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Консультация № 180946
26.11.2010, 01:25
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу Вас ответить на следующий вопрос:
Азот, находящийся в некотором начальном состоянии, сжимают до объема в 10 раз меньше начального. Сжатие производят в одном случае изотермически, в другом – адиабатически. При каком процессе и во сколько раз работа, затраченная на сжатие будет больше? Построить график.
Азот, находящийся в некотором начальном состоянии, сжимают до объема в 10 раз меньше начального. Сжатие производят в одном случае изотермически, в другом – адиабатически. При каком процессе и во сколько раз работа, затраченная на сжатие будет больше? Построить график.
Обсуждение
Неизвестный
26.11.2010, 02:22
общий
это ответ
Здравствуйте, Иван Петрович!
Решение выглядит примерно так:
1) pV = p1V1.
2) pV^Y = p1V1^Y.
Y = (i + 2) / i = 1.4.
1. dA1 = −p • dV. A1 = ∫[V1; V2] (−p • dV).
p = p1V1 / V. A1 = ∫[V1; V2] (−p1V1 • dV / V) = p1V1(ln V1 − ln V2) = p1V1ln (V1 / V2).
2. A2 = ∫[V1; V2] (−pV • dV). p = p1V1^Y / V^Y.
A2 = ∫[V1; V2] (−p1V1^Y • dV / V^Y).
A2 = p1V1^Y [ (1 / (1 − Y)) (V1(1− Y) − V2(1 − Y))].
A2 = p1V1 (1 − (V1 / V2)(Y − 1)) / (1 − Y).
A2 / A1 = [1 − (V1 / V2)(Y − 1)] / [ (1 − Y) ln (V2 / V1) ] = (10(1.4 − 1) − 1) / [(1 − 1.4) ln (1 / 10)] = 1,64 раза
А вот с графиком сложнее сканера нет под рукой ((
Решение выглядит примерно так:
1) pV = p1V1.
2) pV^Y = p1V1^Y.
Y = (i + 2) / i = 1.4.
1. dA1 = −p • dV. A1 = ∫[V1; V2] (−p • dV).
p = p1V1 / V. A1 = ∫[V1; V2] (−p1V1 • dV / V) = p1V1(ln V1 − ln V2) = p1V1ln (V1 / V2).
2. A2 = ∫[V1; V2] (−pV • dV). p = p1V1^Y / V^Y.
A2 = ∫[V1; V2] (−p1V1^Y • dV / V^Y).
A2 = p1V1^Y [ (1 / (1 − Y)) (V1(1− Y) − V2(1 − Y))].
A2 = p1V1 (1 − (V1 / V2)(Y − 1)) / (1 − Y).
A2 / A1 = [1 − (V1 / V2)(Y − 1)] / [ (1 − Y) ln (V2 / V1) ] = (10(1.4 − 1) − 1) / [(1 − 1.4) ln (1 / 10)] = 1,64 раза
А вот с графиком сложнее сканера нет под рукой ((
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