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Номер 96, страница 69 - гдз по физике 7-9 класс сборник задач Московкина, Волков
Авторы: Московкина Е. Г., Волков В. А.
Тип: Сборник задач
Издательство: ВАКО
Год издания: 2011 - 2026
Цвет обложки: синий
ISBN: 978-5-408-00459-1
Популярные ГДЗ в 7 классе
8 класс. Плавление, кристаллизация - номер 96, страница 69.
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" => 1425390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-96" "field_display_title" => "96" "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" => 1424779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "8 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "59" "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" => 4994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1049 #items: array:2 [ …2] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #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" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "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" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 556 "class_subject" => 491 ] ] #original: array:50 [ "id" => 4994 "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 {#1047} "field_author" => Illuminate\Database\Eloquent\Collection {#1049} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053} "field_country" => Illuminate\Database\Eloquent\Collection {#1055} "field_city" => Illuminate\Database\Eloquent\Collection {#1057} "field_series" => Illuminate\Database\Eloquent\Collection {#1059} "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" => null "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" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "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" => "/7-klass/fizika/moskovkina-sbornik-zadach" "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" => 378 "subject" => 556 "class_subject" => 491 ] ] #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" => 1424779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "8 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "59" "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 {#1108 #items: array:2 [ 0 => App\Models\Branch {#1116 #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" => 1424779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "8 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1117 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "59" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1150 #items: array:1 [ 0 => App\Models\Book {#1118 #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" => 4994 "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 {#1120 #items: array:1 [ 0 => App\Models\Term {#1119 #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 {#1121 #items: array:3 [ 0 => App\Models\Term {#1122 #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" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ "field_accusative_case" => "седьмой" "field_creative_case" => "седьмым" "field_dative_case" => "седьмому" "field_genitive_case" => "седьмого" "field_nominative_case" => "седьмой" "field_prepositional_case" => "седьмом" ] "field_translit" => "sedmoj" ] #original: array:6 [ "id" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ "field_accusative_case" => "седьмой" "field_creative_case" => "седьмым" "field_dative_case" => "седьмому" "field_genitive_case" => "седьмого" "field_nominative_case" => "седьмой" "field_prepositional_case" => "седьмом" ] "field_translit" => "sedmoj" ] #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 {#1123 #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 => "*" ] } 2 => App\Models\Term {#1124 #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" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #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 {#1125 #items: array:1 [ 0 => App\Models\Term {#1126 #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" => 5227 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ВАКО" "field_cases" => null "field_translit" => "vako" ] #original: array:6 [ "id" => 5227 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ВАКО" "field_cases" => null "field_translit" => "vako" ] #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 {#1127 #items: array:2 [ 0 => App\Models\Term {#1128 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5285 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Московкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Елена" "field_patronymic" => "Геннадьевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5285 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Московкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Елена" "field_patronymic" => "Геннадьевна" "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 {#1129 #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" => 4026 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Волков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4026 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Волков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Анатольевич" "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 {#1130 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:1 [ 0 => App\Models\Term {#1132 #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" => 6598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Сборник задач" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "сборник задач" "field_creative_case" => "сборником задач" "field_dative_case" => "сборнику задач" "field_genitive_case" => "сборника задач" "field_nominative_case" => "сборник задач" "field_prepositional_case" => "сборнике задач" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "sbornik zadach" ] #original: array:10 [ "id" => 6598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Сборник задач" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "сборник задач" "field_creative_case" => "сборником задач" "field_dative_case" => "сборнику задач" "field_genitive_case" => "сборника задач" "field_nominative_case" => "сборник задач" "field_prepositional_case" => "сборнике задач" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "sbornik zadach" ] #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 {#1133 #items: array:1 [ 0 => App\Models\Term {#1134 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1135 #items: array:1 [ 0 => App\Models\Term {#1136 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 …1 ] "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 {#1137 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1138 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1139 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1140 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1141 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" "alt" => "" "width" => "1466" "height" => "2407" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1143 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Term {#1147 #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" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #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" => 378 "subject" => 556 "class_subject" => 491 ] ] #original: array:50 [ "id" => 4994 "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 {#1120} "field_class" => Illuminate\Database\Eloquent\Collection {#1121} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125} "field_author" => Illuminate\Database\Eloquent\Collection {#1127} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1130} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1131} "field_country" => Illuminate\Database\Eloquent\Collection {#1133} "field_city" => Illuminate\Database\Eloquent\Collection {#1135} "field_series" => Illuminate\Database\Eloquent\Collection {#1137} "field_umk" => Illuminate\Database\Eloquent\Collection {#1138} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1139} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1140} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1141} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" "alt" => "" "width" => "1466" "height" => "2407" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1143} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145} "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 556 "class_subject" => 491 ] ] #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 {#1148 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1424779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "8 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1117} "field_page_start" => "59" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1150} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1149 #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" => 1424783 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Плавление, кристаллизация" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "67" "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 {#1152 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1424783 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Плавление, кристаллизация" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151} "field_page_start" => "67" "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 {#1152} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153} ] #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 {#1071 #items: array:2 [ 0 => App\Models\Element {#1099 #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" => 1677923 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Edition {#1098 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6044 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ …1] #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 {#1095 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6044 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096} "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 {#1095} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1425390" "type" => "task" ] "text" => "<p><strong>96.</strong> При морозе $-10\ ^\circ\text{C}$ каждый квадратный метр поверхности пруда отдает находящемуся над ним воздуху $180\ \text{кДж}$ тепла в час. Какова будет толщина образовавшегося за сутки ледяного покрова, если температура воды у поверхности пруда $0\ ^\circ\text{C}$?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "96-1.jpg" "alt" => null "width" => "2609" "height" => 669 "path" => "/media/fizika_07/moskovkina-sz/0-8/96-1.webp?ts=1758885689" ] ] ] #original: array:7 [ "id" => 1677923 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091} "task" => array:2 [ "refs" => "1425390" "type" => "task" ] "text" => "<p><strong>96.</strong> При морозе $-10\ ^\circ\text{C}$ каждый квадратный метр поверхности пруда отдает находящемуся над ним воздуху $180\ \text{кДж}$ тепла в час. Какова будет толщина образовавшегося за сутки ледяного покрова, если температура воды у поверхности пруда $0\ ^\circ\text{C}$?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "96-1.jpg" "alt" => null "width" => "2609" "height" => 669 "path" => "/media/fizika_07/moskovkina-sz/0-8/96-1.webp?ts=1758885689" ] ] ] #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" => 1781771 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083 #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" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ …1] #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 {#1087 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089} "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 {#1087} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086} "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" => "1425390" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Удельная теплоотдача с поверхности пруда, $q = 180 \frac{\text{кДж}}{\text{м}^2 \cdot \text{ч}}$</p><p>Время, $t = 1 \text{ сутки}$</p><p>Удельная теплота плавления льда, $\lambda = 3.3 \cdot 10^5 \frac{\text{Дж}}{\text{кг}}$ (справочное значение)</p><p>Плотность льда, $\\rho= 900 \frac{\text{кг}}{\text{м}^3}$ (справочное значение)</p><p><em>Перевод данных в систему СИ:</em></p><p>$q = 180 \frac{\text{кДж}}{\text{м}^2 \cdot \text{ч}} = \frac{180 \cdot 1000 \text{ Дж}}{3600 \text{ с} \cdot 1 \text{ м}^2} = 50 \frac{\text{Дж}}{\text{с} \cdot \text{м}^2}$</p><p>$t = 1 \text{ сутки} = 24 \text{ часа} = 24 \cdot 3600 \text{ с} = 86400 \text{ с}$</p><p><strong>Найти:</strong></p><p>Толщину ледяного покрова, $\text{h}$.</p><p><strong>Решение:</strong></p><p>Образование ледяного покрова происходит за счет того, что вода на поверхности пруда, имеющая температуру 0 °С, отдает тепло в окружающий морозный воздух и кристаллизуется. Температура воздуха (-10 °С) обуславливает процесс теплоотдачи, но для расчёта используется уже заданная величина теплового потока. Вся отдаваемая теплота идет на фазовый переход (замерзание).</p><p><strong>1.</strong> Найдем общее количество теплоты $\text{Q}$, которое отдаст каждый квадратный метр ($S = 1 \text{ м}^2$) поверхности пруда за время $\text{t}$.</p><p>$Q = q \cdot S \cdot t$</p><p><strong>2.</strong> Это количество теплоты выделяется при кристаллизации массы воды $\text{m}$. Оно рассчитывается по формуле:</p><p>$Q = \lambda \cdot m$</p><p>где $\lambda$ — удельная теплота кристаллизации (плавления) льда.</p><p><strong>3.</strong> Массу образовавшегося льда $\text{m}$ можно выразить через его плотность $\rho$ и объём $\text{V}$. Объём, в свою очередь, выражается через площадь $\text{S}$ и искомую толщину $\text{h}$:</p><p>$m = \\rho\cdot V = \\rho\cdot S \cdot h$</p><p><strong>4.</strong> Приравняем выражения для количества теплоты (из п.1 и п.2) и подставим выражение для массы (из п.3):</p><p>$q \cdot S \cdot t = \lambda \cdot (\\rho\cdot S \cdot h)$</p><p>Сократив площадь $\text{S}$ в обеих частях уравнения, получим формулу для вычисления толщины льда $\text{h}$:</p><p>$h = \frac{q \cdot t}{\lambda \cdot \rho}$</p><p><strong>5.</strong> Подставим значения величин в системе СИ и произведем расчет:</p><p>$h = \frac{50 \frac{\text{Дж}}{\text{с} \cdot \text{м}^2} \cdot 86400 \text{ с}}{3.3 \cdot 10^5 \frac{\text{Дж}}{\text{кг}} \cdot 900 \frac{\text{кг}}{\text{м}^3}} = \frac{4320000}{297000000} \text{ м} \approx 0.014545... \text{ м}$</p><p><strong>6.</strong> Переведем полученное значение в сантиметры и округлим:</p><p>$h \approx 0.0145 \text{ м} = 1.45 \text{ см}$</p><p><strong>Ответ:</strong> толщина образовавшегося за сутки ледяного покрова составит примерно 1.45 см.</p>" ] #original: array:6 [ "id" => 1781771 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083} "task" => array:2 [ "refs" => "1425390" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Удельная теплоотдача с поверхности пруда, $q = 180 \frac{\text{кДж}}{\text{м}^2 \cdot \text{ч}}$</p><p>Время, $t = 1 \text{ сутки}$</p><p>Удельная теплота плавления льда, $\lambda = 3.3 \cdot 10^5 \frac{\text{Дж}}{\text{кг}}$ (справочное значение)</p><p>Плотность льда, $\\rho= 900 \frac{\text{кг}}{\text{м}^3}$ (справочное значение)</p><p><em>Перевод данных в систему СИ:</em></p><p>$q = 180 \frac{\text{кДж}}{\text{м}^2 \cdot \text{ч}} = \frac{180 \cdot 1000 \text{ Дж}}{3600 \text{ с} \cdot 1 \text{ м}^2} = 50 \frac{\text{Дж}}{\text{с} \cdot \text{м}^2}$</p><p>$t = 1 \text{ сутки} = 24 \text{ часа} = 24 \cdot 3600 \text{ с} = 86400 \text{ с}$</p><p><strong>Найти:</strong></p><p>Толщину ледяного покрова, $\text{h}$.</p><p><strong>Решение:</strong></p><p>Образование ледяного покрова происходит за счет того, что вода на поверхности пруда, имеющая температуру 0 °С, отдает тепло в окружающий морозный воздух и кристаллизуется. Температура воздуха (-10 °С) обуславливает процесс теплоотдачи, но для расчёта используется уже заданная величина теплового потока. Вся отдаваемая теплота идет на фазовый переход (замерзание).</p><p><strong>1.</strong> Найдем общее количество теплоты $\text{Q}$, которое отдаст каждый квадратный метр ($S = 1 \text{ м}^2$) поверхности пруда за время $\text{t}$.</p><p>$Q = q \cdot S \cdot t$</p><p><strong>2.</strong> Это количество теплоты выделяется при кристаллизации массы воды $\text{m}$. Оно рассчитывается по формуле:</p><p>$Q = \lambda \cdot m$</p><p>где $\lambda$ — удельная теплота кристаллизации (плавления) льда.</p><p><strong>3.</strong> Массу образовавшегося льда $\text{m}$ можно выразить через его плотность $\rho$ и объём $\text{V}$. Объём, в свою очередь, выражается через площадь $\text{S}$ и искомую толщину $\text{h}$:</p><p>$m = \\rho\cdot V = \\rho\cdot S \cdot h$</p><p><strong>4.</strong> Приравняем выражения для количества теплоты (из п.1 и п.2) и подставим выражение для массы (из п.3):</p><p>$q \cdot S \cdot t = \lambda \cdot (\\rho\cdot S \cdot h)$</p><p>Сократив площадь $\text{S}$ в обеих частях уравнения, получим формулу для вычисления толщины льда $\text{h}$:</p><p>$h = \frac{q \cdot t}{\lambda \cdot \rho}$</p><p><strong>5.</strong> Подставим значения величин в системе СИ и произведем расчет:</p><p>$h = \frac{50 \frac{\text{Дж}}{\text{с} \cdot \text{м}^2} \cdot 86400 \text{ с}}{3.3 \cdot 10^5 \frac{\text{Дж}}{\text{кг}} \cdot 900 \frac{\text{кг}}{\text{м}^3}} = \frac{4320000}{297000000} \text{ м} \approx 0.014545... \text{ м}$</p><p><strong>6.</strong> Переведем полученное значение в сантиметры и округлим:</p><p>$h \approx 0.0145 \text{ м} = 1.45 \text{ см}$</p><p><strong>Ответ:</strong> толщина образовавшегося за сутки ледяного покрова составит примерно 1.45 см.</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" => "1425391" "type" => "task" ] "previous" => array:2 [ "refs" => "1425389" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\BookPage {#1104 #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" => 1426172 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/page-69" "field_display_title" => "69" "field_folder" => "1" "field_image_name" => "69" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Book {#1118} ] #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 {#1078 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1111 #items: array:1 [ 0 => App\Models\Element {#1115 #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" => 1678704 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1678704 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109 …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" => "1426173" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1426171" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1242 #items: array:9 [ 0 => App\Models\Task {#1258 #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" => 1425386 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => "69" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-92" "field_display_title" => "92" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1259 …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 {#1260 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1261 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1262 …2} "content" => Illuminate\Database\Eloquent\Collection {#1264 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1270 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425386 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => "69" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-92" "field_display_title" => "92" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1259 …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 {#1260 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1261 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1262 …2} "content" => Illuminate\Database\Eloquent\Collection {#1264 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1270 …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 {#1265 #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" => 1425387 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-93" "field_display_title" => "93" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1263 …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 {#1268 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1266 …2} "content" => Illuminate\Database\Eloquent\Collection {#1267 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1282 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425387 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-93" "field_display_title" => "93" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1263 …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 {#1268 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1266 …2} "content" => Illuminate\Database\Eloquent\Collection {#1267 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1282 …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 {#1277 #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" => 1425388 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-94" "field_display_title" => "94" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1269 …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 {#1284 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1280 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1278 …2} "content" => Illuminate\Database\Eloquent\Collection {#1279 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1294 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425388 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-94" "field_display_title" => "94" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1269 …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 {#1284 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1280 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1278 …2} "content" => Illuminate\Database\Eloquent\Collection {#1279 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1294 …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 {#1289 #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" => 1425389 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-95" "field_display_title" => "95" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1281 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1296 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1292 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1290 …2} "content" => Illuminate\Database\Eloquent\Collection {#1291 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1306 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425389 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-95" "field_display_title" => "95" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1281 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1296 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1292 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1290 …2} "content" => Illuminate\Database\Eloquent\Collection {#1291 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1306 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1301 #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" => 1425390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-96" "field_display_title" => "96" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1293 …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 {#1308 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1304 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1302 …2} "content" => Illuminate\Database\Eloquent\Collection {#1305 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1303 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-96" "field_display_title" => "96" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1293 …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 {#1308 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1304 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1302 …2} "content" => Illuminate\Database\Eloquent\Collection {#1305 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1303 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1313 #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" => 1425391 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-97" "field_display_title" => "97" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1314 …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 {#1315 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1316 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1317 …2} "content" => Illuminate\Database\Eloquent\Collection {#1319 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1325 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425391 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-97" "field_display_title" => "97" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1314 …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 {#1315 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1316 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1317 …2} "content" => Illuminate\Database\Eloquent\Collection {#1319 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1325 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Task {#1320 #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" => 1425392 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-98" "field_display_title" => "98" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1318 …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 {#1327 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1323 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1321 …2} "content" => Illuminate\Database\Eloquent\Collection {#1322 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1337 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425392 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-98" "field_display_title" => "98" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1318 …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 {#1327 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1323 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1321 …2} "content" => Illuminate\Database\Eloquent\Collection {#1322 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1337 …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 => "*" ] } 7 => App\Models\Task {#1332 #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" => 1425393 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-99" "field_display_title" => "99" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1324 …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 {#1339 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1335 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1333 …2} "content" => Illuminate\Database\Eloquent\Collection {#1334 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1349 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425393 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-99" "field_display_title" => "99" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1324 …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 {#1339 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1335 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1333 …2} "content" => Illuminate\Database\Eloquent\Collection {#1334 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1349 …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 => "*" ] } 8 => App\Models\Task {#1344 #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" => 1425394 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => "70" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-100" "field_display_title" => "100" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1336 …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 {#1351 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1347 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1345 …2} "content" => Illuminate\Database\Eloquent\Collection {#1346 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1361 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425394 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => "70" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-100" "field_display_title" => "100" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1336 …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 {#1351 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1347 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1345 …2} "content" => Illuminate\Database\Eloquent\Collection {#1346 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1361 …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" => 1426172 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/page-69" "field_display_title" => "69" "field_folder" => "1" "field_image_name" => "69" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1085} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1082} "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 {#1078} "content" => Illuminate\Database\Eloquent\Collection {#1111} "next" => array:2 [ "refs" => "1426173" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1426171" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1242} ] #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" => 1425390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-96" "field_display_title" => "96" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1108} "content" => Illuminate\Database\Eloquent\Collection {#1071} "next" => array:2 [ "refs" => "1425391" "type" => "task" ] "previous" => array:2 [ "refs" => "1425389" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1102} "page" => array:2 [ "refs" => "1426172" "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 => "*" ] }
№96 (с. 69)
Условие. №96 (с. 69)
скриншот условия
96. При морозе $-10\ ^\circ\text{C}$ каждый квадратный метр поверхности пруда отдает находящемуся над ним воздуху $180\ \text{кДж}$ тепла в час. Какова будет толщина образовавшегося за сутки ледяного покрова, если температура воды у поверхности пруда $0\ ^\circ\text{C}$?
Решение. №96 (с. 69)
Дано:
Удельная теплоотдача с поверхности пруда, $q = 180 \frac{\text{кДж}}{\text{м}^2 \cdot \text{ч}}$
Время, $t = 1 \text{ сутки}$
Удельная теплота плавления льда, $\lambda = 3.3 \cdot 10^5 \frac{\text{Дж}}{\text{кг}}$ (справочное значение)
Плотность льда, $\\rho= 900 \frac{\text{кг}}{\text{м}^3}$ (справочное значение)
Перевод данных в систему СИ:
$q = 180 \frac{\text{кДж}}{\text{м}^2 \cdot \text{ч}} = \frac{180 \cdot 1000 \text{ Дж}}{3600 \text{ с} \cdot 1 \text{ м}^2} = 50 \frac{\text{Дж}}{\text{с} \cdot \text{м}^2}$
$t = 1 \text{ сутки} = 24 \text{ часа} = 24 \cdot 3600 \text{ с} = 86400 \text{ с}$
Найти:
Толщину ледяного покрова, $\text{h}$.
Решение:
Образование ледяного покрова происходит за счет того, что вода на поверхности пруда, имеющая температуру 0 °С, отдает тепло в окружающий морозный воздух и кристаллизуется. Температура воздуха (-10 °С) обуславливает процесс теплоотдачи, но для расчёта используется уже заданная величина теплового потока. Вся отдаваемая теплота идет на фазовый переход (замерзание).
1. Найдем общее количество теплоты $\text{Q}$, которое отдаст каждый квадратный метр ($S = 1 \text{ м}^2$) поверхности пруда за время $\text{t}$.
$Q = q \cdot S \cdot t$
2. Это количество теплоты выделяется при кристаллизации массы воды $\text{m}$. Оно рассчитывается по формуле:
$Q = \lambda \cdot m$
где $\lambda$ — удельная теплота кристаллизации (плавления) льда.
3. Массу образовавшегося льда $\text{m}$ можно выразить через его плотность $\rho$ и объём $\text{V}$. Объём, в свою очередь, выражается через площадь $\text{S}$ и искомую толщину $\text{h}$:
$m = \\rho\cdot V = \\rho\cdot S \cdot h$
4. Приравняем выражения для количества теплоты (из п.1 и п.2) и подставим выражение для массы (из п.3):
$q \cdot S \cdot t = \lambda \cdot (\\rho\cdot S \cdot h)$
Сократив площадь $\text{S}$ в обеих частях уравнения, получим формулу для вычисления толщины льда $\text{h}$:
$h = \frac{q \cdot t}{\lambda \cdot \rho}$
5. Подставим значения величин в системе СИ и произведем расчет:
$h = \frac{50 \frac{\text{Дж}}{\text{с} \cdot \text{м}^2} \cdot 86400 \text{ с}}{3.3 \cdot 10^5 \frac{\text{Дж}}{\text{кг}} \cdot 900 \frac{\text{кг}}{\text{м}^3}} = \frac{4320000}{297000000} \text{ м} \approx 0.014545... \text{ м}$
6. Переведем полученное значение в сантиметры и округлим:
$h \approx 0.0145 \text{ м} = 1.45 \text{ см}$
Ответ: толщина образовавшегося за сутки ледяного покрова составит примерно 1.45 см.
Другие задания:
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