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Номер 18.3, страница 134 - гдз по физике 10-11 класс задачник Гельфгат, Генденштейн
Авторы: Гельфгат И. М., Генденштейн Л. Э., Кирик Л. А.
Тип: Задачник
Издательство: Илекса
Год издания: 2008 - 2026
Уровень обучения: профильный
Цвет обложки: красный лупа, парень едет на велосипеде
ISBN: 978-5-89237-252-7
Популярные ГДЗ в 10 классе
Молекулярная физика и термодинамика. Термодинамика. 18. Тепловые двигатели. Упражнения - номер 18.3, страница 134.
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" => 1319603 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "134" "field_page_end" => "135" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/18-3" "field_display_title" => "18.3" "field_outside_task" => "0" "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" => 1319310 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Молекулярная физика и термодинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "104" "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 {#1081 #items: array:1 [ 0 => App\Models\Book {#1048 #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" => 5400 "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 {#1050 #items: array:1 [ 0 => App\Models\Term {#1049 #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 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "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 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "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 {#1051 #items: array:2 [ 0 => App\Models\Term {#1052 #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 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "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 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "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 {#1053 #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 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "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 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "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 {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #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" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #original: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #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 {#1056 #items: array:3 [ 0 => App\Models\Term {#1057 #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" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #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 {#1058 #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" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #original: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #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\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:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => 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_author_foreign" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1061 #items: array:1 [ 0 => App\Models\Term {#1062 #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" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #original: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #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 {#1063 #items: array:1 [ 0 => App\Models\Term {#1064 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1065 #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:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1067 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1069 #items: array:1 [ 0 => App\Models\Term {#1070 #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" => 40 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "профильный" "field_cases" => array:6 [ "field_accusative_case" => "профильный" "field_creative_case" => "профильным" "field_dative_case" => "профильному" "field_genitive_case" => "профильного" "field_nominative_case" => "профильный" "field_prepositional_case" => "профильном" ] "field_translit" => "profilnyy" ] #original: array:6 [ "id" => 40 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "профильный" "field_cases" => array:6 [ "field_accusative_case" => "профильный" "field_creative_case" => "профильным" "field_dative_case" => "профильному" "field_genitive_case" => "профильного" "field_nominative_case" => "профильный" "field_prepositional_case" => "профильном" ] "field_translit" => "profilnyy" ] #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_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Term {#1078 #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" => 46 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "красный" "field_cases" => array:6 [ "field_accusative_case" => "красный" "field_creative_case" => "красным" "field_dative_case" => "красному" "field_genitive_case" => "красного" "field_nominative_case" => "красный" "field_prepositional_case" => "красном" ] "field_translit" => "krasnyy" ] #original: array:6 [ "id" => 46 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "красный" "field_cases" => array:6 [ "field_accusative_case" => "красный" "field_creative_case" => "красным" "field_dative_case" => "красному" "field_genitive_case" => "красного" "field_nominative_case" => "красный" "field_prepositional_case" => "красном" ] "field_translit" => "krasnyy" ] #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" => 5400 "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 {#1050} "field_class" => Illuminate\Database\Eloquent\Collection {#1051} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1060} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1061} "field_country" => Illuminate\Database\Eloquent\Collection {#1063} "field_city" => Illuminate\Database\Eloquent\Collection {#1065} "field_series" => Illuminate\Database\Eloquent\Collection {#1067} "field_umk" => Illuminate\Database\Eloquent\Collection {#1068} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1069} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1072} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1074} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1075} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1076} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1077} "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 {#1079 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319310 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Молекулярная физика и термодинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047} "field_page_start" => "104" "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 {#1081} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1079} ] #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 {#1111 #items: array:4 [ 0 => App\Models\Branch {#1121 #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" => 1319310 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Молекулярная физика и термодинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1122 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "104" "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 {#1123 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1124 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319310 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Молекулярная физика и термодинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1122} "field_page_start" => "104" "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 {#1123} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1124} ] #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 {#1125 #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" => 1319321 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Термодинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1126 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "126" "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 {#1127 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319321 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Термодинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1126} "field_page_start" => "126" "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 {#1127} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1128} ] #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 {#1129 #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" => 1319325 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "18. Тепловые двигатели" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "134" "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 {#1131 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => 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" => 1319321 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Термодинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "126" "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 {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319321 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Термодинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141} "field_page_start" => "126" "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 {#1143} ] #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" => 1319325 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "18. Тепловые двигатели" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_page_start" => "134" "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 {#1131} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1140} ] #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 {#1133 #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" => 1319326 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "134" "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 {#1136 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1149 #items: array:1 [ 0 => App\Models\Branch {#1148 #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" => 1319325 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "18. Тепловые двигатели" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1150 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "134" "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 {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\Branch {#1139} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319325 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "18. Тепловые двигатели" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1150} "field_page_start" => "134" "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 {#1152} ] #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" => 1319326 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132} "field_page_start" => "134" "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 {#1136} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1149} ] #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 {#1102 #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" => 1493813 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Edition {#1101 #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" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Term {#1100 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "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 {#1099 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1097 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1098} "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 {#1099} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1097} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1096} "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" => "1319603" "type" => "task" ] "text" => "<p><strong>18.3.</strong> На рисунке показан цикл из двух изохор и двух изобар. Найдите КПД цикла, если рабочее тело — одноатомный идеальный газ.</p><p>☑ 17 %.</p><p><strong><em>Решение.</em></strong> КПД цикла $ \eta = A'/Q $. Совершенная за цикл работа $A'$ численно равна площади прямоугольника: $ A' = 2p_0V_0 $. Полученное за цикл от нагревателя количество теплоты $ Q = Q_{1-2} + Q_{2-3} $. Из уравнения Клапейрона получаем $ T_2 = 2T_1 $, $ T_3 = 6T_1 $. Используя результаты решения задачи 17.6, находим:</p><p>$ Q_{1-2} = \nu C_V(T_2 - T_1) = 3\nu RT_1/2 $, $ Q_{2-3} = \nu C_p(T_3 - T_2) = 10\nu RT_1 $.</p><p>Здесь $ \nu $ — количество вещества. Подставляя полученные значения в формулу для КПД и используя соотношение $ p_0V_0 = \nu RT_1 $, получаем $ \eta = 4/23 \approx 0,17 $.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1413" "height" => 791 "path" => "/media/fizika_10/gelfgat-z/0-18/3-1.webp?ts=1756251076" ] 1 => array:5 [ "name" => "3-2.jpg" "alt" => null "width" => "1269" "height" => 302 "path" => "/media/fizika_10/gelfgat-z/0-18/3-2.webp?ts=1756251076" ] ] ] #original: array:7 [ "id" => 1493813 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092} "task" => array:2 [ "refs" => "1319603" "type" => "task" ] "text" => "<p><strong>18.3.</strong> На рисунке показан цикл из двух изохор и двух изобар. Найдите КПД цикла, если рабочее тело — одноатомный идеальный газ.</p><p>☑ 17 %.</p><p><strong><em>Решение.</em></strong> КПД цикла $ \eta = A'/Q $. Совершенная за цикл работа $A'$ численно равна площади прямоугольника: $ A' = 2p_0V_0 $. Полученное за цикл от нагревателя количество теплоты $ Q = Q_{1-2} + Q_{2-3} $. Из уравнения Клапейрона получаем $ T_2 = 2T_1 $, $ T_3 = 6T_1 $. Используя результаты решения задачи 17.6, находим:</p><p>$ Q_{1-2} = \nu C_V(T_2 - T_1) = 3\nu RT_1/2 $, $ Q_{2-3} = \nu C_p(T_3 - T_2) = 10\nu RT_1 $.</p><p>Здесь $ \nu $ — количество вещества. Подставляя полученные значения в формулу для КПД и используя соотношение $ p_0V_0 = \nu RT_1 $, получаем $ \eta = 4/23 \approx 0,17 $.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1413" "height" => 791 "path" => "/media/fizika_10/gelfgat-z/0-18/3-1.webp?ts=1756251076" ] 1 => array:5 [ "name" => "3-2.jpg" "alt" => null "width" => "1269" "height" => 302 "path" => "/media/fizika_10/gelfgat-z/0-18/3-2.webp?ts=1756251076" ] ] ] #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 {#1094 #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" => 1691370 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1086 #items: array:1 [ 0 => App\Models\Edition {#1095 #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" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Term {#1093 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "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 {#1091 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1090} "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 {#1091} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1089} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1085} "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" => "1319603" "type" => "task" ] "text" => "<p><strong>Дано:</strong><br>Циклический процесс 1-2-3-4-1.<br>Рабочее тело - одноатомный идеальный газ.<br>Параметры состояний в узловых точках цикла (согласно графику):<br>Точка 1: $p_1 = p_0$, $V_1 = V_0$.<br>Точка 2: $p_2 = 2p_0$, $V_2 = V_0$.<br>Точка 3: $p_3 = 2p_0$, $V_3 = 3V_0$.<br>Точка 4: $p_4 = p_0$, $V_4 = 3V_0$.</p><p><strong>Найти:</strong><br>КПД цикла $\eta$.</p><p><strong>Решение:</strong><br>Коэффициент полезного действия (КПД) теплового двигателя определяется как отношение полезной работы $A'$, совершенной газом за цикл, к количеству теплоты $Q_{нагр}$, полученному от нагревателя:<br>$\eta = \frac{A'}{Q_{нагр}}$</p><p><strong>1.</strong> Полезная работа $A'$ за цикл численно равна площади фигуры, ограниченной графиком цикла на диаграмме в координатах p-V. В данном случае фигура является прямоугольником.<br>$A' = (p_2 - p_1) \cdot (V_3 - V_2) = (2p_0 - p_0) \cdot (3V_0 - V_0) = p_0 \cdot 2V_0 = 2p_0V_0$.</p><p><strong>2.</strong> Количество теплоты $Q_{нагр}$ газ получает на тех участках цикла, где его температура увеличивается. Согласно уравнению состояния идеального газа $pV = \nu RT$, температура растет при увеличении произведения $pV$.<br>- Участок 1-2 (изохорное нагревание): объем постоянен ($V=V_0$), давление растет от $p_0$ до $2p_0$. Произведение $pV$ увеличивается, следовательно, газ получает теплоту $Q_{1-2}$.<br>- Участок 2-3 (изобарное расширение): давление постоянно ($p=2p_0$), объем растет от $V_0$ до $3V_0$. Произведение $pV$ увеличивается, следовательно, газ получает теплоту $Q_{2-3}$.<br>- На участках 3-4 и 4-1 произведение $pV$ уменьшается, значит, температура падает, и газ отдает теплоту холодильнику.<br>Таким образом, общее количество теплоты, полученное от нагревателя, равно:<br>$Q_{нагр} = Q_{1-2} + Q_{2-3}$.</p><p><strong>3.</strong> Рассчитаем количество теплоты для каждого участка по первому началу термодинамики: $Q = \Delta U + A$. Для одноатомного идеального газа изменение внутренней энергии равно $\Delta U = \frac{3}{2}\nu R \Delta T = \frac{3}{2}\Delta(pV)$.<br>Для изохорного процесса 1-2 работа $A_{1-2}=0$.<br>$Q_{1-2} = \Delta U_{1-2} + A_{1-2} = \frac{3}{2}(p_2V_2 - p_1V_1) + 0 = \frac{3}{2}(2p_0V_0 - p_0V_0) = \frac{3}{2}p_0V_0$.</p><p><strong>4.</strong> Для изобарного процесса 2-3 работа газа $A_{2-3} = p_2(V_3 - V_2) = 2p_0(3V_0 - V_0) = 4p_0V_0$.<br>Изменение внутренней энергии $\Delta U_{2-3} = \frac{3}{2}(p_3V_3 - p_2V_2) = \frac{3}{2}(2p_0 \cdot 3V_0 - 2p_0 \cdot V_0) = \frac{3}{2}(6p_0V_0 - 2p_0V_0) = \frac{3}{2}(4p_0V_0) = 6p_0V_0$.<br>Тогда количество теплоты:<br>$Q_{2-3} = \Delta U_{2-3} + A_{2-3} = 6p_0V_0 + 4p_0V_0 = 10p_0V_0$.</p><p><strong>5.</strong> Суммарное количество теплоты, полученное от нагревателя:<br>$Q_{нагр} = Q_{1-2} + Q_{2-3} = \frac{3}{2}p_0V_0 + 10p_0V_0 = (\frac{3}{2} + \frac{20}{2})p_0V_0 = \frac{23}{2}p_0V_0$.</p><p><strong>6.</strong> Наконец, вычисляем КПД цикла:<br>$\eta = \frac{A'}{Q_{нагр}} = \frac{2p_0V_0}{\frac{23}{2}p_0V_0} = \frac{2 \cdot 2}{23} = \frac{4}{23}$.<br>Выразим результат в процентах:<br>$\eta = \frac{4}{23} \cdot 100\% \approx 17.39\% \approx 17\%$.</p><p><strong>Ответ:</strong> $\eta = \frac{4}{23} \approx 17\%$.</p>" ] #original: array:6 [ "id" => 1691370 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1086} "task" => array:2 [ "refs" => "1319603" "type" => "task" ] "text" => "<p><strong>Дано:</strong><br>Циклический процесс 1-2-3-4-1.<br>Рабочее тело - одноатомный идеальный газ.<br>Параметры состояний в узловых точках цикла (согласно графику):<br>Точка 1: $p_1 = p_0$, $V_1 = V_0$.<br>Точка 2: $p_2 = 2p_0$, $V_2 = V_0$.<br>Точка 3: $p_3 = 2p_0$, $V_3 = 3V_0$.<br>Точка 4: $p_4 = p_0$, $V_4 = 3V_0$.</p><p><strong>Найти:</strong><br>КПД цикла $\eta$.</p><p><strong>Решение:</strong><br>Коэффициент полезного действия (КПД) теплового двигателя определяется как отношение полезной работы $A'$, совершенной газом за цикл, к количеству теплоты $Q_{нагр}$, полученному от нагревателя:<br>$\eta = \frac{A'}{Q_{нагр}}$</p><p><strong>1.</strong> Полезная работа $A'$ за цикл численно равна площади фигуры, ограниченной графиком цикла на диаграмме в координатах p-V. В данном случае фигура является прямоугольником.<br>$A' = (p_2 - p_1) \cdot (V_3 - V_2) = (2p_0 - p_0) \cdot (3V_0 - V_0) = p_0 \cdot 2V_0 = 2p_0V_0$.</p><p><strong>2.</strong> Количество теплоты $Q_{нагр}$ газ получает на тех участках цикла, где его температура увеличивается. Согласно уравнению состояния идеального газа $pV = \nu RT$, температура растет при увеличении произведения $pV$.<br>- Участок 1-2 (изохорное нагревание): объем постоянен ($V=V_0$), давление растет от $p_0$ до $2p_0$. Произведение $pV$ увеличивается, следовательно, газ получает теплоту $Q_{1-2}$.<br>- Участок 2-3 (изобарное расширение): давление постоянно ($p=2p_0$), объем растет от $V_0$ до $3V_0$. Произведение $pV$ увеличивается, следовательно, газ получает теплоту $Q_{2-3}$.<br>- На участках 3-4 и 4-1 произведение $pV$ уменьшается, значит, температура падает, и газ отдает теплоту холодильнику.<br>Таким образом, общее количество теплоты, полученное от нагревателя, равно:<br>$Q_{нагр} = Q_{1-2} + Q_{2-3}$.</p><p><strong>3.</strong> Рассчитаем количество теплоты для каждого участка по первому началу термодинамики: $Q = \Delta U + A$. Для одноатомного идеального газа изменение внутренней энергии равно $\Delta U = \frac{3}{2}\nu R \Delta T = \frac{3}{2}\Delta(pV)$.<br>Для изохорного процесса 1-2 работа $A_{1-2}=0$.<br>$Q_{1-2} = \Delta U_{1-2} + A_{1-2} = \frac{3}{2}(p_2V_2 - p_1V_1) + 0 = \frac{3}{2}(2p_0V_0 - p_0V_0) = \frac{3}{2}p_0V_0$.</p><p><strong>4.</strong> Для изобарного процесса 2-3 работа газа $A_{2-3} = p_2(V_3 - V_2) = 2p_0(3V_0 - V_0) = 4p_0V_0$.<br>Изменение внутренней энергии $\Delta U_{2-3} = \frac{3}{2}(p_3V_3 - p_2V_2) = \frac{3}{2}(2p_0 \cdot 3V_0 - 2p_0 \cdot V_0) = \frac{3}{2}(6p_0V_0 - 2p_0V_0) = \frac{3}{2}(4p_0V_0) = 6p_0V_0$.<br>Тогда количество теплоты:<br>$Q_{2-3} = \Delta U_{2-3} + A_{2-3} = 6p_0V_0 + 4p_0V_0 = 10p_0V_0$.</p><p><strong>5.</strong> Суммарное количество теплоты, полученное от нагревателя:<br>$Q_{нагр} = Q_{1-2} + Q_{2-3} = \frac{3}{2}p_0V_0 + 10p_0V_0 = (\frac{3}{2} + \frac{20}{2})p_0V_0 = \frac{23}{2}p_0V_0$.</p><p><strong>6.</strong> Наконец, вычисляем КПД цикла:<br>$\eta = \frac{A'}{Q_{нагр}} = \frac{2p_0V_0}{\frac{23}{2}p_0V_0} = \frac{2 \cdot 2}{23} = \frac{4}{23}$.<br>Выразим результат в процентах:<br>$\eta = \frac{4}{23} \cdot 100\% \approx 17.39\% \approx 17\%$.</p><p><strong>Ответ:</strong> $\eta = \frac{4}{23} \approx 17\%$.</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" => "1319604" "type" => "task" ] "previous" => array:2 [ "refs" => "1319602" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\BookPage {#1107 #connection: "mysql" 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[] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№18.3 (с. 134)
Условие. №18.3 (с. 134)
скриншот условия
18.3. На рисунке показан цикл из двух изохор и двух изобар. Найдите КПД цикла, если рабочее тело — одноатомный идеальный газ.
☑ 17 %.
Решение. КПД цикла $ \eta = A'/Q $. Совершенная за цикл работа $A'$ численно равна площади прямоугольника: $ A' = 2p_0V_0 $. Полученное за цикл от нагревателя количество теплоты $ Q = Q_{1-2} + Q_{2-3} $. Из уравнения Клапейрона получаем $ T_2 = 2T_1 $, $ T_3 = 6T_1 $. Используя результаты решения задачи 17.6, находим:
$ Q_{1-2} = \nu C_V(T_2 - T_1) = 3\nu RT_1/2 $, $ Q_{2-3} = \nu C_p(T_3 - T_2) = 10\nu RT_1 $.
Здесь $ \nu $ — количество вещества. Подставляя полученные значения в формулу для КПД и используя соотношение $ p_0V_0 = \nu RT_1 $, получаем $ \eta = 4/23 \approx 0,17 $.
Решение. №18.3 (с. 134)
Дано:
Циклический процесс 1-2-3-4-1.
Рабочее тело - одноатомный идеальный газ.
Параметры состояний в узловых точках цикла (согласно графику):
Точка 1: $p_1 = p_0$, $V_1 = V_0$.
Точка 2: $p_2 = 2p_0$, $V_2 = V_0$.
Точка 3: $p_3 = 2p_0$, $V_3 = 3V_0$.
Точка 4: $p_4 = p_0$, $V_4 = 3V_0$.
Найти:
КПД цикла $\eta$.
Решение:
Коэффициент полезного действия (КПД) теплового двигателя определяется как отношение полезной работы $A'$, совершенной газом за цикл, к количеству теплоты $Q_{нагр}$, полученному от нагревателя:
$\eta = \frac{A'}{Q_{нагр}}$
1. Полезная работа $A'$ за цикл численно равна площади фигуры, ограниченной графиком цикла на диаграмме в координатах p-V. В данном случае фигура является прямоугольником.
$A' = (p_2 - p_1) \cdot (V_3 - V_2) = (2p_0 - p_0) \cdot (3V_0 - V_0) = p_0 \cdot 2V_0 = 2p_0V_0$.
2. Количество теплоты $Q_{нагр}$ газ получает на тех участках цикла, где его температура увеличивается. Согласно уравнению состояния идеального газа $pV = \nu RT$, температура растет при увеличении произведения $pV$.
- Участок 1-2 (изохорное нагревание): объем постоянен ($V=V_0$), давление растет от $p_0$ до $2p_0$. Произведение $pV$ увеличивается, следовательно, газ получает теплоту $Q_{1-2}$.
- Участок 2-3 (изобарное расширение): давление постоянно ($p=2p_0$), объем растет от $V_0$ до $3V_0$. Произведение $pV$ увеличивается, следовательно, газ получает теплоту $Q_{2-3}$.
- На участках 3-4 и 4-1 произведение $pV$ уменьшается, значит, температура падает, и газ отдает теплоту холодильнику.
Таким образом, общее количество теплоты, полученное от нагревателя, равно:
$Q_{нагр} = Q_{1-2} + Q_{2-3}$.
3. Рассчитаем количество теплоты для каждого участка по первому началу термодинамики: $Q = \Delta U + A$. Для одноатомного идеального газа изменение внутренней энергии равно $\Delta U = \frac{3}{2}\nu R \Delta T = \frac{3}{2}\Delta(pV)$.
Для изохорного процесса 1-2 работа $A_{1-2}=0$.
$Q_{1-2} = \Delta U_{1-2} + A_{1-2} = \frac{3}{2}(p_2V_2 - p_1V_1) + 0 = \frac{3}{2}(2p_0V_0 - p_0V_0) = \frac{3}{2}p_0V_0$.
4. Для изобарного процесса 2-3 работа газа $A_{2-3} = p_2(V_3 - V_2) = 2p_0(3V_0 - V_0) = 4p_0V_0$.
Изменение внутренней энергии $\Delta U_{2-3} = \frac{3}{2}(p_3V_3 - p_2V_2) = \frac{3}{2}(2p_0 \cdot 3V_0 - 2p_0 \cdot V_0) = \frac{3}{2}(6p_0V_0 - 2p_0V_0) = \frac{3}{2}(4p_0V_0) = 6p_0V_0$.
Тогда количество теплоты:
$Q_{2-3} = \Delta U_{2-3} + A_{2-3} = 6p_0V_0 + 4p_0V_0 = 10p_0V_0$.
5. Суммарное количество теплоты, полученное от нагревателя:
$Q_{нагр} = Q_{1-2} + Q_{2-3} = \frac{3}{2}p_0V_0 + 10p_0V_0 = (\frac{3}{2} + \frac{20}{2})p_0V_0 = \frac{23}{2}p_0V_0$.
6. Наконец, вычисляем КПД цикла:
$\eta = \frac{A'}{Q_{нагр}} = \frac{2p_0V_0}{\frac{23}{2}p_0V_0} = \frac{2 \cdot 2}{23} = \frac{4}{23}$.
Выразим результат в процентах:
$\eta = \frac{4}{23} \cdot 100\% \approx 17.39\% \approx 17\%$.
Ответ: $\eta = \frac{4}{23} \approx 17\%$.
Другие задания:
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