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Консультация № 192132
15.12.2017, 18:45
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Газообразный гелий находится в цилиндре под подвижным поршнем. Газ расширяется в процессе 1 – 2, когда его давление p прямо пропорционально объёму V (рис. 29). Затем газ расширяется в адиабатическом процессе 2 – 3, совершая работу A23. Наконец газ сжимается в изотермическом процессе 3 – 1, при этом от него отводится количество теплоты Q31(Q31 > 0). Какую работу совершил газ во всём замкнутом цикле 1 – 2 – 3 – 1?
Газообразный гелий находится в цилиндре под подвижным поршнем. Газ расширяется в процессе 1 – 2, когда его давление p прямо пропорционально объёму V (рис. 29). Затем газ расширяется в адиабатическом процессе 2 – 3, совершая работу A23. Наконец газ сжимается в изотермическом процессе 3 – 1, при этом от него отводится количество теплоты Q31(Q31 > 0). Какую работу совершил газ во всём замкнутом цикле 1 – 2 – 3 – 1?
Обсуждение
16.12.2017, 11:06
общий
это ответ
Здравствуйте, Zarefo10!
Работа на участке 1-2 равна площади под трапецией, которая может быть посчитана как разность площадей треугольников:
A12 = (p2V2 - p1V1)/2. (1)
На участке 2-3 работа, совершаемая газом, равна уменьшению его внутренней энергии U. Для идеального одноатомного газа
U = (3/2)nRT, следовательно
A23 = (3/2)nR(T2 - T3) = (3/2)(p2V2 - p3V3), (2)
где n - число молей.
На учаске 3-1 температура, а, следовательно, и внктренняя энергия, постоянны, поэтому
A31 = - Q31. (3)
Так как p1V1 = p3V3, формула (2) может быть переписана в виде
A23 = (3/2)(p2V2 - p1V1). (4)
Сравнивая (1) и (4), находим
A12 = (1/3)A23.
Работа за цикл равна сумме работ:
A12 + A23 + A31 = (1/3)A23 + A23 - Q31 = (4/3)A23 - Q31.
Работа на участке 1-2 равна площади под трапецией, которая может быть посчитана как разность площадей треугольников:
A12 = (p2V2 - p1V1)/2. (1)
На участке 2-3 работа, совершаемая газом, равна уменьшению его внутренней энергии U. Для идеального одноатомного газа
U = (3/2)nRT, следовательно
A23 = (3/2)nR(T2 - T3) = (3/2)(p2V2 - p3V3), (2)
где n - число молей.
На учаске 3-1 температура, а, следовательно, и внктренняя энергия, постоянны, поэтому
A31 = - Q31. (3)
Так как p1V1 = p3V3, формула (2) может быть переписана в виде
A23 = (3/2)(p2V2 - p1V1). (4)
Сравнивая (1) и (4), находим
A12 = (1/3)A23.
Работа за цикл равна сумме работ:
A12 + A23 + A31 = (1/3)A23 + A23 - Q31 = (4/3)A23 - Q31.
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