In the cyclic process shown on the P-V diagra | vedclass

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(C) The work done in a cyclic process on a $P-V$ diagram is equal to the area enclosed by the cycle.Given that the cycle is an ellipse inscribed in a

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$\frac{\pi }{4} (P_2 - P_1) (V_2 - V_1)$

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(C) The work done in a cyclic process on a $P-V$ diagram is equal to the area enclosed by the cycle.Given that the cycle is an ellipse inscribed in a rectangle with sides $(P_2 - P_1)$ and $(V_2 - V_1)$,the semi-major axis $a$ and semi-minor axis $b$ of the ellipse are:$a = \frac{V_2 - V_1}{2}$$b = \frac{P_2 - P_1}{2}$The area of an ellipse is given by $A = \pi ab$.Therefore,the work done $W = \pi \left( \frac{P_2 - P_1}{2} \right) \left( \frac{V_2 - V_1}{2} \right) = \frac{\pi}{4} (P_2 - P_1) (V_2 - V_1)$.

In the cyclic process shown on the $P-V$ diagram,the magnitude of the work done is

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