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An ideal gas undergoes isothermal expansion from volume V1 to V2 (V2 > V1) starting at pressure P1. It is then compressed adiabatically back to its original volume V1, reaching a final pressure P3. The net work done on/by the gas in the complete cycle is W. Which of the following is correct?

1. (A) P3 > P1, W > 0
2. (B) P3 < P1, W < 0
3. (C) P3 > P1, W < 0
4. (D) P3 = P1, W = 0

Correct answer: (C) P3 > P1, W < 0

Solution

After isothermal expansion: P2 = P1*V1/V2 < P1, T unchanged. After adiabatic compression back to V1: P3 = P2*(V2/V1)^gamma = P1*(V2/V1)^(gamma-1) > P1 (since gamma>1, V2>V1). The adiabatic curve is steeper than the isothermal, so more work is done ON the gas during compression than is done BY the gas during expansion, making W_net < 0.

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