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Номер 2, страница 275 - гдз по физике 10 класс учебник Касьянов
Авторы: Касьянов В. А.
Тип: Учебник
Издательство: Просвещение
Год издания: 2021 - 2026
Уровень обучения: углублённый
Цвет обложки: белый самолет и молнии изображены
ISBN: 978-5-09-103621-3
Популярные ГДЗ в 10 классе
Молекулярная физика. 10. Термодинамика. Параграф 56. Работа газа при изопроцессах. Задачи - номер 2, страница 275.
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" => 1390189 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "275" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/56zad-2" "field_display_title" => "2" "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 {#1073 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1389517 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Молекулярная физика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "219" "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 {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #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" => 7000 "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 {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "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" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 7000 "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 {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "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" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389517 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Молекулярная физика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "219" "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 {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070} ] #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 {#1108 #items: array:4 [ 0 => App\Models\Branch {#1118 #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" => 1389517 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Молекулярная физика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1119 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "219" "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 {#1152 #items: array:1 [ 0 => App\Models\Book {#1120 #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" => 7000 "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 {#1122 #items: array:1 [ 0 => App\Models\Term {#1121 #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 {#1123 #items: array:1 [ 0 => App\Models\Term {#1124 #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 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Term {#1126 #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 {#1127 #items: array:1 [ 0 => App\Models\Term {#1128 #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" => 4566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Касьянов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Валерий" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Касьянов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Валерий" "field_patronymic" => "Алексеевич" "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 {#1129 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Term {#1131 #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" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "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" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "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" => "uchebnik" ] #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 {#1132 #items: array:1 [ 0 => App\Models\Term {#1133 #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 {#1134 #items: array:1 [ 0 => App\Models\Term {#1135 #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 {#1136 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1137 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:1 [ 0 => App\Models\Term {#1139 #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" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ …6] "field_translit" => "uglublennyy" ] #original: array:6 [ "id" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ …6] "field_translit" => "uglublennyy" ] #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 {#1140 #items: array:1 [ 0 => App\Models\Term {#1141 #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" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ 0 => App\Models\Term {#1143 #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 {#1144 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "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" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Term {#1149 #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" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ …6] "field_translit" => "belyy" ] #original: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ …6] "field_translit" => "belyy" ] #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" => 7000 "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 {#1122} "field_class" => Illuminate\Database\Eloquent\Collection {#1123} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125} "field_author" => Illuminate\Database\Eloquent\Collection {#1127} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1129} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_country" => Illuminate\Database\Eloquent\Collection {#1132} "field_city" => Illuminate\Database\Eloquent\Collection {#1134} "field_series" => Illuminate\Database\Eloquent\Collection {#1136} "field_umk" => Illuminate\Database\Eloquent\Collection {#1137} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1140} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1142} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1144} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "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" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1145} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148} "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 {#1150 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389517 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Молекулярная физика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1119} "field_page_start" => "219" "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 {#1152} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1150} ] #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 {#1151 #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" => 1389545 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "10. Термодинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1153 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "268" "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 {#1154 #items: array:1 [ 0 => App\Models\Book {#1120} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389545 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "10. Термодинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1153} "field_page_start" => "268" "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 {#1154} "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 => "*" ] } 2 => App\Models\Branch {#1156 #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" => 1389549 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Работа газа при изопроцессах" "field_branch_order" => "56" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:1 [ 0 => App\Models\Term {#1157 #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" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "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_page_start" => "273" "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 {#1159 #items: array:1 [ 0 => App\Models\Book {#1120} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1168 #items: array:1 [ 0 => App\Models\Branch {#1167 #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" => 1389545 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "10. Термодинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_page_start" => "268" "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 {#1170 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1171 …2} ] #original: array:24 [ "id" => 1389545 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "10. Термодинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_page_start" => "268" "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 {#1170 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1171 …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" => 1389549 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Работа газа при изопроцессах" "field_branch_order" => "56" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1160} "field_page_start" => "273" "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 {#1159} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1168} ] #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 {#1161 #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" => 1389551 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1158 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "275" "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 {#1164 #items: array:1 [ 0 => App\Models\Book {#1120} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1177 #items: array:1 [ 0 => App\Models\Branch {#1176 #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" => 1389549 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Работа газа при изопроцессах" "field_branch_order" => "56" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_page_start" => "273" "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 {#1179 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1180 …2} ] #original: array:24 [ "id" => 1389549 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Работа газа при изопроцессах" "field_branch_order" => "56" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_page_start" => "273" "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 {#1179 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1180 …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" => 1389551 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1158} "field_page_start" => "275" "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 {#1164} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1177} ] #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 {#1071 #items: array:2 [ 0 => App\Models\Element {#1099 #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" => 1640497 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1089 #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" => 5810 "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 {#1096 …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" => 5810 "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 {#1096 …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" => "1390189" "type" => "task" ] "text" => "<p><strong>2.</strong> Кислород массой $m = 50$ г имеет температуру $T_1 = 320$ К. В результате изохорного охлаждения давление кислорода уменьшилось вдвое, а затем после изобарного расширения температура газа в конечном состоянии стала равна первоначальной. Изобразите на $p-V$-диаграмме эти процессы. Покажите графически работу, совершённую газом, и рассчитайте её. Найдите результирующее изменение внутренней энергии.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1662" "height" => 392 "path" => "/media/fizika_10/kasyanov-u/0-56zad/2-1.webp?ts=1757958084" ] ] ] #original: array:7 [ "id" => 1640497 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1089} "task" => array:2 [ "refs" => "1390189" "type" => "task" ] "text" => "<p><strong>2.</strong> Кислород массой $m = 50$ г имеет температуру $T_1 = 320$ К. В результате изохорного охлаждения давление кислорода уменьшилось вдвое, а затем после изобарного расширения температура газа в конечном состоянии стала равна первоначальной. Изобразите на $p-V$-диаграмме эти процессы. Покажите графически работу, совершённую газом, и рассчитайте её. Найдите результирующее изменение внутренней энергии.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1662" "height" => 392 "path" => "/media/fizika_10/kasyanov-u/0-56zad/2-1.webp?ts=1757958084" ] ] ] #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 {#1092 #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" => 1693201 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083 #items: array:1 [ 0 => App\Models\Edition {#1091 #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" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1087 …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 {#1088 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1087 …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 {#1088 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 …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" => "1390189" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>m = 50 г</p><p>T₁ = 320 К</p><p>Газ - кислород (O₂)</p><p>Процесс 1-2 (изохорное охлаждение): $V_1 = V_2$, $p_2 = p_1 / 2$</p><p>Процесс 2-3 (изобарное расширение): $p_2 = p_3$, $T_3 = T_1$</p><p>M(O₂) = 32 г/моль</p><p>R ≈ 8.31 Дж/(моль·К)</p><p><i>Система СИ:</i></p><p>m = 0.05 кг</p><p>M(O₂) = 0.032 кг/моль</p><p><strong>Найти:</strong></p><p>p-V диаграмму</p><p>Работу газа A</p><p>Результирующее изменение внутренней энергии ΔU</p><p><strong>Решение:</strong></p><p>Для решения задачи сначала определим параметры газа в каждом из трех состояний (1, 2, 3).</p><p><strong>Состояние 1:</strong> параметры ($p_1, V_1, T_1$). Известно, что $T_1 = 320 \text{ К}$.</p><p><strong>Процесс 1-2</strong> является изохорным ($V = \text{const}$), следовательно, $V_1 = V_2$. Для этого процесса применим закон Шарля:</p><p>$\frac{p_1}{T_1} = \frac{p_2}{T_2}$</p><p>По условию давление уменьшилось вдвое, то есть $p_2 = p_1 / 2$. Найдем температуру в состоянии 2:</p><p>$T_2 = T_1 \cdot \frac{p_2}{p_1} = T_1 \cdot \frac{p_1/2}{p_1} = \frac{T_1}{2} = \frac{320 \text{ К}}{2} = 160 \text{ К}$.</p><p><strong>Состояние 2:</strong> параметры ($p_2 = p_1/2, V_2=V_1, T_2=160 \text{ К}$).</p><p><strong>Процесс 2-3</strong> является изобарным ($p = \text{const}$), следовательно, $p_2 = p_3$. Для этого процесса применим закон Гей-Люссака:</p><p>$\frac{V_2}{T_2} = \frac{V_3}{T_3}$</p><p>По условию конечная температура стала равна первоначальной: $T_3 = T_1 = 320 \text{ К}$. Найдем объем в состоянии 3:</p><p>$V_3 = V_2 \cdot \frac{T_3}{T_2} = V_1 \cdot \frac{T_1}{T_1/2} = 2V_1$.</p><p><strong>Состояние 3:</strong> параметры ($p_3 = p_1/2, V_3=2V_1, T_3=320 \text{ К}$).</p><p><strong>Изобразите на p—V-диаграмме эти процессы. Покажите графически работу, совершённую газом, и рассчитайте её.</strong></p><p>На p-V диаграмме, где по оси ординат откладывается давление p, а по оси абсцисс — объем V, данные процессы изображаются следующим образом:</p><p><strong>1.</strong> Процесс 1-2 (изохорное охлаждение) — это вертикальный отрезок, идущий вниз от точки 1 ($p_1, V_1$) до точки 2 ($p_1/2, V_1$).</p><p><strong>2.</strong> Процесс 2-3 (изобарное расширение) — это горизонтальный отрезок, идущий вправо от точки 2 ($p_1/2, V_1$) до точки 3 ($p_1/2, 2V_1$).</p><p>Работа, совершённая газом, $A$ равна сумме работ на каждом участке: $A = A_{1-2} + A_{2-3}$.</p><p>На изохорном участке 1-2 объем не меняется ($\Delta V = 0$), поэтому работа газа равна нулю: $A_{1-2} = 0$.</p><p>На изобарном участке 2-3 работа газа вычисляется по формуле $A_{2-3} = p_2(V_3 - V_2)$. Графически эта работа равна площади прямоугольника под отрезком 2-3.</p><p>Таким образом, общая работа $A = A_{2-3}$. Для расчета работы воспользуемся уравнением состояния идеального газа, из которого следует, что $p\Delta V = \nu R \Delta T$ для изобарного процесса. Здесь $\nu = \frac{m}{M}$ — количество вещества.</p><p>Вычислим количество вещества кислорода:</p><p>$\nu = \frac{m}{M} = \frac{0.05 \text{ кг}}{0.032 \text{ кг/моль}} = 1.5625 \text{ моль}$.</p><p>Теперь рассчитаем работу:</p><p>$A = A_{2-3} = \nu R (T_3 - T_2) = 1.5625 \text{ моль} \cdot 8.31 \frac{\text{Дж}}{\text{моль} \cdot \text{К}} \cdot (320 \text{ К} - 160 \text{ К}) = 1.5625 \cdot 8.31 \cdot 160 \text{ Дж} \approx 2077.5 \text{ Дж}$.</p><p><strong>Ответ:</strong> работа, совершённая газом, равна $A \approx 2078$ Дж. Графически она представляет собой площадь под участком 2-3 на p-V диаграмме.</p><p><strong>Найдите результирующее изменение внутренней энергии.</strong></p><p>Изменение внутренней энергии идеального газа $\Delta U$ зависит только от изменения его температуры. Результирующее изменение — это разница между конечной и начальной внутренней энергией: $\Delta U = U_{3} - U_{1}$.</p><p>Начальное состояние газа — точка 1, его температура $T_1 = 320 \text{ К}$.</p><p>Конечное состояние газа — точка 3, его температура $T_3 = 320 \text{ К}$.</p><p>Так как начальная и конечная температуры газа равны ($T_1 = T_3$), то его начальная и конечная внутренние энергии также равны ($U_1 = U_3$).</p><p>Следовательно, результирующее изменение внутренней энергии за весь процесс (1→2→3) равно нулю.</p><p>$\Delta U_{1-3} = U_3 - U_1 = 0$.</p><p>Этот результат можно проверить, сложив изменения внутренней энергии на каждом участке. Для кислорода (двухатомный газ) число степеней свободы $i=5$.</p><p>$\Delta U_{1-2} = \frac{i}{2} \nu R (T_2 - T_1) = \frac{5}{2} \cdot 1.5625 \cdot 8.31 \cdot (160 - 320) \approx -5194 \text{ Дж}$.</p><p>$\Delta U_{2-3} = \frac{i}{2} \nu R (T_3 - T_2) = \frac{5}{2} \cdot 1.5625 \cdot 8.31 \cdot (320 - 160) \approx 5194 \text{ Дж}$.</p><p>$\Delta U_{1-3} = \Delta U_{1-2} + \Delta U_{2-3} \approx -5194 \text{ Дж} + 5194 \text{ Дж} = 0 \text{ Дж}$.</p><p><strong>Ответ:</strong> результирующее изменение внутренней энергии равно 0 Дж.</p>" ] #original: array:6 [ "id" => 1693201 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083} "task" => array:2 [ "refs" => "1390189" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>m = 50 г</p><p>T₁ = 320 К</p><p>Газ - кислород (O₂)</p><p>Процесс 1-2 (изохорное охлаждение): $V_1 = V_2$, $p_2 = p_1 / 2$</p><p>Процесс 2-3 (изобарное расширение): $p_2 = p_3$, $T_3 = T_1$</p><p>M(O₂) = 32 г/моль</p><p>R ≈ 8.31 Дж/(моль·К)</p><p><i>Система СИ:</i></p><p>m = 0.05 кг</p><p>M(O₂) = 0.032 кг/моль</p><p><strong>Найти:</strong></p><p>p-V диаграмму</p><p>Работу газа A</p><p>Результирующее изменение внутренней энергии ΔU</p><p><strong>Решение:</strong></p><p>Для решения задачи сначала определим параметры газа в каждом из трех состояний (1, 2, 3).</p><p><strong>Состояние 1:</strong> параметры ($p_1, V_1, T_1$). Известно, что $T_1 = 320 \text{ К}$.</p><p><strong>Процесс 1-2</strong> является изохорным ($V = \text{const}$), следовательно, $V_1 = V_2$. Для этого процесса применим закон Шарля:</p><p>$\frac{p_1}{T_1} = \frac{p_2}{T_2}$</p><p>По условию давление уменьшилось вдвое, то есть $p_2 = p_1 / 2$. Найдем температуру в состоянии 2:</p><p>$T_2 = T_1 \cdot \frac{p_2}{p_1} = T_1 \cdot \frac{p_1/2}{p_1} = \frac{T_1}{2} = \frac{320 \text{ К}}{2} = 160 \text{ К}$.</p><p><strong>Состояние 2:</strong> параметры ($p_2 = p_1/2, V_2=V_1, T_2=160 \text{ К}$).</p><p><strong>Процесс 2-3</strong> является изобарным ($p = \text{const}$), следовательно, $p_2 = p_3$. Для этого процесса применим закон Гей-Люссака:</p><p>$\frac{V_2}{T_2} = \frac{V_3}{T_3}$</p><p>По условию конечная температура стала равна первоначальной: $T_3 = T_1 = 320 \text{ К}$. Найдем объем в состоянии 3:</p><p>$V_3 = V_2 \cdot \frac{T_3}{T_2} = V_1 \cdot \frac{T_1}{T_1/2} = 2V_1$.</p><p><strong>Состояние 3:</strong> параметры ($p_3 = p_1/2, V_3=2V_1, T_3=320 \text{ К}$).</p><p><strong>Изобразите на p—V-диаграмме эти процессы. Покажите графически работу, совершённую газом, и рассчитайте её.</strong></p><p>На p-V диаграмме, где по оси ординат откладывается давление p, а по оси абсцисс — объем V, данные процессы изображаются следующим образом:</p><p><strong>1.</strong> Процесс 1-2 (изохорное охлаждение) — это вертикальный отрезок, идущий вниз от точки 1 ($p_1, V_1$) до точки 2 ($p_1/2, V_1$).</p><p><strong>2.</strong> Процесс 2-3 (изобарное расширение) — это горизонтальный отрезок, идущий вправо от точки 2 ($p_1/2, V_1$) до точки 3 ($p_1/2, 2V_1$).</p><p>Работа, совершённая газом, $A$ равна сумме работ на каждом участке: $A = A_{1-2} + A_{2-3}$.</p><p>На изохорном участке 1-2 объем не меняется ($\Delta V = 0$), поэтому работа газа равна нулю: $A_{1-2} = 0$.</p><p>На изобарном участке 2-3 работа газа вычисляется по формуле $A_{2-3} = p_2(V_3 - V_2)$. Графически эта работа равна площади прямоугольника под отрезком 2-3.</p><p>Таким образом, общая работа $A = A_{2-3}$. Для расчета работы воспользуемся уравнением состояния идеального газа, из которого следует, что $p\Delta V = \nu R \Delta T$ для изобарного процесса. Здесь $\nu = \frac{m}{M}$ — количество вещества.</p><p>Вычислим количество вещества кислорода:</p><p>$\nu = \frac{m}{M} = \frac{0.05 \text{ кг}}{0.032 \text{ кг/моль}} = 1.5625 \text{ моль}$.</p><p>Теперь рассчитаем работу:</p><p>$A = A_{2-3} = \nu R (T_3 - T_2) = 1.5625 \text{ моль} \cdot 8.31 \frac{\text{Дж}}{\text{моль} \cdot \text{К}} \cdot (320 \text{ К} - 160 \text{ К}) = 1.5625 \cdot 8.31 \cdot 160 \text{ Дж} \approx 2077.5 \text{ Дж}$.</p><p><strong>Ответ:</strong> работа, совершённая газом, равна $A \approx 2078$ Дж. Графически она представляет собой площадь под участком 2-3 на p-V диаграмме.</p><p><strong>Найдите результирующее изменение внутренней энергии.</strong></p><p>Изменение внутренней энергии идеального газа $\Delta U$ зависит только от изменения его температуры. Результирующее изменение — это разница между конечной и начальной внутренней энергией: $\Delta U = U_{3} - U_{1}$.</p><p>Начальное состояние газа — точка 1, его температура $T_1 = 320 \text{ К}$.</p><p>Конечное состояние газа — точка 3, его температура $T_3 = 320 \text{ К}$.</p><p>Так как начальная и конечная температуры газа равны ($T_1 = T_3$), то его начальная и конечная внутренние энергии также равны ($U_1 = U_3$).</p><p>Следовательно, результирующее изменение внутренней энергии за весь процесс (1→2→3) равно нулю.</p><p>$\Delta U_{1-3} = U_3 - U_1 = 0$.</p><p>Этот результат можно проверить, сложив изменения внутренней энергии на каждом участке. Для кислорода (двухатомный газ) число степеней свободы $i=5$.</p><p>$\Delta U_{1-2} = \frac{i}{2} \nu R (T_2 - T_1) = \frac{5}{2} \cdot 1.5625 \cdot 8.31 \cdot (160 - 320) \approx -5194 \text{ Дж}$.</p><p>$\Delta U_{2-3} = \frac{i}{2} \nu R (T_3 - T_2) = \frac{5}{2} \cdot 1.5625 \cdot 8.31 \cdot (320 - 160) \approx 5194 \text{ Дж}$.</p><p>$\Delta U_{1-3} = \Delta U_{1-2} + \Delta U_{2-3} \approx -5194 \text{ Дж} + 5194 \text{ Дж} = 0 \text{ Дж}$.</p><p><strong>Ответ:</strong> результирующее изменение внутренней энергии равно 0 Дж.</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" => "1390190" "type" => "task" ] "previous" => array:2 [ "refs" => "1390188" "type" => "task" ] "book" => 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#hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1454 #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" => 1390186 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "275" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/56vopr-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1462 …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 {#1447 …2} "top_parent_branch" => 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{#1450 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1451 …2} "content" => Illuminate\Database\Eloquent\Collection {#1452 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1430 …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 {#1439 #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" => 1390187 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "275" "field_page_end" => null "field_url" => 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№2 (с. 275)
Условие. №2 (с. 275)
скриншот условия
2. Кислород массой $m = 50$ г имеет температуру $T_1 = 320$ К. В результате изохорного охлаждения давление кислорода уменьшилось вдвое, а затем после изобарного расширения температура газа в конечном состоянии стала равна первоначальной. Изобразите на $p-V$-диаграмме эти процессы. Покажите графически работу, совершённую газом, и рассчитайте её. Найдите результирующее изменение внутренней энергии.
Решение. №2 (с. 275)
Дано:
m = 50 г
T₁ = 320 К
Газ - кислород (O₂)
Процесс 1-2 (изохорное охлаждение): $V_1 = V_2$, $p_2 = p_1 / 2$
Процесс 2-3 (изобарное расширение): $p_2 = p_3$, $T_3 = T_1$
M(O₂) = 32 г/моль
R ≈ 8.31 Дж/(моль·К)
Система СИ:
m = 0.05 кг
M(O₂) = 0.032 кг/моль
Найти:
p-V диаграмму
Работу газа A
Результирующее изменение внутренней энергии ΔU
Решение:
Для решения задачи сначала определим параметры газа в каждом из трех состояний (1, 2, 3).
Состояние 1: параметры ($p_1, V_1, T_1$). Известно, что $T_1 = 320 \text{ К}$.
Процесс 1-2 является изохорным ($V = \text{const}$), следовательно, $V_1 = V_2$. Для этого процесса применим закон Шарля:
$\frac{p_1}{T_1} = \frac{p_2}{T_2}$
По условию давление уменьшилось вдвое, то есть $p_2 = p_1 / 2$. Найдем температуру в состоянии 2:
$T_2 = T_1 \cdot \frac{p_2}{p_1} = T_1 \cdot \frac{p_1/2}{p_1} = \frac{T_1}{2} = \frac{320 \text{ К}}{2} = 160 \text{ К}$.
Состояние 2: параметры ($p_2 = p_1/2, V_2=V_1, T_2=160 \text{ К}$).
Процесс 2-3 является изобарным ($p = \text{const}$), следовательно, $p_2 = p_3$. Для этого процесса применим закон Гей-Люссака:
$\frac{V_2}{T_2} = \frac{V_3}{T_3}$
По условию конечная температура стала равна первоначальной: $T_3 = T_1 = 320 \text{ К}$. Найдем объем в состоянии 3:
$V_3 = V_2 \cdot \frac{T_3}{T_2} = V_1 \cdot \frac{T_1}{T_1/2} = 2V_1$.
Состояние 3: параметры ($p_3 = p_1/2, V_3=2V_1, T_3=320 \text{ К}$).
Изобразите на p—V-диаграмме эти процессы. Покажите графически работу, совершённую газом, и рассчитайте её.
На p-V диаграмме, где по оси ординат откладывается давление p, а по оси абсцисс — объем V, данные процессы изображаются следующим образом:
1. Процесс 1-2 (изохорное охлаждение) — это вертикальный отрезок, идущий вниз от точки 1 ($p_1, V_1$) до точки 2 ($p_1/2, V_1$).
2. Процесс 2-3 (изобарное расширение) — это горизонтальный отрезок, идущий вправо от точки 2 ($p_1/2, V_1$) до точки 3 ($p_1/2, 2V_1$).
Работа, совершённая газом, $A$ равна сумме работ на каждом участке: $A = A_{1-2} + A_{2-3}$.
На изохорном участке 1-2 объем не меняется ($\Delta V = 0$), поэтому работа газа равна нулю: $A_{1-2} = 0$.
На изобарном участке 2-3 работа газа вычисляется по формуле $A_{2-3} = p_2(V_3 - V_2)$. Графически эта работа равна площади прямоугольника под отрезком 2-3.
Таким образом, общая работа $A = A_{2-3}$. Для расчета работы воспользуемся уравнением состояния идеального газа, из которого следует, что $p\Delta V = \nu R \Delta T$ для изобарного процесса. Здесь $\nu = \frac{m}{M}$ — количество вещества.
Вычислим количество вещества кислорода:
$\nu = \frac{m}{M} = \frac{0.05 \text{ кг}}{0.032 \text{ кг/моль}} = 1.5625 \text{ моль}$.
Теперь рассчитаем работу:
$A = A_{2-3} = \nu R (T_3 - T_2) = 1.5625 \text{ моль} \cdot 8.31 \frac{\text{Дж}}{\text{моль} \cdot \text{К}} \cdot (320 \text{ К} - 160 \text{ К}) = 1.5625 \cdot 8.31 \cdot 160 \text{ Дж} \approx 2077.5 \text{ Дж}$.
Ответ: работа, совершённая газом, равна $A \approx 2078$ Дж. Графически она представляет собой площадь под участком 2-3 на p-V диаграмме.
Найдите результирующее изменение внутренней энергии.
Изменение внутренней энергии идеального газа $\Delta U$ зависит только от изменения его температуры. Результирующее изменение — это разница между конечной и начальной внутренней энергией: $\Delta U = U_{3} - U_{1}$.
Начальное состояние газа — точка 1, его температура $T_1 = 320 \text{ К}$.
Конечное состояние газа — точка 3, его температура $T_3 = 320 \text{ К}$.
Так как начальная и конечная температуры газа равны ($T_1 = T_3$), то его начальная и конечная внутренние энергии также равны ($U_1 = U_3$).
Следовательно, результирующее изменение внутренней энергии за весь процесс (1→2→3) равно нулю.
$\Delta U_{1-3} = U_3 - U_1 = 0$.
Этот результат можно проверить, сложив изменения внутренней энергии на каждом участке. Для кислорода (двухатомный газ) число степеней свободы $i=5$.
$\Delta U_{1-2} = \frac{i}{2} \nu R (T_2 - T_1) = \frac{5}{2} \cdot 1.5625 \cdot 8.31 \cdot (160 - 320) \approx -5194 \text{ Дж}$.
$\Delta U_{2-3} = \frac{i}{2} \nu R (T_3 - T_2) = \frac{5}{2} \cdot 1.5625 \cdot 8.31 \cdot (320 - 160) \approx 5194 \text{ Дж}$.
$\Delta U_{1-3} = \Delta U_{1-2} + \Delta U_{2-3} \approx -5194 \text{ Дж} + 5194 \text{ Дж} = 0 \text{ Дж}$.
Ответ: результирующее изменение внутренней энергии равно 0 Дж.
Другие задания:
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