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Q.

An ideal gas expands isothermally from a volume $V_{1}$ to $V_{2}$ and then compressed to original volume $V_{1}$ adiabatically. Initial pressure is $P_{1}$ and final pressure is $P_{3}$ . The total work done is W. Then

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a

$P_{3} > P_{1}, W > 0$

b

$P_{3} < P_{1}, W < 0$

c

$P_{3} > P_{1}, W < 0$

d

$P_{3} = P_{1}, W = 0$

answer is C.

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Detailed Solution

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$W = W_{i} + (- W_{A})$ $∵ W_{A} > W_{i} \Rightarrow W < 0$

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An ideal gas expands isothermally from a volume V1 to V2 and then compressed to original volume V1 adiabatically. Initial pressure is P1 and final pressure is P3 . The total work done is W. Then