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Номер 2, страница 280 - 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 57. Первый закон термодинамики. Задачи - номер 2, страница 280.
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" => 1390199 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "280" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/57zad-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 {#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" => 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 {#1047 #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 {#1080 #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" => 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 {#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 [ …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 {#1051 #items: array:1 [ 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 [ …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 {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 #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 {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 #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 {#1057 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ 0 => App\Models\Term {#1059 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 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 {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 #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 {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #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 {#1064 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #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 {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 #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 {#1070 #items: array:1 [ 0 => App\Models\Term {#1071 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1072 #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 {#1073 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Term {#1077 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 {#1050} "field_class" => Illuminate\Database\Eloquent\Collection {#1051} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1053} "field_author" => Illuminate\Database\Eloquent\Collection {#1055} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1057} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1058} "field_country" => Illuminate\Database\Eloquent\Collection {#1060} "field_city" => Illuminate\Database\Eloquent\Collection {#1062} "field_series" => Illuminate\Database\Eloquent\Collection {#1064} "field_umk" => Illuminate\Database\Eloquent\Collection {#1065} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1066} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1068} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1072} "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 {#1073} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1074} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1075} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1076} "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 {#1078 #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 {#1047} "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 {#1080} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1078} ] #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 {#1109 #items: array:4 [ 0 => App\Models\Branch {#1119 #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 {#1120 #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 {#1121 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1122 #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 {#1120} "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 {#1121} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1122} ] #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 {#1123 #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 {#1124 #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 {#1125 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #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 {#1124} "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 {#1125} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1126} ] #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 {#1127 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1389552 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Первый закон термодинамики" "field_branch_order" => "57" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1131 #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: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" => "276" "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 {#1130 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1139 #items: array:1 [ 0 => App\Models\Branch {#1138 #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 {#1140 …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 {#1141 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1142 …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 {#1140 …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 {#1141 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1142 …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" => 1389552 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Первый закон термодинамики" "field_branch_order" => "57" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1131} "field_page_start" => "276" "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 {#1130} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1139} ] #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 {#1132 #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" => 1389554 "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 {#1129 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "280" "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 {#1135 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Branch {#1147 #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" => 1389552 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Первый закон термодинамики" "field_branch_order" => "57" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1149 …2} "field_page_start" => "276" "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 {#1150 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1151 …2} ] #original: array:24 [ "id" => 1389552 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Первый закон термодинамики" "field_branch_order" => "57" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1149 …2} "field_page_start" => "276" "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 {#1150 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1151 …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" => 1389554 "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 {#1129} "field_page_start" => "280" "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 {#1135} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #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 {#1100 #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" => 1640507 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Edition {#1098 #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 {#1096 …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 {#1097 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095 …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 {#1096 …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 {#1097 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095 …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" => "1390199" "type" => "task" ] "text" => "<p><strong>2.</strong> Кислород массой 32 г находится в закрытом сосуде под давлением 0,1 МПа при температуре 17 °С. После нагревания давление в сосуде увеличилось в 2 раза. Найдите объём сосуда; температуру, до которой нагрели газ; количество теплоты, сообщённое газу.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1697" "height" => 261 "path" => "/media/fizika_10/kasyanov-u/0-57zad/2-1.webp?ts=1757958084" ] ] ] #original: array:7 [ "id" => 1640507 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1390199" "type" => "task" ] "text" => "<p><strong>2.</strong> Кислород массой 32 г находится в закрытом сосуде под давлением 0,1 МПа при температуре 17 °С. После нагревания давление в сосуде увеличилось в 2 раза. Найдите объём сосуда; температуру, до которой нагрели газ; количество теплоты, сообщённое газу.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1697" "height" => 261 "path" => "/media/fizika_10/kasyanov-u/0-57zad/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 {#1093 #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" => 1693211 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1084 #items: array:1 [ 0 => App\Models\Edition {#1092 #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 {#1088 …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 {#1089 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1087 …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 {#1088 …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 {#1089 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1087 …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" => "1390199" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>m = 32 г = 0,032 кг<br>p<sub>1</sub> = 0,1 МПа = 10<sup>5</sup> Па<br>t<sub>1</sub> = 17 °С<br>T<sub>1</sub> = 17 + 273 = 290 К<br>p<sub>2</sub> = 2 · p<sub>1</sub><br>M(O<sub>2</sub>) = 32 г/моль = 0,032 кг/моль<br>R ≈ 8,31 Дж/(моль·К)<br></p><p><strong>Найти:</strong></p><p>V - ?<br>T<sub>2</sub> - ?<br>Q - ?<br></p><p><strong>Решение:</strong></p><p><strong>объём сосуда</strong></p><p>Для нахождения объёма сосуда воспользуемся уравнением состояния идеального газа (уравнением Менделеева-Клапейрона):</p><p>$p_1 V = \nu R T_1$</p><p>где $\nu$ — количество вещества газа, которое можно найти по формуле $\nu = \frac{m}{M}$.</p><p>$\nu = \frac{0,032 \text{ кг}}{0,032 \text{ кг/моль}} = 1 \text{ моль}$</p><p>Теперь выразим объём $V$ из уравнения состояния:</p><p>$V = \frac{\nu R T_1}{p_1}$</p><p>Подставим числовые значения:</p><p>$V = \frac{1 \text{ моль} \cdot 8,31 \frac{\text{Дж}}{\text{моль} \cdot \text{К}} \cdot 290 \text{ К}}{10^5 \text{ Па}} \approx 0,0241 \text{ м}^3$</p><p><strong>Ответ:</strong> объём сосуда примерно равен 0,0241 м³ (или 24,1 л).</p><p><strong>температуру, до которой нагрели газ</strong></p><p>Поскольку газ находится в закрытом сосуде, процесс нагревания является изохорным (объём газа остаётся постоянным, $V = const$). Для изохорного процесса справедлив закон Шарля:</p><p>$\frac{p_1}{T_1} = \frac{p_2}{T_2}$</p><p>По условию задачи, давление увеличилось в 2 раза, то есть $p_2 = 2 p_1$. Подставим это соотношение в закон Шарля:</p><p>$\frac{p_1}{T_1} = \frac{2 p_1}{T_2}$</p><p>Отсюда находим конечную температуру $T_2$:</p><p>$T_2 = 2 T_1 = 2 \cdot 290 \text{ К} = 580 \text{ К}$</p><p>Переведём температуру в градусы Цельсия:</p><p>$t_2 = T_2 - 273 = 580 - 273 = 307 \text{ °C}$</p><p><strong>Ответ:</strong> газ нагрели до температуры 580 К (или 307 °С).</p><p><strong>количество теплоты, сообщённое газу</strong></p><p>Согласно первому началу термодинамики, количество теплоты $Q$, сообщённое системе, идёт на изменение её внутренней энергии $\Delta U$ и на совершение работы $A$ системой против внешних сил:</p><p>$Q = \Delta U + A$</p><p>Так как процесс изохорный ($V = const$), то работа, совершаемая газом, равна нулю ($A = p \Delta V = 0$). Следовательно, вся подведённая теплота идёт на увеличение внутренней энергии газа:</p><p>$Q = \Delta U$</p><p>Изменение внутренней энергии идеального газа вычисляется по формуле:</p><p>$\Delta U = \frac{i}{2} \nu R \Delta T = \frac{i}{2} \nu R (T_2 - T_1)$</p><p>Кислород (O<sub>2</sub>) — двухатомный газ, поэтому число степеней свободы $i = 5$.</p><p>Подставим известные значения:</p><p>$Q = \frac{5}{2} \cdot 1 \text{ моль} \cdot 8,31 \frac{\text{Дж}}{\text{моль} \cdot \text{К}} \cdot (580 \text{ К} - 290 \text{ К})$</p><p>$Q = 2,5 \cdot 8,31 \cdot 290 \text{ Дж} \approx 6024,75 \text{ Дж}$</p><p><strong>Ответ:</strong> количество теплоты, сообщённое газу, составляет примерно 6025 Дж (или 6,025 кДж).</p>" ] #original: array:6 [ "id" => 1693211 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1084} "task" => array:2 [ "refs" => "1390199" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>m = 32 г = 0,032 кг<br>p<sub>1</sub> = 0,1 МПа = 10<sup>5</sup> Па<br>t<sub>1</sub> = 17 °С<br>T<sub>1</sub> = 17 + 273 = 290 К<br>p<sub>2</sub> = 2 · p<sub>1</sub><br>M(O<sub>2</sub>) = 32 г/моль = 0,032 кг/моль<br>R ≈ 8,31 Дж/(моль·К)<br></p><p><strong>Найти:</strong></p><p>V - ?<br>T<sub>2</sub> - ?<br>Q - ?<br></p><p><strong>Решение:</strong></p><p><strong>объём сосуда</strong></p><p>Для нахождения объёма сосуда воспользуемся уравнением состояния идеального газа (уравнением Менделеева-Клапейрона):</p><p>$p_1 V = \nu R T_1$</p><p>где $\nu$ — количество вещества газа, которое можно найти по формуле $\nu = \frac{m}{M}$.</p><p>$\nu = \frac{0,032 \text{ кг}}{0,032 \text{ кг/моль}} = 1 \text{ моль}$</p><p>Теперь выразим объём $V$ из уравнения состояния:</p><p>$V = \frac{\nu R T_1}{p_1}$</p><p>Подставим числовые значения:</p><p>$V = \frac{1 \text{ моль} \cdot 8,31 \frac{\text{Дж}}{\text{моль} \cdot \text{К}} \cdot 290 \text{ К}}{10^5 \text{ Па}} \approx 0,0241 \text{ м}^3$</p><p><strong>Ответ:</strong> объём сосуда примерно равен 0,0241 м³ (или 24,1 л).</p><p><strong>температуру, до которой нагрели газ</strong></p><p>Поскольку газ находится в закрытом сосуде, процесс нагревания является изохорным (объём газа остаётся постоянным, $V = const$). Для изохорного процесса справедлив закон Шарля:</p><p>$\frac{p_1}{T_1} = \frac{p_2}{T_2}$</p><p>По условию задачи, давление увеличилось в 2 раза, то есть $p_2 = 2 p_1$. Подставим это соотношение в закон Шарля:</p><p>$\frac{p_1}{T_1} = \frac{2 p_1}{T_2}$</p><p>Отсюда находим конечную температуру $T_2$:</p><p>$T_2 = 2 T_1 = 2 \cdot 290 \text{ К} = 580 \text{ К}$</p><p>Переведём температуру в градусы Цельсия:</p><p>$t_2 = T_2 - 273 = 580 - 273 = 307 \text{ °C}$</p><p><strong>Ответ:</strong> газ нагрели до температуры 580 К (или 307 °С).</p><p><strong>количество теплоты, сообщённое газу</strong></p><p>Согласно первому началу термодинамики, количество теплоты $Q$, сообщённое системе, идёт на изменение её внутренней энергии $\Delta U$ и на совершение работы $A$ системой против внешних сил:</p><p>$Q = \Delta U + A$</p><p>Так как процесс изохорный ($V = const$), то работа, совершаемая газом, равна нулю ($A = p \Delta V = 0$). Следовательно, вся подведённая теплота идёт на увеличение внутренней энергии газа:</p><p>$Q = \Delta U$</p><p>Изменение внутренней энергии идеального газа вычисляется по формуле:</p><p>$\Delta U = \frac{i}{2} \nu R \Delta T = \frac{i}{2} \nu R (T_2 - T_1)$</p><p>Кислород (O<sub>2</sub>) — двухатомный газ, поэтому число степеней свободы $i = 5$.</p><p>Подставим известные значения:</p><p>$Q = \frac{5}{2} \cdot 1 \text{ моль} \cdot 8,31 \frac{\text{Дж}}{\text{моль} \cdot \text{К}} \cdot (580 \text{ К} - 290 \text{ К})$</p><p>$Q = 2,5 \cdot 8,31 \cdot 290 \text{ Дж} \approx 6024,75 \text{ Дж}$</p><p><strong>Ответ:</strong> количество теплоты, сообщённое газу, составляет примерно 6025 Дж (или 6,025 кДж).</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] 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=> array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1641428 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390929" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1390927" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1220 #items: array:10 [ 0 => App\Models\Task {#1236 #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" => 1390193 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "280" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/57vopr-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1237 …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 {#1238 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1239 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1357 …2} "content" => Illuminate\Database\Eloquent\Collection {#1312 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1353 …2} "page" => array:2 [ …2] ] 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#attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1346 #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" => 1390194 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "280" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/57vopr-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1365 …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 {#1344 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1351 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1347 …2} "content" => Illuminate\Database\Eloquent\Collection {#1350 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1334 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1390194 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "280" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/57vopr-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1365 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] 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{#1322 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1325 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1326 …2} "content" => Illuminate\Database\Eloquent\Collection {#1327 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1314 …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 {#1352 #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" => 1390197 "created_at" => "2026-04-10 13:58:26" "updated_at" => null 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+timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1305 #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" => 1390198 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "280" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/57zad-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1313 …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 {#1300 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1303 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1306 …2} "content" => Illuminate\Database\Eloquent\Collection {#1304 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1290 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1390198 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "280" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/57zad-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1313 …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 {#1300 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection 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#dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№2 (с. 280)
Условие. №2 (с. 280)
скриншот условия
2. Кислород массой 32 г находится в закрытом сосуде под давлением 0,1 МПа при температуре 17 °С. После нагревания давление в сосуде увеличилось в 2 раза. Найдите объём сосуда; температуру, до которой нагрели газ; количество теплоты, сообщённое газу.
Решение. №2 (с. 280)
Дано:
m = 32 г = 0,032 кг
p1 = 0,1 МПа = 105 Па
t1 = 17 °С
T1 = 17 + 273 = 290 К
p2 = 2 · p1
M(O2) = 32 г/моль = 0,032 кг/моль
R ≈ 8,31 Дж/(моль·К)
Найти:
V - ?
T2 - ?
Q - ?
Решение:
объём сосуда
Для нахождения объёма сосуда воспользуемся уравнением состояния идеального газа (уравнением Менделеева-Клапейрона):
$p_1 V = \nu R T_1$
где $\nu$ — количество вещества газа, которое можно найти по формуле $\nu = \frac{m}{M}$.
$\nu = \frac{0,032 \text{ кг}}{0,032 \text{ кг/моль}} = 1 \text{ моль}$
Теперь выразим объём $V$ из уравнения состояния:
$V = \frac{\nu R T_1}{p_1}$
Подставим числовые значения:
$V = \frac{1 \text{ моль} \cdot 8,31 \frac{\text{Дж}}{\text{моль} \cdot \text{К}} \cdot 290 \text{ К}}{10^5 \text{ Па}} \approx 0,0241 \text{ м}^3$
Ответ: объём сосуда примерно равен 0,0241 м³ (или 24,1 л).
температуру, до которой нагрели газ
Поскольку газ находится в закрытом сосуде, процесс нагревания является изохорным (объём газа остаётся постоянным, $V = const$). Для изохорного процесса справедлив закон Шарля:
$\frac{p_1}{T_1} = \frac{p_2}{T_2}$
По условию задачи, давление увеличилось в 2 раза, то есть $p_2 = 2 p_1$. Подставим это соотношение в закон Шарля:
$\frac{p_1}{T_1} = \frac{2 p_1}{T_2}$
Отсюда находим конечную температуру $T_2$:
$T_2 = 2 T_1 = 2 \cdot 290 \text{ К} = 580 \text{ К}$
Переведём температуру в градусы Цельсия:
$t_2 = T_2 - 273 = 580 - 273 = 307 \text{ °C}$
Ответ: газ нагрели до температуры 580 К (или 307 °С).
количество теплоты, сообщённое газу
Согласно первому началу термодинамики, количество теплоты $Q$, сообщённое системе, идёт на изменение её внутренней энергии $\Delta U$ и на совершение работы $A$ системой против внешних сил:
$Q = \Delta U + A$
Так как процесс изохорный ($V = const$), то работа, совершаемая газом, равна нулю ($A = p \Delta V = 0$). Следовательно, вся подведённая теплота идёт на увеличение внутренней энергии газа:
$Q = \Delta U$
Изменение внутренней энергии идеального газа вычисляется по формуле:
$\Delta U = \frac{i}{2} \nu R \Delta T = \frac{i}{2} \nu R (T_2 - T_1)$
Кислород (O2) — двухатомный газ, поэтому число степеней свободы $i = 5$.
Подставим известные значения:
$Q = \frac{5}{2} \cdot 1 \text{ моль} \cdot 8,31 \frac{\text{Дж}}{\text{моль} \cdot \text{К}} \cdot (580 \text{ К} - 290 \text{ К})$
$Q = 2,5 \cdot 8,31 \cdot 290 \text{ Дж} \approx 6024,75 \text{ Дж}$
Ответ: количество теплоты, сообщённое газу, составляет примерно 6025 Дж (или 6,025 кДж).
Другие задания:
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