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Задать вопрос экспертам

Консультация № 200748

27.04.2021, 17:02

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Образование

Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
В сосуде А, что имеет объем V1 = 3 л, находится газ под давлением р0' = 2 ат. В сосуде В объемом V2 = 4 л находится такой же газ под давлением р0" = 1 ат. Температура в обоих сосудах одинакова. Под каким давлением будет находиться газ, если соединить сосуды А и В трубкой?

Обсуждение

давно

Посетитель
226425
1567

27.04.2021, 18:24

общий

27.04.2021, 18:27

это ответ

Здравствуйте, mojo
Дано:
V₁ = 3 л
р₀' = 2 ат
V₂ = 4 л
р₀" = 1 ат
T₁=T₂
Найти: p
Решение:

1. Согласно закону Дальтона, суммарное давление в сосуде равно сумме давлений, создаваемых каждым компонентом смеси в отдельности:
p=p₁+p₂ (1)
Здесь р₁ и р₂ - давления, которые создавали бы газы из сосудов 1 и 2 соответственно при отсутствии другого газа после открытия клапана (см.рис.).
2. Поскольку температура в сосудах одинакова, теплообмен отсутствует. В отсутствие теплообмена процесс можно считать изотермическим. При этом из закона Бойля-Мариотта следует, что
p₁(V₁+V₂)=p_o`V₁
Отсюда
p₁=p_o`V₁/(V₁+V₂) (2)
Аналогично
p₂=p_o"V₂/(V₁+V₂) (3)
3. Подставим выражения (2) и (3) в (1), получим
p=(p_o`V₁+p_o"V₂)/(V₁+V₂) (4)
подставляем значения в последнюю формулу, получаем
p=(2ат*3л+1ат*4л)/(3+4)л = 10/7 ат
*******
Удачи

Об авторе:
С уважением
shvetski

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