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Задать вопрос экспертам

Консультация № 188409

12.12.2015, 14:11

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0 2 1

Образование

Здравствуйте! У меня возникли сложности с таким вопросом:
Расширение 8 молей криптона происходит так, что давление газа увеличивается пропорционально объему. Найти приращение энтропии газа прb увеличении объема в 4 раза.

Обсуждение

давно

Гордиенко Андрей Владимирович

Мастер-Эксперт
17387
18345

12.12.2015, 14:14

общий

Адресаты:

Какие сложности у Вас возникли с этим вопросом?

Об авторе:
Facta loquuntur.

давно

Roman Chaplinsky / Химик CH

Модератор
156417
2175

12.12.2015, 20:03

общий

это ответ

Здравствуйте, 125484848!
Обозначим начальные условия как p₀, V₀, T₀
Удобно ввести координату процесса x=V/V₀
согласно условию, x изменяется от 1 до 4.
Выражаем:
V=xV₀
Согласно условию p=xp₀
При этом температура
T=T₀[$183$]pV/(p₀V₀)=x²T₀

При изменении параметра на dx
совершённая газом работа
dA=pdV=p[$183$]V₀dx=xp₀V₀dx=xR(m/M)T₀dx
изменение внутренней энергии
dU=(3/2)R(m/M)dT=3xR(m/M)T₀dx
полученная теплота
dQ=dA+dU=4xR(m/M)T₀dx
приращение энтропии
dS=dQ/T=4xR(m/M)T₀dx/(x²T₀)=4R(m/M)dx/x
интегрируем
[$916$]S=₁⁴[$8747$]4R(m/M)dx/x=4R(m/M)ln(4/1)=4[$183$]8,314Дж/(моль[$183$]К)[$183$]8моль[$183$]ln4=368,8 Дж/К

5

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