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Консультация № 146338
07.10.2008, 15:55
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При каком процессе выгоднее производить нагревание 2 молей аргона на 100 К: а) изобарическом; б) изохорическом.
Обсуждение
Неизвестный
08.10.2008, 17:24
общий
это ответ
Здравствуйте, Жаскенов Данияр Джамбулатович!
В обоих случаях выполняется 1-ое начало термодинамики, которое гласит, что количество теплоты Q, подведенное газу, равно сумме работы A, совершенной газом и приращения ΔU его внутренней энергии:
Q=ΔU+A (1)
Изменение внутренней энергии для двухатомного (каковым является аргон) газа дается формулой:
ΔU=5*p*ΔV/2 или ΔU=5*ν*R*ΔT/2 (2)
где ν=2 моля - количество вещества газа, ΔV - изменение объёма, ΔT - температуры, р - давление газа, R=8,31 Дж/(К*моль)
В случае изобарического процесса выражение для работы газа выглядит как:
A=p*ΔV=v*R*ΔT (3)
Подставляя (3) и 2-ой вариант (2) в (1) получаем:
Q изобар =7*v*R*ΔT/2=7*2*8,31*100/2=5817 Дж
В случае изохорического процесса объём газа постоянен -> работа газа А=0 и в выражении (1) для количества теплоты будет только изменение внутренней энергии, получаем:
Q изохор =5*v*R*ΔT/2=5*2*8,31*100/2=4155 Дж
Как видите Q изохор <Q изобар за счет того, что в ходе изохорического процесса вся теплота, сообщаемая газу, идёт на его нагревание, значит выгоднее нагревать газ изохорически
В обоих случаях выполняется 1-ое начало термодинамики, которое гласит, что количество теплоты Q, подведенное газу, равно сумме работы A, совершенной газом и приращения ΔU его внутренней энергии:
Q=ΔU+A (1)
Изменение внутренней энергии для двухатомного (каковым является аргон) газа дается формулой:
ΔU=5*p*ΔV/2 или ΔU=5*ν*R*ΔT/2 (2)
где ν=2 моля - количество вещества газа, ΔV - изменение объёма, ΔT - температуры, р - давление газа, R=8,31 Дж/(К*моль)
В случае изобарического процесса выражение для работы газа выглядит как:
A=p*ΔV=v*R*ΔT (3)
Подставляя (3) и 2-ой вариант (2) в (1) получаем:
Q изобар =7*v*R*ΔT/2=7*2*8,31*100/2=5817 Дж
В случае изохорического процесса объём газа постоянен -> работа газа А=0 и в выражении (1) для количества теплоты будет только изменение внутренней энергии, получаем:
Q изохор =5*v*R*ΔT/2=5*2*8,31*100/2=4155 Дж
Как видите Q изохор <Q изобар за счет того, что в ходе изохорического процесса вся теплота, сообщаемая газу, идёт на его нагревание, значит выгоднее нагревать газ изохорически
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