gdz.top
Номер 2, страница 51 - 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
Глава 1. Тепловые явления. Параграф 13. Энергия топлива. Удельная теплота сгорания. Задание 8 - номер 2, страница 51.
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" => 598923 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "51" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/13-3-2" "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" => 598563 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тепловые явления" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => 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_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1081 #items: array:1 [ 0 => App\Models\Book {#1049 #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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #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 {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1056 #items: array:1 [ 0 => App\Models\Term {#1057 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 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 {#1058 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1059 #items: array:1 [ 0 => App\Models\Term {#1060 #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 {#1061 #items: array:1 [ 0 => App\Models\Term {#1062 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 {#1063 #items: array:1 [ 0 => App\Models\Term {#1064 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1065 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1067 #items: array:1 [ 0 => App\Models\Term {#1068 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1069 #items: array:1 [ 0 => App\Models\Term {#1070 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 {#1071 #items: array:1 [ 0 => App\Models\Term {#1072 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1073 #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 {#1074 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/peryshkin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Term {#1078 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1058} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1059} "field_country" => Illuminate\Database\Eloquent\Collection {#1061} "field_city" => Illuminate\Database\Eloquent\Collection {#1063} "field_series" => Illuminate\Database\Eloquent\Collection {#1065} "field_umk" => Illuminate\Database\Eloquent\Collection {#1066} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1067} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1069} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1071} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1073} "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 {#1074} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1075} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1076} "field_url" => "/8-klass/fizika/peryshkin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1077} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 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 {#1079 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 598563 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тепловые явления" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1081} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1079} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:3 [ 0 => App\Models\Branch {#1120 #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" => 598563 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тепловые явления" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "3" "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 {#1122 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1123 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 598563 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тепловые явления" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121} "field_page_start" => "3" "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 {#1122} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1123} ] #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 {#1124 #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" => 598606 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Энергия топлива. Удельная теплота сгорания" "field_branch_order" => "13" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1128 #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: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" => "48" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1127 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 598606 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Энергия топлива. Удельная теплота сгорания" "field_branch_order" => "13" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1128} "field_page_start" => "48" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1127} "branch_parent" => Illuminate\Database\Eloquent\Collection {#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 {#1129 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 598609 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задание 8" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "51" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Branch {#1139 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 598606 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Энергия топлива. Удельная теплота сгорания" "field_branch_order" => "13" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_page_start" => "48" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1142 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143 …2} ] #original: array:24 [ "id" => 598606 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Энергия топлива. Удельная теплота сгорания" "field_branch_order" => "13" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_page_start" => "48" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1142 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143 …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" => 598609 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задание 8" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_page_start" => "51" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1131} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1140} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:5 [ 0 => App\Models\Element {#1098 #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" => 745263 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Edition {#1099 #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 {#1097 …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 {#1095 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …2} "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 {#1097 …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 {#1095 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …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" => "598923" "type" => "task" ] "text" => "<p> <b>2.</b> Определите минимальное количество природного газа, необходимое для того, чтобы довести до кипения воду в чайнике, которым вы пользуетесь. Почему на практике газа требуется больше? Как уменьшить расход газа? </p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.png" "alt" => null "width" => "752" "height" => 140 "path" => "/media/fizika_08/Peryshkin-u23/0-13-3/2-1.webp?ts=1738080832" ] ] ] #original: array:7 [ "id" => 745263 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091} "task" => array:2 [ "refs" => "598923" "type" => "task" ] "text" => "<p> <b>2.</b> Определите минимальное количество природного газа, необходимое для того, чтобы довести до кипения воду в чайнике, которым вы пользуетесь. Почему на практике газа требуется больше? Как уменьшить расход газа? </p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.png" "alt" => null "width" => "752" "height" => 140 "path" => "/media/fizika_08/Peryshkin-u23/0-13-3/2-1.webp?ts=1738080832" ] ] ] #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" => 745456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1080 #items: array:1 [ 0 => App\Models\Edition {#1090 #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 {#1089 …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" => "Колесникович" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 …2} "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 {#1089 …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" => "Колесникович" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "598923" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "2061" "height" => 2382 "path" => "/media/fizika_08/Peryshkin-u23/1-13-3/2-1.webp?ts=1738080862" ] ] ] #original: array:6 [ "id" => 745456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1080} "task" => array:2 [ "refs" => "598923" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "2061" "height" => 2382 "path" => "/media/fizika_08/Peryshkin-u23/1-13-3/2-1.webp?ts=1738080862" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true 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"field_responsible" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1113 …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 {#1114 …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 {#1112 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1115 …2} 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=> 559 "path" => "/media/fizika_08/Peryshkin-u23/2-13-3/2-1.webp?ts=1738080981" ] ] ] #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 {#1133 #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" => 1466728 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Edition {#1132 #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 {#1137 …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 {#1135 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1145 …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 {#1137 …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 {#1135 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1145 …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" => "598923" "type" => "task" ] "text" => "<p><strong>Определите минимальное количество природного газа, необходимое для того, чтобы довести до кипения воду в чайнике, которым вы пользуетесь.</strong><p>Для проведения расчета необходимо принять некоторые допущения о параметрах чайника и воды, так как они не указаны в условии. Возьмем типичные значения для стандартного бытового чайника.</p><strong>Дано:</strong><p>Объем воды, $V_в = 1,5 \text{ л}$<br>Начальная температура воды, $t_1 = 15 \text{ °C}$<br>Конечная температура воды (кипение), $t_2 = 100 \text{ °C}$<br>Материал чайника - алюминий, масса $m_ч = 0,5 \text{ кг}$<br>Удельная теплоемкость воды, $c_в = 4200 \frac{Дж}{кг \cdot К}$<br>Удельная теплоемкость алюминия, $c_{ал} = 920 \frac{Дж}{кг \cdot К}$<br>Плотность воды, $\rho_в = 1000 \frac{кг}{м^3}$<br>Удельная теплота сгорания природного газа, $q_г = 3,6 \cdot 10^7 \frac{Дж}{м^3}$</p><p><strong>Перевод в СИ:</strong><br>$V_в = 1,5 \text{ л} = 1,5 \cdot 10^{-3} \text{ м}^3$<br>Остальные величины уже представлены в системе СИ.</p><strong>Найти:</strong><p>Минимальный объем природного газа $V_г - ?$</p><strong>Решение:</strong><p><strong>1.</strong> Найдем массу воды в чайнике по формуле $m = \rho \cdot V$:</p><p>$m_в = \rho_в \cdot V_в = 1000 \frac{кг}{м^3} \cdot 1,5 \cdot 10^{-3} \text{ м}^3 = 1,5 \text{ кг}$</p><p><strong>2.</strong> Рассчитаем количество теплоты $Q$, необходимое для нагрева, по формуле $Q = c \cdot m \cdot \Delta t$. Сначала для воды:</p><p>$Q_в = c_в \cdot m_в \cdot (t_2 - t_1) = 4200 \frac{Дж}{кг \cdot К} \cdot 1,5 \text{ кг} \cdot (100 - 15) \text{ К} = 535 500 \text{ Дж}$</p><p><strong>3.</strong> Теперь рассчитаем количество теплоты для нагрева самого чайника:</p><p>$Q_ч = c_{ал} \cdot m_ч \cdot (t_2 - t_1) = 920 \frac{Дж}{кг \cdot К} \cdot 0,5 \text{ кг} \cdot (100 - 15) \text{ К} = 39 100 \text{ Дж}$</p><p><strong>4.</strong> Суммарное полезное количество теплоты равно сумме теплоты для нагрева воды и чайника:</p><p>$Q_{полезн} = Q_в + Q_ч = 535 500 \text{ Дж} + 39 100 \text{ Дж} = 574 600 \text{ Дж}$</p><p><strong>5.</strong> Минимальное количество газа соответствует идеальному случаю, когда вся энергия от сгорания идет на нагрев (КПД = 100%). Количество теплоты, выделяемое при сгорании объема газа $V_г$, равно $Q_г = q_г \cdot V_г$. Приравнивая полезную и полученную теплоту ($Q_{полезн} = Q_г$), найдем объем газа:</p><p>$V_г = \frac{Q_{полезн}}{q_г} = \frac{574 600 \text{ Дж}}{3,6 \cdot 10^7 \frac{Дж}{м^3}} \approx 0,01596 \text{ м}^3$</p><p>Округлим результат и переведем в литры для наглядности: $0,016 \text{ м}^3 = 16 \text{ л}$.</p><p><strong>Ответ:</strong> минимальное количество природного газа, необходимое для кипячения 1,5 л воды в 0,5-килограммовом алюминиевом чайнике с начальной температурой 15 °C, составляет примерно $0,016 \text{ м}^3$ (16 литров).</p><p><strong>Почему на практике газа требуется больше?</strong><p>На практике расход газа всегда больше теоретического минимума из-за неизбежных потерь энергии. Коэффициент полезного действия (КПД) газовой плиты при кипячении воды редко превышает 50%. Это означает, что более половины энергии, выделившейся при сгорании газа, теряется и не идет на нагрев воды. Основные причины потерь:</p><ul><li><strong>Нагрев окружающего воздуха:</strong> пламя конфорки нагревает не только дно чайника, но и воздух вокруг него. Горячие продукты сгорания уносят с собой значительную часть тепла.</li><li><strong>Тепловое излучение и конвекция:</strong> нагретый чайник сам начинает терять тепло, отдавая его в окружающее пространство через излучение и нагрев прилегающих слоев воздуха (конвекцию).</li><li><strong>Испарение воды до закипания:</strong> часть энергии расходуется на испарение воды с ее поверхности еще до того, как она достигнет температуры кипения.</li><li><strong>Неполное сгорание газа:</strong> при недостатке кислорода или неправильной настройке горелки газ может сгорать не полностью, выделяя меньше тепла, чем теоретически возможно.</li></ul><p><strong>Ответ:</strong> на практике газа требуется больше из-за значительных тепловых потерь в окружающую среду (нагрев воздуха, излучение, конвекция) и неидеального процесса горения, что снижает общий КПД процесса нагрева.</p><p><strong>Как уменьшить расход газа?</strong><p>Чтобы уменьшить расход газа при кипячении воды, необходимо минимизировать тепловые потери и повысить эффективность теплопередачи. Вот несколько практических советов:</p><ul><li><strong>Используйте крышку:</strong> всегда накрывайте чайник крышкой. Это значительно уменьшает потери тепла за счет испарения и конвекции с поверхности воды.</li><li><strong>Подбирайте размер конфорки:</strong> диаметр пламени должен соответствовать диаметру дна чайника. Если пламя "облизывает" стенки, большая часть тепла уходит впустую.</li><li><strong>Кипятите необходимое количество воды:</strong> не стоит наливать полный чайник, если вам нужна всего одна чашка. Нагрев лишней воды — это прямой перерасход энергии.</li><li><strong>Очищайте чайник от накипи:</strong> слой накипи на внутренней стороне дна является теплоизолятором и замедляет процесс нагрева, что ведет к увеличению времени работы конфорки и расхода газа.</li><li><strong>Используйте чайник с широким и чистым дном:</strong> широкое дно обеспечивает большую площадь контакта с пламенем и улучшает теплопередачу. Чистое дно без нагара также способствует лучшей теплопроводности.</li><li><strong>Не давайте воде сильно перекипать:</strong> как только вода закипела, выключайте газ. Длительное бурное кипение не делает воду "горячее" (ее температура остается 100 °C) и лишь расходует газ на превращение воды в пар.</li></ul><p><strong>Ответ:</strong> чтобы уменьшить расход газа, следует накрывать чайник крышкой, использовать конфорку, соответствующую размеру дна, кипятить только нужный объем воды, своевременно очищать чайник от накипи и выключать газ сразу после закипания.</p>" ] #original: array:6 [ "id" => 1466728 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1148} "task" => array:2 [ "refs" => "598923" "type" => "task" ] "text" => "<p><strong>Определите минимальное количество природного газа, необходимое для того, чтобы довести до кипения воду в чайнике, которым вы пользуетесь.</strong><p>Для проведения расчета необходимо принять некоторые допущения о параметрах чайника и воды, так как они не указаны в условии. Возьмем типичные значения для стандартного бытового чайника.</p><strong>Дано:</strong><p>Объем воды, $V_в = 1,5 \text{ л}$<br>Начальная температура воды, $t_1 = 15 \text{ °C}$<br>Конечная температура воды (кипение), $t_2 = 100 \text{ °C}$<br>Материал чайника - алюминий, масса $m_ч = 0,5 \text{ кг}$<br>Удельная теплоемкость воды, $c_в = 4200 \frac{Дж}{кг \cdot К}$<br>Удельная теплоемкость алюминия, $c_{ал} = 920 \frac{Дж}{кг \cdot К}$<br>Плотность воды, $\rho_в = 1000 \frac{кг}{м^3}$<br>Удельная теплота сгорания природного газа, $q_г = 3,6 \cdot 10^7 \frac{Дж}{м^3}$</p><p><strong>Перевод в СИ:</strong><br>$V_в = 1,5 \text{ л} = 1,5 \cdot 10^{-3} \text{ м}^3$<br>Остальные величины уже представлены в системе СИ.</p><strong>Найти:</strong><p>Минимальный объем природного газа $V_г - ?$</p><strong>Решение:</strong><p><strong>1.</strong> Найдем массу воды в чайнике по формуле $m = \rho \cdot V$:</p><p>$m_в = \rho_в \cdot V_в = 1000 \frac{кг}{м^3} \cdot 1,5 \cdot 10^{-3} \text{ м}^3 = 1,5 \text{ кг}$</p><p><strong>2.</strong> Рассчитаем количество теплоты $Q$, необходимое для нагрева, по формуле $Q = c \cdot m \cdot \Delta t$. Сначала для воды:</p><p>$Q_в = c_в \cdot m_в \cdot (t_2 - t_1) = 4200 \frac{Дж}{кг \cdot К} \cdot 1,5 \text{ кг} \cdot (100 - 15) \text{ К} = 535 500 \text{ Дж}$</p><p><strong>3.</strong> Теперь рассчитаем количество теплоты для нагрева самого чайника:</p><p>$Q_ч = c_{ал} \cdot m_ч \cdot (t_2 - t_1) = 920 \frac{Дж}{кг \cdot К} \cdot 0,5 \text{ кг} \cdot (100 - 15) \text{ К} = 39 100 \text{ Дж}$</p><p><strong>4.</strong> Суммарное полезное количество теплоты равно сумме теплоты для нагрева воды и чайника:</p><p>$Q_{полезн} = Q_в + Q_ч = 535 500 \text{ Дж} + 39 100 \text{ Дж} = 574 600 \text{ Дж}$</p><p><strong>5.</strong> Минимальное количество газа соответствует идеальному случаю, когда вся энергия от сгорания идет на нагрев (КПД = 100%). Количество теплоты, выделяемое при сгорании объема газа $V_г$, равно $Q_г = q_г \cdot V_г$. Приравнивая полезную и полученную теплоту ($Q_{полезн} = Q_г$), найдем объем газа:</p><p>$V_г = \frac{Q_{полезн}}{q_г} = \frac{574 600 \text{ Дж}}{3,6 \cdot 10^7 \frac{Дж}{м^3}} \approx 0,01596 \text{ м}^3$</p><p>Округлим результат и переведем в литры для наглядности: $0,016 \text{ м}^3 = 16 \text{ л}$.</p><p><strong>Ответ:</strong> минимальное количество природного газа, необходимое для кипячения 1,5 л воды в 0,5-килограммовом алюминиевом чайнике с начальной температурой 15 °C, составляет примерно $0,016 \text{ м}^3$ (16 литров).</p><p><strong>Почему на практике газа требуется больше?</strong><p>На практике расход газа всегда больше теоретического минимума из-за неизбежных потерь энергии. Коэффициент полезного действия (КПД) газовой плиты при кипячении воды редко превышает 50%. Это означает, что более половины энергии, выделившейся при сгорании газа, теряется и не идет на нагрев воды. Основные причины потерь:</p><ul><li><strong>Нагрев окружающего воздуха:</strong> пламя конфорки нагревает не только дно чайника, но и воздух вокруг него. Горячие продукты сгорания уносят с собой значительную часть тепла.</li><li><strong>Тепловое излучение и конвекция:</strong> нагретый чайник сам начинает терять тепло, отдавая его в окружающее пространство через излучение и нагрев прилегающих слоев воздуха (конвекцию).</li><li><strong>Испарение воды до закипания:</strong> часть энергии расходуется на испарение воды с ее поверхности еще до того, как она достигнет температуры кипения.</li><li><strong>Неполное сгорание газа:</strong> при недостатке кислорода или неправильной настройке горелки газ может сгорать не полностью, выделяя меньше тепла, чем теоретически возможно.</li></ul><p><strong>Ответ:</strong> на практике газа требуется больше из-за значительных тепловых потерь в окружающую среду (нагрев воздуха, излучение, конвекция) и неидеального процесса горения, что снижает общий КПД процесса нагрева.</p><p><strong>Как уменьшить расход газа?</strong><p>Чтобы уменьшить расход газа при кипячении воды, необходимо минимизировать тепловые потери и повысить эффективность теплопередачи. Вот несколько практических советов:</p><ul><li><strong>Используйте крышку:</strong> всегда накрывайте чайник крышкой. Это значительно уменьшает потери тепла за счет испарения и конвекции с поверхности воды.</li><li><strong>Подбирайте размер конфорки:</strong> диаметр пламени должен соответствовать диаметру дна чайника. Если пламя "облизывает" стенки, большая часть тепла уходит впустую.</li><li><strong>Кипятите необходимое количество воды:</strong> не стоит наливать полный чайник, если вам нужна всего одна чашка. Нагрев лишней воды — это прямой перерасход энергии.</li><li><strong>Очищайте чайник от накипи:</strong> слой накипи на внутренней стороне дна является теплоизолятором и замедляет процесс нагрева, что ведет к увеличению времени работы конфорки и расхода газа.</li><li><strong>Используйте чайник с широким и чистым дном:</strong> широкое дно обеспечивает большую площадь контакта с пламенем и улучшает теплопередачу. Чистое дно без нагара также способствует лучшей теплопроводности.</li><li><strong>Не давайте воде сильно перекипать:</strong> как только вода закипела, выключайте газ. Длительное бурное кипение не делает воду "горячее" (ее температура остается 100 °C) и лишь расходует газ на превращение воды в пар.</li></ul><p><strong>Ответ:</strong> чтобы уменьшить расход газа, следует накрывать чайник крышкой, использовать конфорку, соответствующую размеру дна, кипятить только нужный объем воды, своевременно очищать чайник от накипи и выключать газ сразу после закипания.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "598924" "type" => "task" ] "previous" => array:2 [ "refs" => "598922" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => 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№2 (с. 51)
Условие. №2 (с. 51)
скриншот условия
2. Определите минимальное количество природного газа, необходимое для того, чтобы довести до кипения воду в чайнике, которым вы пользуетесь. Почему на практике газа требуется больше? Как уменьшить расход газа?
Решение 1. №2 (с. 51)
Решение 2. №2 (с. 51)
Решение 3. №2 (с. 51)
Решение 4. №2 (с. 51)
Определите минимальное количество природного газа, необходимое для того, чтобы довести до кипения воду в чайнике, которым вы пользуетесь.
Для проведения расчета необходимо принять некоторые допущения о параметрах чайника и воды, так как они не указаны в условии. Возьмем типичные значения для стандартного бытового чайника.
Дано:Объем воды, $V_в = 1,5 \text{ л}$
Начальная температура воды, $t_1 = 15 \text{ °C}$
Конечная температура воды (кипение), $t_2 = 100 \text{ °C}$
Материал чайника - алюминий, масса $m_ч = 0,5 \text{ кг}$
Удельная теплоемкость воды, $c_в = 4200 \frac{Дж}{кг \cdot К}$
Удельная теплоемкость алюминия, $c_{ал} = 920 \frac{Дж}{кг \cdot К}$
Плотность воды, $\rho_в = 1000 \frac{кг}{м^3}$
Удельная теплота сгорания природного газа, $q_г = 3,6 \cdot 10^7 \frac{Дж}{м^3}$
Перевод в СИ:
$V_в = 1,5 \text{ л} = 1,5 \cdot 10^{-3} \text{ м}^3$
Остальные величины уже представлены в системе СИ.
Минимальный объем природного газа $V_г - ?$
Решение:1. Найдем массу воды в чайнике по формуле $m = \rho \cdot V$:
$m_в = \rho_в \cdot V_в = 1000 \frac{кг}{м^3} \cdot 1,5 \cdot 10^{-3} \text{ м}^3 = 1,5 \text{ кг}$
2. Рассчитаем количество теплоты $Q$, необходимое для нагрева, по формуле $Q = c \cdot m \cdot \Delta t$. Сначала для воды:
$Q_в = c_в \cdot m_в \cdot (t_2 - t_1) = 4200 \frac{Дж}{кг \cdot К} \cdot 1,5 \text{ кг} \cdot (100 - 15) \text{ К} = 535 500 \text{ Дж}$
3. Теперь рассчитаем количество теплоты для нагрева самого чайника:
$Q_ч = c_{ал} \cdot m_ч \cdot (t_2 - t_1) = 920 \frac{Дж}{кг \cdot К} \cdot 0,5 \text{ кг} \cdot (100 - 15) \text{ К} = 39 100 \text{ Дж}$
4. Суммарное полезное количество теплоты равно сумме теплоты для нагрева воды и чайника:
$Q_{полезн} = Q_в + Q_ч = 535 500 \text{ Дж} + 39 100 \text{ Дж} = 574 600 \text{ Дж}$
5. Минимальное количество газа соответствует идеальному случаю, когда вся энергия от сгорания идет на нагрев (КПД = 100%). Количество теплоты, выделяемое при сгорании объема газа $V_г$, равно $Q_г = q_г \cdot V_г$. Приравнивая полезную и полученную теплоту ($Q_{полезн} = Q_г$), найдем объем газа:
$V_г = \frac{Q_{полезн}}{q_г} = \frac{574 600 \text{ Дж}}{3,6 \cdot 10^7 \frac{Дж}{м^3}} \approx 0,01596 \text{ м}^3$
Округлим результат и переведем в литры для наглядности: $0,016 \text{ м}^3 = 16 \text{ л}$.
Ответ: минимальное количество природного газа, необходимое для кипячения 1,5 л воды в 0,5-килограммовом алюминиевом чайнике с начальной температурой 15 °C, составляет примерно $0,016 \text{ м}^3$ (16 литров).
Почему на практике газа требуется больше?
На практике расход газа всегда больше теоретического минимума из-за неизбежных потерь энергии. Коэффициент полезного действия (КПД) газовой плиты при кипячении воды редко превышает 50%. Это означает, что более половины энергии, выделившейся при сгорании газа, теряется и не идет на нагрев воды. Основные причины потерь:
- Нагрев окружающего воздуха: пламя конфорки нагревает не только дно чайника, но и воздух вокруг него. Горячие продукты сгорания уносят с собой значительную часть тепла.
- Тепловое излучение и конвекция: нагретый чайник сам начинает терять тепло, отдавая его в окружающее пространство через излучение и нагрев прилегающих слоев воздуха (конвекцию).
- Испарение воды до закипания: часть энергии расходуется на испарение воды с ее поверхности еще до того, как она достигнет температуры кипения.
- Неполное сгорание газа: при недостатке кислорода или неправильной настройке горелки газ может сгорать не полностью, выделяя меньше тепла, чем теоретически возможно.
Ответ: на практике газа требуется больше из-за значительных тепловых потерь в окружающую среду (нагрев воздуха, излучение, конвекция) и неидеального процесса горения, что снижает общий КПД процесса нагрева.
Как уменьшить расход газа?
Чтобы уменьшить расход газа при кипячении воды, необходимо минимизировать тепловые потери и повысить эффективность теплопередачи. Вот несколько практических советов:
- Используйте крышку: всегда накрывайте чайник крышкой. Это значительно уменьшает потери тепла за счет испарения и конвекции с поверхности воды.
- Подбирайте размер конфорки: диаметр пламени должен соответствовать диаметру дна чайника. Если пламя "облизывает" стенки, большая часть тепла уходит впустую.
- Кипятите необходимое количество воды: не стоит наливать полный чайник, если вам нужна всего одна чашка. Нагрев лишней воды — это прямой перерасход энергии.
- Очищайте чайник от накипи: слой накипи на внутренней стороне дна является теплоизолятором и замедляет процесс нагрева, что ведет к увеличению времени работы конфорки и расхода газа.
- Используйте чайник с широким и чистым дном: широкое дно обеспечивает большую площадь контакта с пламенем и улучшает теплопередачу. Чистое дно без нагара также способствует лучшей теплопроводности.
- Не давайте воде сильно перекипать: как только вода закипела, выключайте газ. Длительное бурное кипение не делает воду "горячее" (ее температура остается 100 °C) и лишь расходует газ на превращение воды в пар.
Ответ: чтобы уменьшить расход газа, следует накрывать чайник крышкой, использовать конфорку, соответствующую размеру дна, кипятить только нужный объем воды, своевременно очищать чайник от накипи и выключать газ сразу после закипания.
Другие задания:
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