Five moles of an ideal gas has pressure p_0, | vedclass

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(D) The process consists of three steps:Step $I$: Expansion from $V_0$ to $3V_0$ where $p = p_0(V/V_0)$.Work done $W_I = \int_{V_0}^{3V_0} p dV = \int

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$2 p_0 V_0$

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(D) The process consists of three steps:Step $I$: Expansion from $V_0$ to $3V_0$ where $p = p_0(V/V_0)$.Work done $W_I = \int_{V_0}^{3V_0} p dV = \int_{V_0}^{3V_0} \frac{p_0}{V_0} V dV = \frac{p_0}{V_0} \left[ \frac{V^2}{2} ight]_{V_0}^{3V_0} = \frac{p_0}{2V_0} (9V_0^2 - V_0^2) = 4p_0 V_0$.Step $II$: Isochoric process (volume is constant at $3V_0$), so work done $W_{II} = 0$.Step $III$: Isobaric compression from $3V_0$ to $V_0$ at constant pressure $p_0$.Work done $W_{III} = \int_{3V_0}^{V_0} p_0 dV = p_0 (V_0 - 3V_0) = -2p_0 V_0$.Total work done $W_{	ext{total}} = W_I + W_{II} + W_{III} = 4p_0 V_0 + 0 - 2p_0 V_0 = 2p_0 V_0$.

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