gdz.top
Номер 4, страница 82 - 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 21. Кипение. Упражнение 18 - номер 4, страница 82.
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" => 599023 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/21-3-4" "field_display_title" => "4" "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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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" => 598640 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кипение" "field_branch_order" => "21" "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 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" …4 ] "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" => "79" "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" => 598640 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кипение" "field_branch_order" => "21" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1128} "field_page_start" => "79" "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" => 598643 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнение 18" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "81" "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" => 598640 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кипение" "field_branch_order" => "21" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_page_start" => "79" "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" => 598640 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кипение" "field_branch_order" => "21" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_page_start" => "79" "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" => 598643 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнение 18" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_page_start" => "81" "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" => 745480 "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" => "599023" "type" => "task" ] "text" => "<p> <b>4</b>. На одной координатной плоскости изобразите примерные графики зависимости температуры от времени при нагревании и кипении воды и спирта одинаковой массы. Жидкости нагреваются на одинаковых горелках. </p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.png" "alt" => null "width" => "746" "height" => 142 "path" => "/media/fizika_08/Peryshkin-u23/0-21-3/4-1.webp?ts=1738080879" ] ] ] #original: array:7 [ "id" => 745480 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091} "task" => array:2 [ "refs" => "599023" "type" => "task" ] "text" => "<p> <b>4</b>. На одной координатной плоскости изобразите примерные графики зависимости температуры от времени при нагревании и кипении воды и спирта одинаковой массы. Жидкости нагреваются на одинаковых горелках. </p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.png" "alt" => null "width" => "746" "height" => 142 "path" => "/media/fizika_08/Peryshkin-u23/0-21-3/4-1.webp?ts=1738080879" ] ] ] #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" => 745643 "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" => "599023" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1895" "height" => 1246 "path" => "/media/fizika_08/Peryshkin-u23/1-21-3/4-1.webp?ts=1738080915" ] ] ] #original: array:6 [ "id" => 745643 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1080} "task" => array:2 [ "refs" => "599023" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1895" "height" => 1246 "path" => "/media/fizika_08/Peryshkin-u23/1-21-3/4-1.webp?ts=1738080915" ] ] ] #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 {#1083 #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" => 746689 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\Edition {#1084 #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 {#1043 …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" => "3-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1034 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1039 …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 {#1043 …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" => "3-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1034 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1039 …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" => "599023" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "4-1.png" "alt" => null "width" => "700" "height" => 881 "path" => "/media/fizika_08/Peryshkin-u23/3-21-3/4-1.webp?ts=1738080958" ] ] ] #original: array:6 [ "id" => 746689 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116} "task" => array:2 [ "refs" => "599023" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "4-1.png" "alt" => null "width" => "700" "height" => 881 "path" => "/media/fizika_08/Peryshkin-u23/3-21-3/4-1.webp?ts=1738080958" ] ] ] #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 {#1111 #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" => 746999 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Edition {#1109 #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 {#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} "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} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1113 …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" => "599023" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "4-1.png" "alt" => null "width" => "837" "height" => 963 "path" => "/media/fizika_08/Peryshkin-u23/2-21-3/4-1.webp?ts=1738081024" ] ] ] #original: array:6 [ "id" => 746999 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1136} "task" => array:2 [ "refs" => "599023" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "4-1.png" "alt" => null "width" => "837" "height" => 963 "path" => "/media/fizika_08/Peryshkin-u23/2-21-3/4-1.webp?ts=1738081024" ] ] ] #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" => 1466828 "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" => "599023" "type" => "task" ] "text" => "<p>Для построения графиков зависимости температуры от времени для воды и спирта необходимо проанализировать два процесса: нагревание до температуры кипения и само кипение.</p><p><strong>Дано:</strong></p><p>Масса воды равна массе спирта: $m_{воды} = m_{спирта} = m$</p><p>Жидкости нагреваются на одинаковых горелках, следовательно, подводимая мощность (количество теплоты в единицу времени) одинакова: $P_{воды} = P_{спирта} = P$</p><p>Для решения задачи потребуются справочные данные (при нормальном атмосферном давлении):</p><ul><li>Удельная теплоемкость воды: $c_{воды} \approx 4200 \, \frac{Дж}{кг \cdot °C}$</li><li>Удельная теплоемкость спирта (этанола): $c_{спирта} \approx 2400 \, \frac{Дж}{кг \cdot °C}$</li><li>Температура кипения воды: $T_{кип, воды} = 100 \, °C$</li><li>Температура кипения спирта (этанола): $T_{кип, спирта} \approx 78 \, °C$</li></ul><p><strong>Найти:</strong></p><p>Изобразить на одной координатной плоскости примерные графики зависимости температуры от времени $T(t)$ для воды и спирта.</p><p><strong>Решение:</strong></p><p>Процесс, описываемый в задаче, состоит из двух этапов для каждой жидкости.</p><p><strong>1.</strong> Нагревание жидкости до температуры кипения.</p><p>Количество теплоты $Q$, необходимое для нагревания тела массой $m$ на температуру $\Delta T$, определяется формулой:</p><p>$Q = c \cdot m \cdot \Delta T$</p><p>где $c$ — удельная теплоемкость вещества.</p><p>Так как жидкости нагреваются на одинаковых горелках, они получают одинаковое количество теплоты $Q$ за одно и то же время $t$. Мощность горелки $P = \frac{Q}{t}$, откуда $Q = P \cdot t$.</p><p>Приравняв выражения для $Q$, получаем: $P \cdot t = c \cdot m \cdot \Delta T$.</p><p>Выразим изменение температуры $\Delta T$ через время $t$:</p><p>$\Delta T = \frac{P}{c \cdot m} \cdot t$</p><p>Скорость нагревания (тангенс угла наклона графика $T(t)$) равна $\frac{\Delta T}{t} = \frac{P}{c \cdot m}$.</p><p>Сравним скорости нагревания воды и спирта. Так как $P$ и $m$ одинаковы для обеих жидкостей, скорость нагревания обратно пропорциональна удельной теплоемкости $c$.</p><p>Поскольку удельная теплоемкость воды ($c_{воды} \approx 4200 \, \frac{Дж}{кг \cdot °C}$) больше удельной теплоемкости спирта ($c_{спирта} \approx 2400 \, \frac{Дж}{кг \cdot °C}$), то есть $c_{воды} > c_{спирта}$, то скорость нагревания воды будет меньше скорости нагревания спирта. Это означает, что на графике $T(t)$ прямая для спирта будет идти круче (под большим углом к оси времени), чем для воды.</p><p><strong>2.</strong> Кипение жидкости.</p><p>Кипение — это процесс парообразования, который происходит при постоянной температуре, называемой температурой кипения. Для воды эта температура составляет $100 \, °C$, а для спирта — около $78 \, °C$.</p><p>На графике $T(t)$ этот процесс будет изображаться горизонтальным участком на уровне соответствующей температуры кипения.</p><p><strong>Построение графиков.</strong></p><p>Примем, что начальная температура обеих жидкостей одинакова (например, комнатная, $T_0 < 78 \, °C$).</p><ul><li>Оба графика начинаются из одной точки $(0, T_0)$.</li><li>График для спирта представляет собой прямую, идущую под большим углом, до достижения температуры $78 \, °C$. Затем он становится горизонтальным.</li><li>График для воды представляет собой прямую, идущую под меньшим углом, до достижения температуры $100 \, °C$. Затем он также становится горизонтальным.</li><li>Спирт достигнет своей температуры кипения и начнет кипеть раньше, чем вода.</li></ul><p>Итоговый график будет выглядеть следующим образом:</p><svg width="500" height="350" xmlns="http://www.w3.org/2000/svg" style="font-family: sans-serif; font-size: 14px;"><!-- Стили --><style> .axis { stroke: black; stroke-width: 2; } .grid-line { stroke: #ccc; stroke-width: 1; stroke-dasharray: 4 2; } .label { fill: black; text-anchor: middle; } .axis-label { fill: black; text-anchor: middle; font-weight: bold; } .water-line { stroke: blue; stroke-width: 2.5; fill: none; } .alcohol-line { stroke: red; stroke-width: 2.5; fill: none; } </style><!-- Оси --><line x1="50" y1="300" x2="480" y2="300" class="axis" marker-end="url(#arrow)"/><!-- Ось t --><line x1="50" y1="300" x2="50" y2="20" class="axis" marker-end="url(#arrow)"/><!-- Ось T --><defs><marker id="arrow" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse"><path d="M 0 0 L 10 5 L 0 10 z" fill="black"/></marker></defs><!-- Метки на осях --><text x="485" y="320" class="axis-label">t, время</text><text x="20" y="30" class="axis-label" transform="rotate(-90, 20, 30)">T, °C</text><text x="35" y="305" class="label">0</text><!-- Метки температуры --><text x="35" y="142.5" class="label">78</text><line x1="50" y1="137.5" x2="150" y2="137.5" class="grid-line"/><text x="30" y="97" class="label">100</text><line x1="50" y1="92" x2="291" y2="92" class="grid-line"/><!-- Графики --><!-- Начальная точка (t=0, T=20), y = 300 - 20 * 2.1 = 258 --><!-- Спирт: кипение (T=78) y=137.5. Время t1, x=150 --><!-- Вода: кипение (T=100) y=92. Время t2 > t1, x=291 --><polyline points="50,258 150,137.5 250,137.5" class="alcohol-line"/><polyline points="50,258 291,92 400,92" class="water-line"/><!-- Легенда --><rect x="330" y="180" width="120" height="60" fill="white" stroke="black"/><line x1="340" y1="200" x2="360" y2="200" class="water-line"/><text x="370" y="205">Вода</text><line x1="340" y1="220" x2="360" y2="220" class="alcohol-line"/><text x="370" y="225">Спирт</text></svg><p><strong>Ответ:</strong></p><p>Примерные графики зависимости температуры от времени для воды и спирта представлены на рисунке выше. График для спирта (красная линия) имеет более крутой наклон на участке нагревания и переходит в горизонтальный участок (кипение) при температуре $78 \, °C$. График для воды (синяя линия) имеет менее крутой наклон и переходит в горизонтальный участок при температуре $100 \, °C$.</p>" ] #original: array:6 [ "id" => 1466828 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1148} "task" => array:2 [ "refs" => "599023" "type" => "task" ] "text" => "<p>Для построения графиков зависимости температуры от времени для воды и спирта необходимо проанализировать два процесса: нагревание до температуры кипения и само кипение.</p><p><strong>Дано:</strong></p><p>Масса воды равна массе спирта: $m_{воды} = m_{спирта} = m$</p><p>Жидкости нагреваются на одинаковых горелках, следовательно, подводимая мощность (количество теплоты в единицу времени) одинакова: $P_{воды} = P_{спирта} = P$</p><p>Для решения задачи потребуются справочные данные (при нормальном атмосферном давлении):</p><ul><li>Удельная теплоемкость воды: $c_{воды} \approx 4200 \, \frac{Дж}{кг \cdot °C}$</li><li>Удельная теплоемкость спирта (этанола): $c_{спирта} \approx 2400 \, \frac{Дж}{кг \cdot °C}$</li><li>Температура кипения воды: $T_{кип, воды} = 100 \, °C$</li><li>Температура кипения спирта (этанола): $T_{кип, спирта} \approx 78 \, °C$</li></ul><p><strong>Найти:</strong></p><p>Изобразить на одной координатной плоскости примерные графики зависимости температуры от времени $T(t)$ для воды и спирта.</p><p><strong>Решение:</strong></p><p>Процесс, описываемый в задаче, состоит из двух этапов для каждой жидкости.</p><p><strong>1.</strong> Нагревание жидкости до температуры кипения.</p><p>Количество теплоты $Q$, необходимое для нагревания тела массой $m$ на температуру $\Delta T$, определяется формулой:</p><p>$Q = c \cdot m \cdot \Delta T$</p><p>где $c$ — удельная теплоемкость вещества.</p><p>Так как жидкости нагреваются на одинаковых горелках, они получают одинаковое количество теплоты $Q$ за одно и то же время $t$. Мощность горелки $P = \frac{Q}{t}$, откуда $Q = P \cdot t$.</p><p>Приравняв выражения для $Q$, получаем: $P \cdot t = c \cdot m \cdot \Delta T$.</p><p>Выразим изменение температуры $\Delta T$ через время $t$:</p><p>$\Delta T = \frac{P}{c \cdot m} \cdot t$</p><p>Скорость нагревания (тангенс угла наклона графика $T(t)$) равна $\frac{\Delta T}{t} = \frac{P}{c \cdot m}$.</p><p>Сравним скорости нагревания воды и спирта. Так как $P$ и $m$ одинаковы для обеих жидкостей, скорость нагревания обратно пропорциональна удельной теплоемкости $c$.</p><p>Поскольку удельная теплоемкость воды ($c_{воды} \approx 4200 \, \frac{Дж}{кг \cdot °C}$) больше удельной теплоемкости спирта ($c_{спирта} \approx 2400 \, \frac{Дж}{кг \cdot °C}$), то есть $c_{воды} > c_{спирта}$, то скорость нагревания воды будет меньше скорости нагревания спирта. Это означает, что на графике $T(t)$ прямая для спирта будет идти круче (под большим углом к оси времени), чем для воды.</p><p><strong>2.</strong> Кипение жидкости.</p><p>Кипение — это процесс парообразования, который происходит при постоянной температуре, называемой температурой кипения. Для воды эта температура составляет $100 \, °C$, а для спирта — около $78 \, °C$.</p><p>На графике $T(t)$ этот процесс будет изображаться горизонтальным участком на уровне соответствующей температуры кипения.</p><p><strong>Построение графиков.</strong></p><p>Примем, что начальная температура обеих жидкостей одинакова (например, комнатная, $T_0 < 78 \, °C$).</p><ul><li>Оба графика начинаются из одной точки $(0, T_0)$.</li><li>График для спирта представляет собой прямую, идущую под большим углом, до достижения температуры $78 \, °C$. Затем он становится горизонтальным.</li><li>График для воды представляет собой прямую, идущую под меньшим углом, до достижения температуры $100 \, °C$. Затем он также становится горизонтальным.</li><li>Спирт достигнет своей температуры кипения и начнет кипеть раньше, чем вода.</li></ul><p>Итоговый график будет выглядеть следующим образом:</p><svg width="500" height="350" xmlns="http://www.w3.org/2000/svg" style="font-family: sans-serif; font-size: 14px;"><!-- Стили --><style> .axis { stroke: black; stroke-width: 2; } .grid-line { stroke: #ccc; stroke-width: 1; stroke-dasharray: 4 2; } .label { fill: black; text-anchor: middle; } .axis-label { fill: black; text-anchor: middle; font-weight: bold; } .water-line { stroke: blue; stroke-width: 2.5; fill: none; } .alcohol-line { stroke: red; stroke-width: 2.5; fill: none; } </style><!-- Оси --><line x1="50" y1="300" x2="480" y2="300" class="axis" marker-end="url(#arrow)"/><!-- Ось t --><line x1="50" y1="300" x2="50" y2="20" class="axis" marker-end="url(#arrow)"/><!-- Ось T --><defs><marker id="arrow" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse"><path d="M 0 0 L 10 5 L 0 10 z" fill="black"/></marker></defs><!-- Метки на осях --><text x="485" y="320" class="axis-label">t, время</text><text x="20" y="30" class="axis-label" transform="rotate(-90, 20, 30)">T, °C</text><text x="35" y="305" class="label">0</text><!-- Метки температуры --><text x="35" y="142.5" class="label">78</text><line x1="50" y1="137.5" x2="150" y2="137.5" class="grid-line"/><text x="30" y="97" class="label">100</text><line x1="50" y1="92" x2="291" y2="92" class="grid-line"/><!-- Графики --><!-- Начальная точка (t=0, T=20), y = 300 - 20 * 2.1 = 258 --><!-- Спирт: кипение (T=78) y=137.5. Время t1, x=150 --><!-- Вода: кипение (T=100) y=92. Время t2 > t1, x=291 --><polyline points="50,258 150,137.5 250,137.5" class="alcohol-line"/><polyline points="50,258 291,92 400,92" class="water-line"/><!-- Легенда --><rect x="330" y="180" width="120" height="60" fill="white" stroke="black"/><line x1="340" y1="200" x2="360" y2="200" class="water-line"/><text x="370" y="205">Вода</text><line x1="340" y1="220" x2="360" y2="220" class="alcohol-line"/><text x="370" y="225">Спирт</text></svg><p><strong>Ответ:</strong></p><p>Примерные графики зависимости температуры от времени для воды и спирта представлены на рисунке выше. График для спирта (красная линия) имеет более крутой наклон на участке нагревания и переходит в горизонтальный участок (кипение) при температуре $78 \, °C$. График для воды (синяя линия) имеет менее крутой наклон и переходит в горизонтальный участок при температуре $100 \, °C$.</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" => "599024" "type" => "task" ] "previous" => array:2 [ "refs" => "599022" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1106 #items: array:1 [ 0 => App\Models\BookPage {#1103 #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" => 991446 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_url" => "/8-klass/fizika/peryshkin-uchebnik/page-82" "field_display_title" => "82" "field_folder" => "1" "field_image_name" => "82" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1042 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1107 #items: array:1 [ 0 => App\Models\Book {#1049} ] #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 {#1040 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1156 #items: array:1 [ 0 => App\Models\Element {#1155 #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" => 1173106 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1157 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1173106 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1157 …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" => "991447" "type" => "book_page" ] "previous" => array:2 [ "refs" => "991445" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1253 #items: array:4 [ 0 => App\Models\Task {#1263 #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" => 599023 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/21-3-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1264 …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 {#1265 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1266 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1267 …2} "content" => Illuminate\Database\Eloquent\Collection {#1268 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1269 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 599023 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/21-3-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1264 …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 {#1265 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1266 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1267 …2} "content" => Illuminate\Database\Eloquent\Collection {#1268 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1269 …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 {#1270 #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" => 599024 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/21-3-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1271 …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 {#1272 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1273 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1274 …2} "content" => Illuminate\Database\Eloquent\Collection {#1277 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1286 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 599024 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/21-3-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1271 …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 {#1272 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1273 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1274 …2} "content" => Illuminate\Database\Eloquent\Collection {#1277 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1286 …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 {#1276 #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" => 599025 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/21-3-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1275 …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 {#1285 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1283 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1282 …2} "content" => Illuminate\Database\Eloquent\Collection {#1278 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1304 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 599025 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/21-3-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1275 …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 {#1285 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1283 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1282 …2} "content" => Illuminate\Database\Eloquent\Collection {#1278 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1304 …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 {#1280 #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" => 599026 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/21-4-1" "field_display_title" => "Это любопытно" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1284 …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 {#1303 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1301 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1300 …2} "content" => Illuminate\Database\Eloquent\Collection {#1298 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1321 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 599026 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/21-4-1" "field_display_title" => "Это любопытно" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1284 …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 {#1303 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1301 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1300 …2} "content" => Illuminate\Database\Eloquent\Collection {#1298 …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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 991446 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_url" => "/8-klass/fizika/peryshkin-uchebnik/page-82" "field_display_title" => "82" "field_folder" => "1" "field_image_name" => "82" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1042} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1107} "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 {#1040} "content" => Illuminate\Database\Eloquent\Collection {#1156} "next" => array:2 [ "refs" => "991447" "type" => "book_page" ] "previous" => array:2 [ "refs" => "991445" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1253} ] #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" => 599023 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/21-3-4" "field_display_title" => "4" "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 {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1110} "content" => Illuminate\Database\Eloquent\Collection {#1108} "next" => array:2 [ "refs" => "599024" "type" => "task" ] "previous" => array:2 [ "refs" => "599022" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1100} "page" => array:2 [ "refs" => "991446" "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 => "*" ] }
№4 (с. 82)
Условие. №4 (с. 82)
скриншот условия
4. На одной координатной плоскости изобразите примерные графики зависимости температуры от времени при нагревании и кипении воды и спирта одинаковой массы. Жидкости нагреваются на одинаковых горелках.
Решение 1. №4 (с. 82)
Решение 2. №4 (с. 82)
Решение 3. №4 (с. 82)
Решение 4. №4 (с. 82)
Для построения графиков зависимости температуры от времени для воды и спирта необходимо проанализировать два процесса: нагревание до температуры кипения и само кипение.
Дано:
Масса воды равна массе спирта: $m_{воды} = m_{спирта} = m$
Жидкости нагреваются на одинаковых горелках, следовательно, подводимая мощность (количество теплоты в единицу времени) одинакова: $P_{воды} = P_{спирта} = P$
Для решения задачи потребуются справочные данные (при нормальном атмосферном давлении):
- Удельная теплоемкость воды: $c_{воды} \approx 4200 \, \frac{Дж}{кг \cdot °C}$
- Удельная теплоемкость спирта (этанола): $c_{спирта} \approx 2400 \, \frac{Дж}{кг \cdot °C}$
- Температура кипения воды: $T_{кип, воды} = 100 \, °C$
- Температура кипения спирта (этанола): $T_{кип, спирта} \approx 78 \, °C$
Найти:
Изобразить на одной координатной плоскости примерные графики зависимости температуры от времени $T(t)$ для воды и спирта.
Решение:
Процесс, описываемый в задаче, состоит из двух этапов для каждой жидкости.
1. Нагревание жидкости до температуры кипения.
Количество теплоты $Q$, необходимое для нагревания тела массой $m$ на температуру $\Delta T$, определяется формулой:
$Q = c \cdot m \cdot \Delta T$
где $c$ — удельная теплоемкость вещества.
Так как жидкости нагреваются на одинаковых горелках, они получают одинаковое количество теплоты $Q$ за одно и то же время $t$. Мощность горелки $P = \frac{Q}{t}$, откуда $Q = P \cdot t$.
Приравняв выражения для $Q$, получаем: $P \cdot t = c \cdot m \cdot \Delta T$.
Выразим изменение температуры $\Delta T$ через время $t$:
$\Delta T = \frac{P}{c \cdot m} \cdot t$
Скорость нагревания (тангенс угла наклона графика $T(t)$) равна $\frac{\Delta T}{t} = \frac{P}{c \cdot m}$.
Сравним скорости нагревания воды и спирта. Так как $P$ и $m$ одинаковы для обеих жидкостей, скорость нагревания обратно пропорциональна удельной теплоемкости $c$.
Поскольку удельная теплоемкость воды ($c_{воды} \approx 4200 \, \frac{Дж}{кг \cdot °C}$) больше удельной теплоемкости спирта ($c_{спирта} \approx 2400 \, \frac{Дж}{кг \cdot °C}$), то есть $c_{воды} > c_{спирта}$, то скорость нагревания воды будет меньше скорости нагревания спирта. Это означает, что на графике $T(t)$ прямая для спирта будет идти круче (под большим углом к оси времени), чем для воды.
2. Кипение жидкости.
Кипение — это процесс парообразования, который происходит при постоянной температуре, называемой температурой кипения. Для воды эта температура составляет $100 \, °C$, а для спирта — около $78 \, °C$.
На графике $T(t)$ этот процесс будет изображаться горизонтальным участком на уровне соответствующей температуры кипения.
Построение графиков.
Примем, что начальная температура обеих жидкостей одинакова (например, комнатная, $T_0 < 78 \, °C$).
- Оба графика начинаются из одной точки $(0, T_0)$.
- График для спирта представляет собой прямую, идущую под большим углом, до достижения температуры $78 \, °C$. Затем он становится горизонтальным.
- График для воды представляет собой прямую, идущую под меньшим углом, до достижения температуры $100 \, °C$. Затем он также становится горизонтальным.
- Спирт достигнет своей температуры кипения и начнет кипеть раньше, чем вода.
Итоговый график будет выглядеть следующим образом:
Ответ:
Примерные графики зависимости температуры от времени для воды и спирта представлены на рисунке выше. График для спирта (красная линия) имеет более крутой наклон на участке нагревания и переходит в горизонтальный участок (кипение) при температуре $78 \, °C$. График для воды (синяя линия) имеет менее крутой наклон и переходит в горизонтальный участок при температуре $100 \, °C$.
Другие задания:
Помогло решение? Оставьте отзыв в комментариях ниже.
Присоединяйтесь к Телеграм-группе @top_gdz
ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по физике за 8 класс, для упражнения номер 4 расположенного на странице 82 к учебнику 2023 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №4 (с. 82), автора: Пёрышкин (И М), ФГОС (новый, красный) базовый уровень обучения учебного пособия издательства Просвещение.