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Консультация № 191877
24.11.2017, 17:06
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Газ расширяется от давления p1 = 2kПа до давления p1 =1кПа по за-
кону p1 = a -bV, где a -const, b =0,5 кПа/м . Найдите работу, совершае-
мую газом при таком расширении
Газ расширяется от давления p1 = 2kПа до давления p1 =1кПа по за-
кону p1 = a -bV, где a -const, b =0,5 кПа/м . Найдите работу, совершае-
мую газом при таком расширении
Обсуждение
24.11.2017, 21:26
общий
24.11.2017, 21:26
Адресаты:
Вероятно, что размерность коэффициента b должна быть кПа/м^3, так?
Об авторе:
С уважением
shvetski
С уважением
shvetski
25.11.2017, 23:12
общий
это ответ
Здравствуйте, KSIW2S!
Дано:
p1=2 кПа
р2=1 кПа
p(V)=a-bV
а-const
b=0.5 кПа/м3
Найти: А
Решение:
Газ расширяется по линейному закону.
Построим график функции p(V).
Работу газа можно найти как площадь трапеции в пределах от V1 до V2 (фиолетовая область) (см. рис.)
[img]
[/img]
Тогда работа газа будет равна
A=(1/2)*(p1+p2)*(V2-V1) (*)
Переместим ось ординат в точку V1 (точечный пунктир) - площадь трапеции от этого не изменится и при этом окажется, что
V1=0
a=p1=2 кПа
Тогда, из уравнения p(V)
V2=(a-p2)/b = (2-1)/0.5 = 2 м3
Тогда, согласно формулe (*)
A = (1/2)*(1+2)*(2-0) = 3 кДж
Удачи
Дано:
p1=2 кПа
р2=1 кПа
p(V)=a-bV
а-const
b=0.5 кПа/м3
Найти: А
Решение:
Газ расширяется по линейному закону.
Построим график функции p(V).
Работу газа можно найти как площадь трапеции в пределах от V1 до V2 (фиолетовая область) (см. рис.)
[img]
Тогда работа газа будет равна
A=(1/2)*(p1+p2)*(V2-V1) (*)
Переместим ось ординат в точку V1 (точечный пунктир) - площадь трапеции от этого не изменится и при этом окажется, что
V1=0
a=p1=2 кПа
Тогда, из уравнения p(V)
V2=(a-p2)/b = (2-1)/0.5 = 2 м3
Тогда, согласно формулe (*)
A = (1/2)*(1+2)*(2-0) = 3 кДж
Удачи
Об авторе:
С уважением
shvetski
С уважением
shvetski
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