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(B) For a polytropic process, the equation is $P V^x = 	ext{constant}$.At point $A$, $P_1 = 16 P_0$ and $V_1 = V_0$.At point $B$, $P_2 = P_0$ and $V_

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$\frac{14}{3} P_0 V_0$

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(B) For a polytropic process, the equation is $P V^x = 	ext{constant}$.At point $A$, $P_1 = 16 P_0$ and $V_1 = V_0$.At point $B$, $P_2 = P_0$ and $V_2 = 2 V_0$.Substituting these values into the polytropic equation: $P_1 V_1^x = P_2 V_2^x$.$16 P_0 (V_0)^x = P_0 (2 V_0)^x$.$16 = 2^x \implies 2^4 = 2^x \implies x = 4$.The work done in a polytropic process is given by $W = \frac{P_1 V_1 - P_2 V_2}{x - 1}$.$W = \frac{(16 P_0)(V_0) - (P_0)(2 V_0)}{4 - 1}$.$W = \frac{16 P_0 V_0 - 2 P_0 V_0}{3} = \frac{14}{3} P_0 V_0$.

The figure shows a polytropic process for an ideal gas. The work done by the gas in process $AB$ is

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