gdz.top
Номер 5, страница 241 - гдз по физике 8 класс учебник Пёрышкин
Авторы: Пёрышкин И. М.
Тип: Учебник
Издательство: Просвещение
Год издания: 2023 - 2026
Уровень обучения: базовый
Цвет обложки: белый с градусником
ISBN: 978-5-09-102555-2
Допущено Министерством просвещения Российской Федерации
Популярные ГДЗ в 8 классе
Задачи для повторения - номер 5, страница 241.
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" => 599443 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-5" "field_display_title" => "5" "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" => 598781 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи для повторения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "241" "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" => 51 "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 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "с градусником" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => "Допущено Министерством просвещения Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "706" "field_priority" => "2" "field_default_folder" => "/fizika_08/Peryshkin-u23/" "field_isbn" => "978-5-09-102555-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/Peryshkin-u23/covers/cover1.webp?ts=1737917825" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/peryshkin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ …1] #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" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 51 "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} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045} "field_author" => Illuminate\Database\Eloquent\Collection {#1047} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_country" => Illuminate\Database\Eloquent\Collection {#1052} "field_city" => Illuminate\Database\Eloquent\Collection {#1054} "field_series" => Illuminate\Database\Eloquent\Collection {#1056} "field_umk" => Illuminate\Database\Eloquent\Collection {#1057} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064} "field_under_the_edition_degree" => null "field_cover_description" => "с градусником" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => "Допущено Министерством просвещения Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "706" "field_priority" => "2" "field_default_folder" => "/fizika_08/Peryshkin-u23/" "field_isbn" => "978-5-09-102555-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/Peryshkin-u23/covers/cover1.webp?ts=1737917825" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_url" => "/8-klass/fizika/peryshkin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #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" => 598781 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи для повторения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "241" "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 {#1071 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:5 [ 0 => App\Models\Element {#1086 #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" => 746447 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095 #items: array:1 [ 0 => App\Models\Edition {#1087 #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" => 1636 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1090 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 1636 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089} "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 {#1090} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092} "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" => "599443" "type" => "task" ] "text" => """ <p><span style="color:blue;">5.</span> На графике (рис. 182) показано изменение температуры некоторого твёрдого тела с течением времени. Определите начальную и конечную температуру тела. Охарактеризуйте изменение внутренней энергии тела на каждом участке графика за всё время наблюдения.</p><figure><figure class="align-center">\n <img src="/media/fizika_08/Peryshkin-u23/0-zp/5.webp?ts=1743680600" alt="Охарактеризовать изменение внутренней энергии тела на каждом участке графика за всё время наблюдения" loading="lazy" width="766" height="552">\n </figure>\n <figcaption> </figcaption></figure> """ "img" => array:2 [ 0 => array:5 [ "name" => "5-1.png" "alt" => null "width" => "733" "height" => 155 "path" => "/media/fizika_08/Peryshkin-u23/0-zp/5-1.webp?ts=1738081089" ] 1 => array:5 [ "name" => "5-2.png" "alt" => null "width" => "389" "height" => 280 "path" => "/media/fizika_08/Peryshkin-u23/0-zp/5-2.webp?ts=1738081089" ] ] ] #original: array:7 [ "id" => 746447 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095} "task" => array:2 [ "refs" => "599443" "type" => "task" ] "text" => """ <p><span style="color:blue;">5.</span> На графике (рис. 182) показано изменение температуры некоторого твёрдого тела с течением времени. Определите начальную и конечную температуру тела. Охарактеризуйте изменение внутренней энергии тела на каждом участке графика за всё время наблюдения.</p><figure><figure class="align-center">\n <img src="/media/fizika_08/Peryshkin-u23/0-zp/5.webp?ts=1743680600" alt="Охарактеризовать изменение внутренней энергии тела на каждом участке графика за всё время наблюдения" loading="lazy" width="766" height="552">\n </figure>\n <figcaption> </figcaption></figure> """ "img" => array:2 [ 0 => array:5 [ "name" => "5-1.png" "alt" => null "width" => "733" "height" => 155 "path" => "/media/fizika_08/Peryshkin-u23/0-zp/5-1.webp?ts=1738081089" ] 1 => array:5 [ "name" => "5-2.png" "alt" => null "width" => "389" "height" => 280 "path" => "/media/fizika_08/Peryshkin-u23/0-zp/5-2.webp?ts=1738081089" ] ] ] #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" => 746771 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Edition {#1094 #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" => 1637 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 1" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Колесникович" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1098 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1099 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 1637 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 1" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Колесникович" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1098} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1099} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100} "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" => "599443" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "2026" "height" => 1008 "path" => "/media/fizika_08/Peryshkin-u23/1-zp/5-1.webp?ts=1738081146" ] ] ] #original: array:6 [ "id" => 746771 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1103} "task" => array:2 [ "refs" => "599443" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "2026" "height" => 1008 "path" => "/media/fizika_08/Peryshkin-u23/1-zp/5-1.webp?ts=1738081146" ] ] ] #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\Element {#1101 #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" => 747442 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1111 #items: array:1 [ 0 => App\Models\Edition {#1102 #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" => 1638 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:1 [ …1] …1 } "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "3-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_content_source" => null ] #original: array:21 [ "id" => 1638 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1105 …1} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "3-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1108 …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" => "599443" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "5-1.png" "alt" => null "width" => "700" "height" => 2655 "path" => "/media/fizika_08/Peryshkin-u23/3-zp/5-1.webp?ts=1738081106" ] ] ] #original: array:6 [ "id" => 747442 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1111} "task" => array:2 [ "refs" => "599443" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "5-1.png" "alt" => null "width" => "700" "height" => 2655 "path" => "/media/fizika_08/Peryshkin-u23/3-zp/5-1.webp?ts=1738081106" ] ] ] #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\Element {#1109 #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" => 747631 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ 0 => App\Models\Edition {#1110 #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" => 1639 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 3" "field_order" => "4" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_content_source" => null ] #original: array:21 [ "id" => 1639 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 3" "field_order" => "4" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1116 …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" => "599443" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "5-1.png" "alt" => null "width" => "845" "height" => 479 "path" => "/media/fizika_08/Peryshkin-u23/2-zp/5-1.webp?ts=1738081242" ] ] ] #original: array:6 [ "id" => 747631 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1119} "task" => array:2 [ "refs" => "599443" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "5-1.png" "alt" => null "width" => "845" "height" => 479 "path" => "/media/fizika_08/Peryshkin-u23/2-zp/5-1.webp?ts=1738081242" ] ] ] #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\Element {#1117 #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" => 1467248 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1127 #items: array:1 [ 0 => App\Models\Edition {#1118 #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" => 5406 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4" "field_order" => "5" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1121 …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" => "4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1122 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5406 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4" "field_order" => "5" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1121 …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" => "4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1122 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1124 …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" => "599443" "type" => "task" ] "text" => "<p><strong>Дано:</strong><br>График зависимости температуры твердого тела от времени $t(\tau)$.<br>Масштаб по оси времени ($\tau$, мин): 1 клетка = 1 мин.<br>Масштаб по оси температуры ($t$, °C): 1 клетка = 10 °C.</p><p><strong>Найти:</strong><br>Начальную температуру $t_{нач}$ — ?<br>Конечную температуру $t_{кон}$ — ?<br>Охарактеризовать изменение внутренней энергии $\Delta U$ на каждом участке.</p><p><strong>Решение:</strong><br>Задача состоит из двух частей: определение начальной и конечной температуры и анализ изменения внутренней энергии на разных этапах процесса.</p><p><strong>1. Определение начальной и конечной температуры.</strong><br>Для определения температур воспользуемся графиком.</p><p>Начальная температура — это температура тела в начальный момент времени, то есть при $\tau = 0$ мин. Из графика видно, что в этот момент времени значение температуры соответствует 4 делениям по оси $t$. Учитывая, что цена одного деления составляет 10 °C, начальная температура равна: $t_{нач} = 4 \cdot 10 \text{ °C} = 40 \text{ °C}$.</p><p>Конечная температура — это температура тела в конце наблюдения. Процесс заканчивается в момент времени $\tau = 17$ мин. В этот момент график достигает оси времени, что соответствует температуре: $t_{кон} = 0 \text{ °C}$.</p><p><strong>Ответ:</strong> Начальная температура тела составляет 40 °C, конечная температура — 0 °C.</p><p><strong>2. Характеристика изменения внутренней энергии.</strong><br>Внутренняя энергия тела ($U$) связана с температурой и агрегатным состоянием вещества. Она складывается из кинетической энергии движения частиц и потенциальной энергии их взаимодействия. При изменении температуры меняется кинетическая энергия частиц, а при фазовом переходе (например, плавлении) — потенциальная. Изменение внутренней энергии $\Delta U$ происходит, когда тело получает или отдает теплоту ($Q$). Если $Q > 0$ (тепло подводится), внутренняя энергия увеличивается. Если $Q < 0$ (тепло отводится), внутренняя энергия уменьшается.</p><p>Разобьем весь процесс на четыре участка:</p><ul><li><strong>Участок 1 (от 0 до 5 мин):</strong><br>Температура тела линейно уменьшается с 40 °C до 20 °C. Так как температура падает, средняя кинетическая энергия молекул уменьшается. Это означает, что тело отдает теплоту в окружающую среду ($Q < 0$). Следовательно, внутренняя энергия тела на этом участке <em>уменьшается</em>. </li><li><strong>Участок 2 (от 5 до 10 мин):</strong><br>Температура тела линейно увеличивается с 20 °C до 80 °C. Рост температуры свидетельствует об увеличении средней кинетической энергии молекул. Тело получает теплоту ($Q > 0$). Следовательно, внутренняя энергия тела на этом участке <em>увеличивается</em>. </li><li><strong>Участок 3 (от 10 до 15 мин):</strong><br>Температура тела остается постоянной и равной 80 °C. Поскольку изначально тело было твердым, а процесс нагрева продолжается (время идет), постоянство температуры указывает на фазовый переход — плавление. Во время плавления тело поглощает теплоту ($Q_{пл} > 0$), которая идет не на увеличение кинетической энергии молекул (температура не растет), а на разрушение кристаллической решетки, что увеличивает потенциальную энергию взаимодействия молекул. Таким образом, внутренняя энергия тела на этом участке <em>увеличивается</em>. </li><li><strong>Участок 4 (от 15 до 17 мин):</strong><br>Температура тела (которое, вероятно, уже находится в жидком состоянии) линейно уменьшается с 80 °C до 0 °C. Снижение температуры означает, что тело отдает теплоту ($Q < 0$), и его внутренняя энергия <em>уменьшается</em>. </li></ul><p><strong>Ответ:</strong><ul><li>На участке от 0 до 5 мин внутренняя энергия уменьшается.</li><li>На участке от 5 до 10 мин внутренняя энергия увеличивается.</li><li>На участке от 10 до 15 мин (плавление) внутренняя энергия увеличивается.</li><li>На участке от 15 до 17 мин внутренняя энергия уменьшается.</li></ul>" ] #original: array:6 [ "id" => 1467248 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1127} "task" => array:2 [ "refs" => "599443" "type" => "task" ] "text" => "<p><strong>Дано:</strong><br>График зависимости температуры твердого тела от времени $t(\tau)$.<br>Масштаб по оси времени ($\tau$, мин): 1 клетка = 1 мин.<br>Масштаб по оси температуры ($t$, °C): 1 клетка = 10 °C.</p><p><strong>Найти:</strong><br>Начальную температуру $t_{нач}$ — ?<br>Конечную температуру $t_{кон}$ — ?<br>Охарактеризовать изменение внутренней энергии $\Delta U$ на каждом участке.</p><p><strong>Решение:</strong><br>Задача состоит из двух частей: определение начальной и конечной температуры и анализ изменения внутренней энергии на разных этапах процесса.</p><p><strong>1. Определение начальной и конечной температуры.</strong><br>Для определения температур воспользуемся графиком.</p><p>Начальная температура — это температура тела в начальный момент времени, то есть при $\tau = 0$ мин. Из графика видно, что в этот момент времени значение температуры соответствует 4 делениям по оси $t$. Учитывая, что цена одного деления составляет 10 °C, начальная температура равна: $t_{нач} = 4 \cdot 10 \text{ °C} = 40 \text{ °C}$.</p><p>Конечная температура — это температура тела в конце наблюдения. Процесс заканчивается в момент времени $\tau = 17$ мин. В этот момент график достигает оси времени, что соответствует температуре: $t_{кон} = 0 \text{ °C}$.</p><p><strong>Ответ:</strong> Начальная температура тела составляет 40 °C, конечная температура — 0 °C.</p><p><strong>2. Характеристика изменения внутренней энергии.</strong><br>Внутренняя энергия тела ($U$) связана с температурой и агрегатным состоянием вещества. Она складывается из кинетической энергии движения частиц и потенциальной энергии их взаимодействия. При изменении температуры меняется кинетическая энергия частиц, а при фазовом переходе (например, плавлении) — потенциальная. Изменение внутренней энергии $\Delta U$ происходит, когда тело получает или отдает теплоту ($Q$). Если $Q > 0$ (тепло подводится), внутренняя энергия увеличивается. Если $Q < 0$ (тепло отводится), внутренняя энергия уменьшается.</p><p>Разобьем весь процесс на четыре участка:</p><ul><li><strong>Участок 1 (от 0 до 5 мин):</strong><br>Температура тела линейно уменьшается с 40 °C до 20 °C. Так как температура падает, средняя кинетическая энергия молекул уменьшается. Это означает, что тело отдает теплоту в окружающую среду ($Q < 0$). Следовательно, внутренняя энергия тела на этом участке <em>уменьшается</em>. </li><li><strong>Участок 2 (от 5 до 10 мин):</strong><br>Температура тела линейно увеличивается с 20 °C до 80 °C. Рост температуры свидетельствует об увеличении средней кинетической энергии молекул. Тело получает теплоту ($Q > 0$). Следовательно, внутренняя энергия тела на этом участке <em>увеличивается</em>. </li><li><strong>Участок 3 (от 10 до 15 мин):</strong><br>Температура тела остается постоянной и равной 80 °C. Поскольку изначально тело было твердым, а процесс нагрева продолжается (время идет), постоянство температуры указывает на фазовый переход — плавление. Во время плавления тело поглощает теплоту ($Q_{пл} > 0$), которая идет не на увеличение кинетической энергии молекул (температура не растет), а на разрушение кристаллической решетки, что увеличивает потенциальную энергию взаимодействия молекул. Таким образом, внутренняя энергия тела на этом участке <em>увеличивается</em>. </li><li><strong>Участок 4 (от 15 до 17 мин):</strong><br>Температура тела (которое, вероятно, уже находится в жидком состоянии) линейно уменьшается с 80 °C до 0 °C. Снижение температуры означает, что тело отдает теплоту ($Q < 0$), и его внутренняя энергия <em>уменьшается</em>. </li></ul><p><strong>Ответ:</strong><ul><li>На участке от 0 до 5 мин внутренняя энергия уменьшается.</li><li>На участке от 5 до 10 мин внутренняя энергия увеличивается.</li><li>На участке от 10 до 15 мин (плавление) внутренняя энергия увеличивается.</li><li>На участке от 15 до 17 мин внутренняя энергия уменьшается.</li></ul>" ] #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" => "599444" "type" => "task" ] "previous" => array:2 [ "refs" => "599442" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1147 #items: array:1 [ 0 => App\Models\Book {#1084 #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" => 51 "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 {#1072 #items: array:1 [ 0 => App\Models\Term {#1074 #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 {#1083 #items: array:1 [ 0 => App\Models\Term {#1081 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #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 {#1080 #items: array:1 [ 0 => App\Models\Term {#1082 #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 {#1078 #items: array:1 [ 0 => App\Models\Term {#1076 #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" => 6884 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Пёрышкин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "И" "field_patronymic" => "М" "field_surname_rp" => null ] #original: array:12 [ "id" => 6884 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Пёрышкин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "И" "field_patronymic" => "М" "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 {#1079 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Term {#1125 #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 {#1126 #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: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 {#1129 #items: array:1 [ 0 => App\Models\Term {#1130 #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 {#1131 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1132 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Term {#1134 #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" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ …6] "field_translit" => "bazovyy" ] #original: array:6 [ "id" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ …6] "field_translit" => "bazovyy" ] #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 {#1135 #items: array:1 [ 0 => App\Models\Term {#1136 #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" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "field_cases" => array:6 [ …6] "field_color" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #original: array:10 [ "id" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "field_cases" => array:6 [ …6] "field_color" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #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" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1137 #items: array:1 [ 0 => App\Models\Term {#1138 #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" => 34 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное" "field_cases" => array:6 [ …6] "field_translit" => "pererabotannoe" ] #original: array:6 [ "id" => 34 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное" "field_cases" => array:6 [ …6] "field_translit" => "pererabotannoe" ] #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 {#1139 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "с градусником" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => "Допущено Министерством просвещения Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "706" "field_priority" => "2" "field_default_folder" => "/fizika_08/Peryshkin-u23/" "field_isbn" => "978-5-09-102555-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/Peryshkin-u23/covers/cover1.webp?ts=1737917825" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/Peryshkin-u23/covers/cover1.webp?ts=1737917825" "alt" => "" "width" => "1350" "height" => "1772" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1140 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1141 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/peryshkin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1143 #items: array:1 [ 0 => App\Models\Term {#1144 #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" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 51 "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 {#1072} "field_class" => Illuminate\Database\Eloquent\Collection {#1083} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1080} "field_author" => Illuminate\Database\Eloquent\Collection {#1078} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1079} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1077} "field_country" => Illuminate\Database\Eloquent\Collection {#1126} "field_city" => Illuminate\Database\Eloquent\Collection {#1129} "field_series" => Illuminate\Database\Eloquent\Collection {#1131} "field_umk" => Illuminate\Database\Eloquent\Collection {#1132} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1133} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1135} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1137} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1139} "field_under_the_edition_degree" => null "field_cover_description" => "с градусником" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => "Допущено Министерством просвещения Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "706" "field_priority" => "2" "field_default_folder" => "/fizika_08/Peryshkin-u23/" "field_isbn" => "978-5-09-102555-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/Peryshkin-u23/covers/cover1.webp?ts=1737917825" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/Peryshkin-u23/covers/cover1.webp?ts=1737917825" "alt" => "" "width" => "1350" "height" => "1772" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1140} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1141} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1142} "field_url" => "/8-klass/fizika/peryshkin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1143} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\BookPage {#1151 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 991605 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_url" => "/8-klass/fizika/peryshkin-uchebnik/page-241" "field_display_title" => "241" "field_folder" => "1" "field_image_name" => "241" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1153 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1154 #items: array:1 [ 0 => App\Models\Book {#1084} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1155 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1165 #items: array:1 [ 0 => App\Models\Element {#1164 #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" => 1173265 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1166 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1173265 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1166 …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" => "991606" "type" => "book_page" ] "previous" => array:2 [ "refs" => "991604" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1273 #items: array:7 [ 0 => App\Models\Task {#1287 #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" => 599439 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1288 …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 {#1289 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1290 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1291 …2} "content" => Illuminate\Database\Eloquent\Collection {#1294 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1303 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 599439 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1288 …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 {#1289 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1290 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1291 …2} "content" => Illuminate\Database\Eloquent\Collection {#1294 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1303 …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 => "*" ] } 1 => App\Models\Task {#1293 #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" => 599440 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1292 …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 {#1302 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1300 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1299 …2} "content" => Illuminate\Database\Eloquent\Collection {#1295 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1321 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 599440 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1292 …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 {#1302 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1300 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1299 …2} "content" => Illuminate\Database\Eloquent\Collection {#1295 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1321 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1297 #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" => 599441 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1301 …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 {#1320 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1318 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1317 …2} "content" => Illuminate\Database\Eloquent\Collection {#1298 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1339 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 599441 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1301 …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 {#1320 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1318 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1317 …2} "content" => Illuminate\Database\Eloquent\Collection {#1298 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1339 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1315 #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" => 599442 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1319 …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 {#1338 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1336 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1335 …2} "content" => Illuminate\Database\Eloquent\Collection {#1316 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1357 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 599442 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1319 …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 {#1338 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1336 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1335 …2} "content" => Illuminate\Database\Eloquent\Collection {#1316 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1357 …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 {#1333 #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" => 599443 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1337 …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 {#1356 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1354 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1353 …2} "content" => Illuminate\Database\Eloquent\Collection {#1355 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1351 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 599443 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1337 …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 {#1356 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1354 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1353 …2} "content" => Illuminate\Database\Eloquent\Collection {#1355 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1351 …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 => "*" ] } 5 => App\Models\Task {#1334 #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" => 599444 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1352 …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 {#1296 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1369 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1370 …2} "content" => Illuminate\Database\Eloquent\Collection {#1373 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1382 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 599444 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1352 …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 {#1296 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1369 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1370 …2} "content" => Illuminate\Database\Eloquent\Collection {#1373 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1382 …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 => "*" ] } 6 => App\Models\Task {#1372 #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" => 599445 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1371 …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 {#1381 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1379 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1378 …2} "content" => Illuminate\Database\Eloquent\Collection {#1374 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1400 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 599445 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1371 …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 {#1381 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1379 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1378 …2} "content" => Illuminate\Database\Eloquent\Collection {#1374 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1400 …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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 991605 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_url" => "/8-klass/fizika/peryshkin-uchebnik/page-241" "field_display_title" => "241" "field_folder" => "1" "field_image_name" => "241" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1153} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1154} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1155} "content" => Illuminate\Database\Eloquent\Collection {#1165} "next" => array:2 [ "refs" => "991606" "type" => "book_page" ] "previous" => array:2 [ "refs" => "991604" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1273} ] #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" => 599443 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/zp-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1071} "content" => Illuminate\Database\Eloquent\Collection {#1075} "next" => array:2 [ "refs" => "599444" "type" => "task" ] "previous" => array:2 [ "refs" => "599442" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1147} "page" => array:2 [ "refs" => "991605" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№5 (с. 241)
Условие. №5 (с. 241)
скриншот условия
5. На графике (рис. 182) показано изменение температуры некоторого твёрдого тела с течением времени. Определите начальную и конечную температуру тела. Охарактеризуйте изменение внутренней энергии тела на каждом участке графика за всё время наблюдения.
Решение 1. №5 (с. 241)
Решение 2. №5 (с. 241)
Решение 3. №5 (с. 241)
Решение 4. №5 (с. 241)
Дано:
График зависимости температуры твердого тела от времени $t(\tau)$.
Масштаб по оси времени ($\tau$, мин): 1 клетка = 1 мин.
Масштаб по оси температуры ($t$, °C): 1 клетка = 10 °C.
Найти:
Начальную температуру $t_{нач}$ — ?
Конечную температуру $t_{кон}$ — ?
Охарактеризовать изменение внутренней энергии $\Delta U$ на каждом участке.
Решение:
Задача состоит из двух частей: определение начальной и конечной температуры и анализ изменения внутренней энергии на разных этапах процесса.
1. Определение начальной и конечной температуры.
Для определения температур воспользуемся графиком.
Начальная температура — это температура тела в начальный момент времени, то есть при $\tau = 0$ мин. Из графика видно, что в этот момент времени значение температуры соответствует 4 делениям по оси $t$. Учитывая, что цена одного деления составляет 10 °C, начальная температура равна: $t_{нач} = 4 \cdot 10 \text{ °C} = 40 \text{ °C}$.
Конечная температура — это температура тела в конце наблюдения. Процесс заканчивается в момент времени $\tau = 17$ мин. В этот момент график достигает оси времени, что соответствует температуре: $t_{кон} = 0 \text{ °C}$.
Ответ: Начальная температура тела составляет 40 °C, конечная температура — 0 °C.
2. Характеристика изменения внутренней энергии.
Внутренняя энергия тела ($U$) связана с температурой и агрегатным состоянием вещества. Она складывается из кинетической энергии движения частиц и потенциальной энергии их взаимодействия. При изменении температуры меняется кинетическая энергия частиц, а при фазовом переходе (например, плавлении) — потенциальная. Изменение внутренней энергии $\Delta U$ происходит, когда тело получает или отдает теплоту ($Q$). Если $Q > 0$ (тепло подводится), внутренняя энергия увеличивается. Если $Q < 0$ (тепло отводится), внутренняя энергия уменьшается.
Разобьем весь процесс на четыре участка:
- Участок 1 (от 0 до 5 мин):
Температура тела линейно уменьшается с 40 °C до 20 °C. Так как температура падает, средняя кинетическая энергия молекул уменьшается. Это означает, что тело отдает теплоту в окружающую среду ($Q < 0$). Следовательно, внутренняя энергия тела на этом участке уменьшается. - Участок 2 (от 5 до 10 мин):
Температура тела линейно увеличивается с 20 °C до 80 °C. Рост температуры свидетельствует об увеличении средней кинетической энергии молекул. Тело получает теплоту ($Q > 0$). Следовательно, внутренняя энергия тела на этом участке увеличивается. - Участок 3 (от 10 до 15 мин):
Температура тела остается постоянной и равной 80 °C. Поскольку изначально тело было твердым, а процесс нагрева продолжается (время идет), постоянство температуры указывает на фазовый переход — плавление. Во время плавления тело поглощает теплоту ($Q_{пл} > 0$), которая идет не на увеличение кинетической энергии молекул (температура не растет), а на разрушение кристаллической решетки, что увеличивает потенциальную энергию взаимодействия молекул. Таким образом, внутренняя энергия тела на этом участке увеличивается. - Участок 4 (от 15 до 17 мин):
Температура тела (которое, вероятно, уже находится в жидком состоянии) линейно уменьшается с 80 °C до 0 °C. Снижение температуры означает, что тело отдает теплоту ($Q < 0$), и его внутренняя энергия уменьшается.
Ответ:
- На участке от 0 до 5 мин внутренняя энергия уменьшается.
- На участке от 5 до 10 мин внутренняя энергия увеличивается.
- На участке от 10 до 15 мин (плавление) внутренняя энергия увеличивается.
- На участке от 15 до 17 мин внутренняя энергия уменьшается.
Другие задания:
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