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Задать вопрос экспертам

Консультация № 110278

20.11.2007, 13:20

0.00 руб.

0 1 1

Образование

Помогите пожалуйста с решением задачек. Заране огромное спасибо.

1) При изотермическом расширении газа, занимавшего объём V = 2 м³ , давление его меняется от P1 = 0,5 МПа до P2 = 0,4 МПа. Найти работу, совершенную при этом.

2) Газ расширяется адиабатически, при этом объём его увеличивается вдвое, а температура (абсолютная) падает в 1,32 раза. Какое число степеней свободы имеют молекулы этого газа?

Обсуждение

Неизвестный

20.11.2007, 16:03

общий

22.05.2009, 14:00

это ответ

Здравствуйте, Ivan_petrov!
1)запишем раверноство:
p*V/T=const
т.к. T тоже константа то ее можно исключить, итого получим:
p*V=const
p₁*V₁=p₂*V₂
V₂=p₁*V₁/p₂
работа определяется как интеграл по обьему от давления [$8747$]p dV
найдем зависимость от давления от обьема, для этого воспользуемся уравнением Мендилеева-Клайперона:
p*V=n*R*T
p=n*R*T/V
подставим в интеграл:
A=_{V[size=1]1[/size]}^{V[size=1]2[/size]}[$8747$] n*R*T/V dV=nRT*ln(V₂/V₁)=p₁*V₁*ln(V₂/V₁)=
p₁*V₁*ln((V₂*p₁*V₁)/(V₁*p₂*V₂))=p₁*V₁*ln(p₁/p₂)
итого:
A=p₁*V₁*ln(p₁/p₂)

2)для адиабатного процесса:
T*V^y-1=const
T₁*V₁^y-1=T₂*V₂^y-1
T₁/T₂=(V₂/V₁)^y-1
ln(T₁/T₂)=(y-1)ln(V₂/V₁)
y-1=ln(V₂/V₁) / ln(T₁/T₂)
y=(i+2)/i
yi-i=2
i(y-1)=2
i=2/(y-1)=2/(ln(V₂/V₁) / ln(T₁/T₂))=2*ln(T₁/T₂) / ln(V₂/V₁)

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