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Задать вопрос экспертам

Консультация № 174798

02.12.2009, 23:31

0.00 руб.

0 1 1

Образование

Решите пожалуйста задачу: Один моль идеального газа, молярная теплоемкость которого при постоянном давлении C_p=30 Дж/моль[$149$]К, совершает процесс по закону Р=Р₀+а/V, где ро=10⁵ Па и а=1000 м3. Найти сообщенное газу тепло при его расширении от V₁=2л до V₂=3л

Обсуждение

давно

Roman Chaplinsky / Химик CH

Модератор
156417
2175

03.12.2009, 01:14

общий

это ответ

Здравствуйте, Андронов Сергей Филипович.
Первый закон термодинамики Q=A+[$916$]U
Работа является интегралом давления по изменению объёма
A=_V1^V2[$8747$]p dV=_V1^V2[$8747$]p₀+a/V dV=(V₂-V₁)p₀+a*ln(V₂/V₁)
размерность величины а должна быть не м³, а Па*м³=Дж, иначе величины не сходятся
А=0,001м[sup]3[/sup]*10⁵Па+1000Дж*ln(3/2)=505 Дж

Для определения изменения внтренней энергии потребутся найти изменение температуры
[$916$]T=T₂-T₁=(p₂V₂-p₁V₁)/Rn=((p₀+a/V₂)V₂-(p₀+a/V₁)V₁)/Rn=(p₀V₂+a-p₀V₁-a)/Rn=(V₂-V₁)p₀/Rn
Изменение внутренней энергии
[$916$]U=C_Vn[$916$]T=(C_p-R)n*(V₂-V₁)p₀/Rn=(C_p-R)*(V₂-V₁)p₀/R=
=(30-8,314 Дж/(моль*К))*(0,003-0,002 м[sup]3[/sup])*10⁵Па/8,314 Дж/(моль*К)=261 Дж

Q=A+[$916$]U=766 Дж

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