t°2}} = \frac{\frac{13}{2} p_1 V_1}{\frac{11}{2} p_1 V_1} = \frac{13}{11}$.</p><p><strong>Ответ:</strong> $\frac{13}{11}$.</p>" ] #original: array:6 [ "id" => 1724599 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1053} "task" => array:2 [ "refs" => "1320514" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Газ одноатомный<br>$V_2 = 2V_1$<br>$p_2 = 2p_1$</p><p><strong>Найти:</strong></p><p>$\frac{Q_{1 \t°3 \t°2}}{Q_{1 \t°4 \t°2}}$</p><p><strong>Решение:</strong></p><p>Для решения задачи воспользуемся первым началом термодинамики, согласно которому количество теплоты $\text{Q}$, переданное системе, идет на изменение ее внутренней энергии $\Delta U$ и на совершение системой работы $\text{A}$ над внешними силами:</p><p>$Q = \Delta U + A$</p><p>Для одноатомного идеального газа изменение внутренней энергии определяется формулой:</p><p>$\Delta U = \frac{3}{2}\nu R \Delta T = \frac{3}{2}(p_k V_k - p_н V_н)$, где $p_н, V_н$ — начальные давление и объем, а $p_k, V_k$ — конечные.</p><p>Работа газа $\text{A}$ при изохорном процессе ($V=const$) равна нулю, а при изобарном процессе ($p=const$) вычисляется как $A = p \Delta V$.</p><p>Рассмотрим первый способ перевода газа из состояния 1 в состояние 2: через точку 3 (процесс 1 → 3 → 2).</p><p><strong>1.</strong> Процесс 1 → 3 является изохорным, так как объем не меняется ($V_1 = V_3 = const$).</p><p>Работа газа на этом участке равна нулю: $A_{13} = 0$.</p><p>Изменение внутренней энергии: $\Delta U_{13} = \frac{3}{2}(p_3 V_3 - p_1 V_1) = \frac{3}{2}(p_2 V_1 - p_1 V_1) = \frac{3}{2} V_1 (p_2 - p_1)$.</p><p>Количество теплоты: $Q_{13} = \Delta U_{13} + A_{13} = \frac{3}{2} V_1 (p_2 - p_1)$.</p><p><strong>2.</strong> Процесс 3 → 2 является изобарным, так как давление не меняется ($p_3 = p_2 = const$).</p><p>Работа газа: $A_{32} = p_2 (V_2 - V_3) = p_2 (V_2 - V_1)$.</p><p>Изменение внутренней энергии: $\Delta U_{32} = \frac{3}{2}(p_2 V_2 - p_3 V_3) = \frac{3}{2}(p_2 V_2 - p_2 V_1) = \frac{3}{2} p_2 (V_2 - V_1)$.</p><p>Количество теплоты: $Q_{32} = \Delta U_{32} + A_{32} = \frac{3}{2} p_2 (V_2 - V_1) + p_2 (V_2 - V_1) = \frac{5}{2} p_2 (V_2 - V_1)$.</p><p>Суммарное количество теплоты для процесса 1 → 3 → 2:</p><p>$Q_{1 \t°3 \t°2} = Q_{13} + Q_{32} = \frac{3}{2} V_1 (p_2 - p_1) + \frac{5}{2} p_2 (V_2 - V_1)$.</p><p>Подставим известные соотношения $V_2 = 2V_1$ и $p_2 = 2p_1$:</p><p>$Q_{1 \t°3 \t°2} = \frac{3}{2} V_1 (2p_1 - p_1) + \frac{5}{2} (2p_1) (2V_1 - V_1) = \frac{3}{2} V_1 p_1 + \frac{5}{2} (2p_1) V_1 = \frac{3}{2} p_1 V_1 + 5 p_1 V_1 = \frac{13}{2} p_1 V_1$.</p><p>Рассмотрим второй способ перевода газа из состояния 1 в состояние 2: через точку 4 (процесс 1 → 4 → 2).</p><p><strong>1.</strong> Процесс 1 → 4 является изобарным ($p_1 = p_4 = const$).</p><p>Работа газа: $A_{14} = p_1 (V_4 - V_1) = p_1 (V_2 - V_1)$.</p><p>Изменение внутренней энергии: $\Delta U_{14} = \frac{3}{2}(p_4 V_4 - p_1 V_1) = \frac{3}{2}(p_1 V_2 - p_1 V_1) = \frac{3}{2} p_1 (V_2 - V_1)$.</p><p>Количество теплоты: $Q_{14} = \Delta U_{14} + A_{14} = \frac{3}{2} p_1 (V_2 - V_1) + p_1 (V_2 - V_1) = \frac{5}{2} p_1 (V_2 - V_1)$.</p><p><strong>2.</strong> Процесс 4 → 2 является изохорным ($V_4 = V_2 = const$).</p><p>Работа газа: $A_{42} = 0$.</p><p>Изменение внутренней энергии: $\Delta U_{42} = \frac{3}{2}(p_2 V_2 - p_4 V_4) = \frac{3}{2}(p_2 V_2 - p_1 V_2) = \frac{3}{2} V_2 (p_2 - p_1)$.</p><p>Количество теплоты: $Q_{42} = \Delta U_{42} + A_{42} = \frac{3}{2} V_2 (p_2 - p_1)$.</p><p>Суммарное количество теплоты для процесса 1 → 4 → 2:</p><p>$Q_{1 \t°4 \t°2} = Q_{14} + Q_{42} = \frac{5}{2} p_1 (V_2 - V_1) + \frac{3}{2} V_2 (p_2 - p_1)$.</p><p>Подставим известные соотношения $V_2 = 2V_1$ и $p_2 = 2p_1$:</p><p>$Q_{1 \t°4 \t°2} = \frac{5}{2} p_1 (2V_1 - V_1) + \frac{3}{2} (2V_1) (2p_1 - p_1) = \frac{5}{2} p_1 V_1 + \frac{3}{2} (2V_1) p_1 = \frac{5}{2} p_1 V_1 + 3 p_1 V_1 = \frac{11}{2} p_1 V_1$.</p><p>Теперь найдем искомое отношение количеств теплоты:</p><p>$\frac{Q_{1 \t°3 \t°2}}{Q_{1 \t°4 \t°2}} = \frac{\frac{13}{2} p_1 V_1}{\frac{11}{2} p_1 V_1} = \frac{13}{11}$.</p><p><strong>Ответ:</strong> $\frac{13}{11}$.</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" => "1320515" "type" => "task" ] "previous" => array:2 [ "refs" => "1320513" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\BookPage {#1112 #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 {#1105 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1101 #items: array:1 [ 0 => App\Models\Book {#1057} ] #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 {#1103 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ 0 => App\Models\Element {#1122 #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 {#1119 …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 {#1119 …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 {#1245 #items: array:6 [ 0 => App\Models\Task {#1257 #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 {#1258 …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 {#1259 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1260 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1261 …2} "content" => Illuminate\Database\Eloquent\Collection {#1262 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1263 …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 "field_task_type" => Illuminate\Database\Eloquent\Collection {#1258 …2} "field_metatags_title" => 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#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 {#1265 …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 {#1266 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1267 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1268 …2} "content" => Illuminate\Database\Eloquent\Collection {#1270 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1276 …2} "page" => array:2 [ …2] ] #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 {#1265 …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 {#1266 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1267 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1268 …2} "content" => Illuminate\Database\Eloquent\Collection {#1270 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1276 …2} "page" => array:2 [ …2] ] #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\Task {#1271 #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" => 1320516 "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/1-513" "field_display_title" => "513" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1269 …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 {#1278 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1274 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1449 …2} "content" => Illuminate\Database\Eloquent\Collection {#1400 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1443 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1320516 "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/1-513" "field_display_title" => "513" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1269 …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 {#1278 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1274 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1449 …2} "content" => Illuminate\Database\Eloquent\Collection {#1400 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1443 …2} "page" => array:2 [ …2] ] #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\Task {#1434 #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" => 1320517 "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/1-514" "field_display_title" => "514" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1459 …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 {#1446 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1439 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1435 …2} "content" => Illuminate\Database\Eloquent\Collection {#1438 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1424 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1320517 "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/1-514" "field_display_title" => "514" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1459 …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 {#1446 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1439 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1435 …2} "content" => Illuminate\Database\Eloquent\Collection {#1438 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1424 …2} "page" => array:2 [ …2] ] #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\Task {#1430 #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" => 1320518 "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/1-515" "field_display_title" => "515" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1442 …2} "field_metatags_title" => null 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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 {#1105} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1101} "field_metatags_title" => null 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true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№511 (с. 70)
Условие. №511 (с. 70)
скриншот условия
511. [432] Одноатомный газ переводят из состояния 1 в состояние 2, для чего используют изохорный и изобарный процессы (рис. 101). При этом $V_2 = 2V_1$, $p_2 = 2p_1$. Определите отношение количеств теплоты, необходимой для совершения перехода из состояния 1 в состояние 2 в одном случае через состояние 3, в другом через состояние 4.
Рис. 101
Решение. №511 (с. 70)
Дано:
Газ одноатомный
$V_2 = 2V_1$
$p_2 = 2p_1$
Найти:
$\frac{Q_{1 \t°3 \t°2}}{Q_{1 \t°4 \t°2}}$
Решение:
Для решения задачи воспользуемся первым началом термодинамики, согласно которому количество теплоты $\text{Q}$, переданное системе, идет на изменение ее внутренней энергии $\Delta U$ и на совершение системой работы $\text{A}$ над внешними силами:
$Q = \Delta U + A$
Для одноатомного идеального газа изменение внутренней энергии определяется формулой:
$\Delta U = \frac{3}{2}\nu R \Delta T = \frac{3}{2}(p_k V_k - p_н V_н)$, где $p_н, V_н$ — начальные давление и объем, а $p_k, V_k$ — конечные.
Работа газа $\text{A}$ при изохорном процессе ($V=const$) равна нулю, а при изобарном процессе ($p=const$) вычисляется как $A = p \Delta V$.
Рассмотрим первый способ перевода газа из состояния 1 в состояние 2: через точку 3 (процесс 1 → 3 → 2).
1. Процесс 1 → 3 является изохорным, так как объем не меняется ($V_1 = V_3 = const$).
Работа газа на этом участке равна нулю: $A_{13} = 0$.
Изменение внутренней энергии: $\Delta U_{13} = \frac{3}{2}(p_3 V_3 - p_1 V_1) = \frac{3}{2}(p_2 V_1 - p_1 V_1) = \frac{3}{2} V_1 (p_2 - p_1)$.
Количество теплоты: $Q_{13} = \Delta U_{13} + A_{13} = \frac{3}{2} V_1 (p_2 - p_1)$.
2. Процесс 3 → 2 является изобарным, так как давление не меняется ($p_3 = p_2 = const$).
Работа газа: $A_{32} = p_2 (V_2 - V_3) = p_2 (V_2 - V_1)$.
Изменение внутренней энергии: $\Delta U_{32} = \frac{3}{2}(p_2 V_2 - p_3 V_3) = \frac{3}{2}(p_2 V_2 - p_2 V_1) = \frac{3}{2} p_2 (V_2 - V_1)$.
Количество теплоты: $Q_{32} = \Delta U_{32} + A_{32} = \frac{3}{2} p_2 (V_2 - V_1) + p_2 (V_2 - V_1) = \frac{5}{2} p_2 (V_2 - V_1)$.
Суммарное количество теплоты для процесса 1 → 3 → 2:
$Q_{1 \t°3 \t°2} = Q_{13} + Q_{32} = \frac{3}{2} V_1 (p_2 - p_1) + \frac{5}{2} p_2 (V_2 - V_1)$.
Подставим известные соотношения $V_2 = 2V_1$ и $p_2 = 2p_1$:
$Q_{1 \t°3 \t°2} = \frac{3}{2} V_1 (2p_1 - p_1) + \frac{5}{2} (2p_1) (2V_1 - V_1) = \frac{3}{2} V_1 p_1 + \frac{5}{2} (2p_1) V_1 = \frac{3}{2} p_1 V_1 + 5 p_1 V_1 = \frac{13}{2} p_1 V_1$.
Рассмотрим второй способ перевода газа из состояния 1 в состояние 2: через точку 4 (процесс 1 → 4 → 2).
1. Процесс 1 → 4 является изобарным ($p_1 = p_4 = const$).
Работа газа: $A_{14} = p_1 (V_4 - V_1) = p_1 (V_2 - V_1)$.
Изменение внутренней энергии: $\Delta U_{14} = \frac{3}{2}(p_4 V_4 - p_1 V_1) = \frac{3}{2}(p_1 V_2 - p_1 V_1) = \frac{3}{2} p_1 (V_2 - V_1)$.
Количество теплоты: $Q_{14} = \Delta U_{14} + A_{14} = \frac{3}{2} p_1 (V_2 - V_1) + p_1 (V_2 - V_1) = \frac{5}{2} p_1 (V_2 - V_1)$.
2. Процесс 4 → 2 является изохорным ($V_4 = V_2 = const$).
Работа газа: $A_{42} = 0$.
Изменение внутренней энергии: $\Delta U_{42} = \frac{3}{2}(p_2 V_2 - p_4 V_4) = \frac{3}{2}(p_2 V_2 - p_1 V_2) = \frac{3}{2} V_2 (p_2 - p_1)$.
Количество теплоты: $Q_{42} = \Delta U_{42} + A_{42} = \frac{3}{2} V_2 (p_2 - p_1)$.
Суммарное количество теплоты для процесса 1 → 4 → 2:
$Q_{1 \t°4 \t°2} = Q_{14} + Q_{42} = \frac{5}{2} p_1 (V_2 - V_1) + \frac{3}{2} V_2 (p_2 - p_1)$.
Подставим известные соотношения $V_2 = 2V_1$ и $p_2 = 2p_1$:
$Q_{1 \t°4 \t°2} = \frac{5}{2} p_1 (2V_1 - V_1) + \frac{3}{2} (2V_1) (2p_1 - p_1) = \frac{5}{2} p_1 V_1 + \frac{3}{2} (2V_1) p_1 = \frac{5}{2} p_1 V_1 + 3 p_1 V_1 = \frac{11}{2} p_1 V_1$.
Теперь найдем искомое отношение количеств теплоты:
$\frac{Q_{1 \t°3 \t°2}}{Q_{1 \t°4 \t°2}} = \frac{\frac{13}{2} p_1 V_1}{\frac{11}{2} p_1 V_1} = \frac{13}{11}$.
Ответ: $\frac{13}{11}$.
Другие задания:
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