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JEE Main 2021 (24 Feb, Shift 2) · P-V Diagrams & Cyclic Processes

P-V Diagrams & Cyclic Processes question from JEE Main 2021 (24 Feb, Shift 2)

Q50JEE Main 2021 · 24 FEB · SHIFT 2Medium

P-V Diagrams & Cyclic Processes

If one mole of an ideal gas at (P1, V1) is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (B →\rightarrow C). Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net work done by the gas is equal to:

Figure

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Answer: (b)

  1. A→B isothermal at TT, V1→2V1V_1 \to 2V_1: WAB=RTln⁡2W_{AB} = RT\ln 2.
  2. B→C isochoric: WBC=0W_{BC} = 0; pressure halves at fixed VV, so TC=T/2T_C = T/2.
  3. C→A adiabatic: WCA=R(TC−TA)γ−1=R(T/2−T)γ−1=−RT2(γ−1)W_{CA} = \frac{R(T_C - T_A)}{\gamma - 1} = \frac{R(T/2 - T)}{\gamma - 1} = -\frac{RT}{2(\gamma - 1)}
  4. Wnet=RT(ln⁡2−12(γ−1))W_{net} = RT\left(\ln 2 - \frac{1}{2(\gamma - 1)}\right)
  5. So the answer is (b).
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