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Номер 1.35, страница 7 - гдз по физике 8 класс задачник Артеменков, Ломаченков
Авторы: Артеменков Д. А., Ломаченков И. А., Панебратцев Ю. А.
Тип: Задачник
Серия: сферы
Издательство: Просвещение
Год издания: 2010 - 2026
Цвет обложки: фиолетовый
ISBN: 978-5-09-046040-8
Популярные ГДЗ в 8 классе
I. Внутренняя энергия - номер 1.35, страница 7.
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" => 1460087 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-35" "field_display_title" => "1.35" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1460044 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "I. Внутренняя энергия" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 1646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:1 [ 0 => App\Models\Term {#1042 #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 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Term {#1044 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ 0 => App\Models\Term {#1046 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:3 [ 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:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1049 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1050 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_book_type" => 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: [] …23 } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ 0 => App\Models\Term {#1057 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ 0 => App\Models\Term {#1059 …30} ] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1050} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 …30} ] #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" => 1646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045} "field_author" => Illuminate\Database\Eloquent\Collection {#1047} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052} "field_country" => Illuminate\Database\Eloquent\Collection {#1054} "field_city" => Illuminate\Database\Eloquent\Collection {#1056} "field_series" => Illuminate\Database\Eloquent\Collection {#1058} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1460044 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "I. Внутренняя энергия" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:2 [ 0 => 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:7 [ "id" => 1753585 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092 #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" => 6390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1086 #items: array:1 [ 0 => App\Models\Term {#1085 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "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 {#1087 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1086} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "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 {#1087} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1088} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1089} "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" => "1460087" "type" => "task" ] "text" => "<p><strong>1.35</strong> Вещество массой $m_1$ и температурой $t_1$ смешали с тем же веществом массой $m_2$ и температурой $t_2$. Выведите общую формулу для определения температуры смеси.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "35-1.jpg" "alt" => null "width" => "1757" "height" => 263 "path" => "/media/fizika_08/artemenkov-zd/0-01/35-1.webp?ts=1760701704" ] ] ] #original: array:7 [ "id" => 1753585 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092} "task" => array:2 [ "refs" => "1460087" "type" => "task" ] "text" => "<p><strong>1.35</strong> Вещество массой $m_1$ и температурой $t_1$ смешали с тем же веществом массой $m_2$ и температурой $t_2$. Выведите общую формулу для определения температуры смеси.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "35-1.jpg" "alt" => null "width" => "1757" "height" => 263 "path" => "/media/fizika_08/artemenkov-zd/0-01/35-1.webp?ts=1760701704" ] ] ] #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 {#1090 #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" => 1821692 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ 0 => App\Models\Edition {#1091 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6688 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1094 #items: array:1 [ 0 => App\Models\Term {#1093 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1095 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1097 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6688 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1094} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1095} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1096} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1097} "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" => "1460087" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Масса первого количества вещества: $m_1$<br>Температура первого количества вещества: $t_1$<br>Масса второго количества вещества: $m_2$<br>Температура второго количества вещества: $t_2$<br>Вещество одно и то же, следовательно, его удельная теплоемкость $\text{c}$ одинакова для обеих порций.</p><p>Данные в задаче представлены в общем виде. В системе СИ:<br>Масса $\text{m}$ измеряется в килограммах (кг).<br>Температура $\text{t}$ измеряется в Кельвинах (К). Формула также будет верна для градусов Цельсия (°C), так как является линейной относительно температур.</p><p><strong>Найти:</strong></p><p>Общую формулу для определения температуры смеси $\text{t}$.</p><p><strong>Решение:</strong></p><p>При смешивании двух порций вещества с разными температурами происходит теплообмен. Та порция вещества, которая имеет более высокую температуру, отдает тепло, а та, у которой температура ниже, — получает. Этот процесс продолжается до тех пор, пока система не придет в состояние теплового равновесия, то есть пока температура всей смеси не станет одинаковой. Обозначим эту конечную температуру как $\text{t}$.</p><p>Будем считать систему теплоизолированной, то есть теплообмен с окружающей средой отсутствует. В этом случае выполняется закон сохранения энергии, который для тепловых процессов формулируется как уравнение теплового баланса: количество теплоты, отданное более горячим телом ($Q_{отданное}$), равно количеству теплоты, полученному более холодным телом ($Q_{полученное}$).</p><p>$Q_{отданное} = Q_{полученное}$</p><p>Для определенности предположим, что $t_1 > t_2$. Тогда первая порция вещества будет остывать до температуры $\text{t}$, а вторая — нагреваться до той же температуры $\text{t}$. Конечная температура смеси будет находиться в интервале $t_2 < t < t_1$.</p><p>Количество теплоты, которое отдаст первая порция вещества, определяется по формуле: $Q_{отданное} = c \cdot m_1 \cdot (t_1 - t)$</p><p>Количество теплоты, которое получит вторая порция вещества: $Q_{полученное} = c \cdot m_2 \cdot (t - t_2)$</p><p>Теперь составим уравнение теплового баланса, приравняв отданное и полученное количество теплоты: $c \cdot m_1 \cdot (t_1 - t) = c \cdot m_2 \cdot (t - t_2)$</p><p>Так как вещество одно и то же, его удельная теплоемкость $\text{c}$ в левой и правой частях уравнения одинакова. Мы можем сократить ее: $m_1 \cdot (t_1 - t) = m_2 \cdot (t - t_2)$</p><p>Теперь необходимо решить это уравнение относительно конечной температуры $\text{t}$. Для этого сначала раскроем скобки: $m_1 t_1 - m_1 t = m_2 t - m_2 t_2$</p><p>Перенесем все слагаемые, содержащие искомую температуру $\text{t}$, в одну часть уравнения, а остальные слагаемые — в другую: $m_1 t_1 + m_2 t_2 = m_1 t + m_2 t$</p><p>В правой части вынесем $\text{t}$ за скобки: $m_1 t_1 + m_2 t_2 = t(m_1 + m_2)$</p><p>Наконец, выразим конечную температуру смеси $\text{t}$: $t = \frac{m_1 t_1 + m_2 t_2}{m_1 + m_2}$</p><p>Полученная формула является общей и не зависит от того, какая из начальных температур была выше. Она показывает, что конечная температура смеси является средневзвешенным значением начальных температур, где в качестве весов выступают массы.</p><p><strong>Ответ:</strong> $t = \frac{m_1 t_1 + m_2 t_2}{m_1 + m_2}$</p>" ] #original: array:6 [ "id" => 1821692 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100} "task" => array:2 [ "refs" => "1460087" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Масса первого количества вещества: $m_1$<br>Температура первого количества вещества: $t_1$<br>Масса второго количества вещества: $m_2$<br>Температура второго количества вещества: $t_2$<br>Вещество одно и то же, следовательно, его удельная теплоемкость $\text{c}$ одинакова для обеих порций.</p><p>Данные в задаче представлены в общем виде. В системе СИ:<br>Масса $\text{m}$ измеряется в килограммах (кг).<br>Температура $\text{t}$ измеряется в Кельвинах (К). Формула также будет верна для градусов Цельсия (°C), так как является линейной относительно температур.</p><p><strong>Найти:</strong></p><p>Общую формулу для определения температуры смеси $\text{t}$.</p><p><strong>Решение:</strong></p><p>При смешивании двух порций вещества с разными температурами происходит теплообмен. Та порция вещества, которая имеет более высокую температуру, отдает тепло, а та, у которой температура ниже, — получает. Этот процесс продолжается до тех пор, пока система не придет в состояние теплового равновесия, то есть пока температура всей смеси не станет одинаковой. Обозначим эту конечную температуру как $\text{t}$.</p><p>Будем считать систему теплоизолированной, то есть теплообмен с окружающей средой отсутствует. В этом случае выполняется закон сохранения энергии, который для тепловых процессов формулируется как уравнение теплового баланса: количество теплоты, отданное более горячим телом ($Q_{отданное}$), равно количеству теплоты, полученному более холодным телом ($Q_{полученное}$).</p><p>$Q_{отданное} = Q_{полученное}$</p><p>Для определенности предположим, что $t_1 > t_2$. Тогда первая порция вещества будет остывать до температуры $\text{t}$, а вторая — нагреваться до той же температуры $\text{t}$. Конечная температура смеси будет находиться в интервале $t_2 < t < t_1$.</p><p>Количество теплоты, которое отдаст первая порция вещества, определяется по формуле: $Q_{отданное} = c \cdot m_1 \cdot (t_1 - t)$</p><p>Количество теплоты, которое получит вторая порция вещества: $Q_{полученное} = c \cdot m_2 \cdot (t - t_2)$</p><p>Теперь составим уравнение теплового баланса, приравняв отданное и полученное количество теплоты: $c \cdot m_1 \cdot (t_1 - t) = c \cdot m_2 \cdot (t - t_2)$</p><p>Так как вещество одно и то же, его удельная теплоемкость $\text{c}$ в левой и правой частях уравнения одинакова. Мы можем сократить ее: $m_1 \cdot (t_1 - t) = m_2 \cdot (t - t_2)$</p><p>Теперь необходимо решить это уравнение относительно конечной температуры $\text{t}$. Для этого сначала раскроем скобки: $m_1 t_1 - m_1 t = m_2 t - m_2 t_2$</p><p>Перенесем все слагаемые, содержащие искомую температуру $\text{t}$, в одну часть уравнения, а остальные слагаемые — в другую: $m_1 t_1 + m_2 t_2 = m_1 t + m_2 t$</p><p>В правой части вынесем $\text{t}$ за скобки: $m_1 t_1 + m_2 t_2 = t(m_1 + m_2)$</p><p>Наконец, выразим конечную температуру смеси $\text{t}$: $t = \frac{m_1 t_1 + m_2 t_2}{m_1 + m_2}$</p><p>Полученная формула является общей и не зависит от того, какая из начальных температур была выше. Она показывает, что конечная температура смеси является средневзвешенным значением начальных температур, где в качестве весов выступают массы.</p><p><strong>Ответ:</strong> $t = \frac{m_1 t_1 + m_2 t_2}{m_1 + m_2}$</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" => "1460088" "type" => "task" ] "previous" => array:2 [ "refs" => "1460086" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Book {#1080 #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" => 1646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:1 [ 0 => App\Models\Term {#1075 #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 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "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 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "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 {#1082 #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" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "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 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "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 {#1076 #items: array:1 [ 0 => App\Models\Term {#1079 #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 {#1077 #items: array:3 [ 0 => App\Models\Term {#1098 #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" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "field_patronymic" => "Александрович" "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 => "*" ] } 1 => App\Models\Term {#1099 #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" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1101 #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" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #original: array:12 [ "id" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #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 {#1102 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Term {#1104 #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" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #original: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #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 {#1105 #items: array:1 [ 0 => App\Models\Term {#1106 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1107 #items: array:1 [ 0 => App\Models\Term {#1108 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1109 #items: array:1 [ 0 => App\Models\Term {#1110 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #original: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #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_umk" => Illuminate\Database\Eloquent\Collection {#1111 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1112 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1113 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1114 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Term {#1101} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1116 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1117 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1118 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ 0 => App\Models\Term {#1120 #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" => 48 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "фиолетовый" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "fioletovyy" ] #original: array:6 [ "id" => 48 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "фиолетовый" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "fioletovyy" ] #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" => 1646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1072} "field_class" => Illuminate\Database\Eloquent\Collection {#1082} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1076} "field_author" => Illuminate\Database\Eloquent\Collection {#1077} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1102} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1103} "field_country" => Illuminate\Database\Eloquent\Collection {#1105} "field_city" => Illuminate\Database\Eloquent\Collection {#1107} "field_series" => Illuminate\Database\Eloquent\Collection {#1109} "field_umk" => Illuminate\Database\Eloquent\Collection {#1111} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1112} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1113} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1114} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1115} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1116} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1117} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1118} "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1119} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\BookPage {#1127 #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" => 1462304 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_url" => "/8-klass/fizika/artemenkov-zadachnik/page-7" "field_display_title" => "7" "field_folder" => "1" "field_image_name" => "7" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1129 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Book {#1080} ] #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 {#1131 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1141 #items: array:1 [ 0 => App\Models\Element {#1140 #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" => 1753865 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ 0 => App\Models\Edition {#1084} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1462304" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_08/artemenkov-zd/0-1/7-1.webp?ts=1760705527" ] ] ] #original: array:6 [ "id" => 1753865 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1142} "book_page" => array:2 [ "refs" => "1462304" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_08/artemenkov-zd/0-1/7-1.webp?ts=1760705527" ] ] ] #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" => "1462305" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1462303" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1226 #items: array:6 [ 0 => App\Models\Task {#1238 #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" => 1460083 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "6" "field_page_end" => "7" "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-31" "field_display_title" => "1.31" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1239 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1240 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1241 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1242 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1244 #items: array:2 [ 0 => App\Models\Element {#1253 …30} 1 => App\Models\Element {#1255 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460084" "type" => "task" ] "previous" => array:2 [ "refs" => "1460082" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1250 #items: array:1 [ 0 => App\Models\Book {#1080} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462303" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460083 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "6" "field_page_end" => "7" "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-31" "field_display_title" => "1.31" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1239} "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 {#1240} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1241} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1242} "content" => Illuminate\Database\Eloquent\Collection {#1244} "next" => array:2 [ "refs" => "1460084" "type" => "task" ] "previous" => array:2 [ "refs" => "1460082" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1250} "page" => array:2 [ "refs" => "1462303" "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 => "*" ] } 1 => App\Models\Task {#1245 #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" => 1460084 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-32" "field_display_title" => "1.32" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1252 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1248 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1246 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1247 #items: array:2 [ 0 => App\Models\Element {#1265 …30} 1 => App\Models\Element {#1267 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460085" "type" => "task" ] "previous" => array:2 [ "refs" => "1460083" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1262 #items: array:1 [ 0 => App\Models\Book {#1080} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462304" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460084 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-32" "field_display_title" => "1.32" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1243} "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 {#1252} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1248} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1246} "content" => Illuminate\Database\Eloquent\Collection {#1247} "next" => array:2 [ "refs" => "1460085" "type" => "task" ] "previous" => array:2 [ "refs" => "1460083" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1262} "page" => array:2 [ "refs" => "1462304" "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 => "*" ] } 2 => App\Models\Task {#1257 #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" => 1460085 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-33" "field_display_title" => "1.33" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1249 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1264 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1260 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1258 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1259 #items: array:2 [ 0 => App\Models\Element {#1277 …30} 1 => App\Models\Element {#1279 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460086" "type" => "task" ] "previous" => array:2 [ "refs" => "1460084" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1274 #items: array:1 [ 0 => App\Models\Book {#1080} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462304" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460085 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-33" "field_display_title" => "1.33" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1249} "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 {#1264} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1260} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1258} "content" => Illuminate\Database\Eloquent\Collection {#1259} "next" => array:2 [ "refs" => "1460086" "type" => "task" ] "previous" => array:2 [ "refs" => "1460084" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1274} "page" => array:2 [ "refs" => "1462304" "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 => "*" ] } 3 => App\Models\Task {#1269 #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" => 1460086 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-34" "field_display_title" => "1.34" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1261 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1276 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1272 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1270 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1271 #items: array:2 [ 0 => App\Models\Element {#1289 …30} 1 => App\Models\Element {#1291 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460087" "type" => "task" ] "previous" => array:2 [ "refs" => "1460085" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1286 #items: array:1 [ 0 => App\Models\Book {#1080} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462304" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460086 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-34" "field_display_title" => "1.34" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1261} "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 {#1276} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1272} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1270} "content" => Illuminate\Database\Eloquent\Collection {#1271} "next" => array:2 [ "refs" => "1460087" "type" => "task" ] "previous" => array:2 [ "refs" => "1460085" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1286} "page" => array:2 [ "refs" => "1462304" "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 => App\Models\Task {#1281 #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" => 1460087 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-35" "field_display_title" => "1.35" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1273 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1288 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1284 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1282 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1285 #items: array:2 [ 0 => App\Models\Element {#1083} 1 => App\Models\Element {#1090} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460088" "type" => "task" ] "previous" => array:2 [ "refs" => "1460086" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1283 #items: array:1 [ 0 => App\Models\Book {#1080} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462304" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460087 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-35" "field_display_title" => "1.35" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1273} "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 {#1288} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1284} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1282} "content" => Illuminate\Database\Eloquent\Collection {#1285} "next" => array:2 [ "refs" => "1460088" "type" => "task" ] "previous" => array:2 [ "refs" => "1460086" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1283} "page" => array:2 [ "refs" => "1462304" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1293 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1460088 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-36" "field_display_title" => "1.36" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1294 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1295 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1296 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1297 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1299 #items: array:2 [ 0 => App\Models\Element {#1308 …30} 1 => App\Models\Element {#1310 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460089" "type" => "task" ] "previous" => array:2 [ "refs" => "1460087" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1305 #items: array:1 [ 0 => App\Models\Book {#1080} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462304" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460088 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/01-36" "field_display_title" => "1.36" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1294} "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 {#1295} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1296} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1297} "content" => Illuminate\Database\Eloquent\Collection {#1299} "next" => array:2 [ "refs" => "1460089" "type" => "task" ] "previous" => array:2 [ "refs" => "1460087" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1305} "page" => array:2 [ "refs" => "1462304" "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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1462304 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "7" "field_url" => "/8-klass/fizika/artemenkov-zadachnik/page-7" "field_display_title" => "7" "field_folder" => "1" "field_image_name" => "7" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1129} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1130} "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 {#1131} "content" => Illuminate\Database\Eloquent\Collection {#1141} "next" => array:2 [ "refs" => "1462305" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1462303" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1226} ] #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" => 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№1.35 (с. 7)
Условие. №1.35 (с. 7)
скриншот условия
1.35 Вещество массой $m_1$ и температурой $t_1$ смешали с тем же веществом массой $m_2$ и температурой $t_2$. Выведите общую формулу для определения температуры смеси.
Решение. №1.35 (с. 7)
Дано:
Масса первого количества вещества: $m_1$
Температура первого количества вещества: $t_1$
Масса второго количества вещества: $m_2$
Температура второго количества вещества: $t_2$
Вещество одно и то же, следовательно, его удельная теплоемкость $\text{c}$ одинакова для обеих порций.
Данные в задаче представлены в общем виде. В системе СИ:
Масса $\text{m}$ измеряется в килограммах (кг).
Температура $\text{t}$ измеряется в Кельвинах (К). Формула также будет верна для градусов Цельсия (°C), так как является линейной относительно температур.
Найти:
Общую формулу для определения температуры смеси $\text{t}$.
Решение:
При смешивании двух порций вещества с разными температурами происходит теплообмен. Та порция вещества, которая имеет более высокую температуру, отдает тепло, а та, у которой температура ниже, — получает. Этот процесс продолжается до тех пор, пока система не придет в состояние теплового равновесия, то есть пока температура всей смеси не станет одинаковой. Обозначим эту конечную температуру как $\text{t}$.
Будем считать систему теплоизолированной, то есть теплообмен с окружающей средой отсутствует. В этом случае выполняется закон сохранения энергии, который для тепловых процессов формулируется как уравнение теплового баланса: количество теплоты, отданное более горячим телом ($Q_{отданное}$), равно количеству теплоты, полученному более холодным телом ($Q_{полученное}$).
$Q_{отданное} = Q_{полученное}$
Для определенности предположим, что $t_1 > t_2$. Тогда первая порция вещества будет остывать до температуры $\text{t}$, а вторая — нагреваться до той же температуры $\text{t}$. Конечная температура смеси будет находиться в интервале $t_2 < t < t_1$.
Количество теплоты, которое отдаст первая порция вещества, определяется по формуле: $Q_{отданное} = c \cdot m_1 \cdot (t_1 - t)$
Количество теплоты, которое получит вторая порция вещества: $Q_{полученное} = c \cdot m_2 \cdot (t - t_2)$
Теперь составим уравнение теплового баланса, приравняв отданное и полученное количество теплоты: $c \cdot m_1 \cdot (t_1 - t) = c \cdot m_2 \cdot (t - t_2)$
Так как вещество одно и то же, его удельная теплоемкость $\text{c}$ в левой и правой частях уравнения одинакова. Мы можем сократить ее: $m_1 \cdot (t_1 - t) = m_2 \cdot (t - t_2)$
Теперь необходимо решить это уравнение относительно конечной температуры $\text{t}$. Для этого сначала раскроем скобки: $m_1 t_1 - m_1 t = m_2 t - m_2 t_2$
Перенесем все слагаемые, содержащие искомую температуру $\text{t}$, в одну часть уравнения, а остальные слагаемые — в другую: $m_1 t_1 + m_2 t_2 = m_1 t + m_2 t$
В правой части вынесем $\text{t}$ за скобки: $m_1 t_1 + m_2 t_2 = t(m_1 + m_2)$
Наконец, выразим конечную температуру смеси $\text{t}$: $t = \frac{m_1 t_1 + m_2 t_2}{m_1 + m_2}$
Полученная формула является общей и не зависит от того, какая из начальных температур была выше. Она показывает, что конечная температура смеси является средневзвешенным значением начальных температур, где в качестве весов выступают массы.
Ответ: $t = \frac{m_1 t_1 + m_2 t_2}{m_1 + m_2}$
Другие задания:
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