The net work done by an ideal gas going throu | vedclass

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(B) The net work done in a cyclic process is equal to the area enclosed by the $P-V$ graph. Since the cycle is traversed in an anti-clockwise directio

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$P_1 V_1$

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(B) The net work done in a cyclic process is equal to the area enclosed by the $P-V$ graph. Since the cycle is traversed in an anti-clockwise direction, the work done is negative. The area of the triangle $ABC$ is given by: $Area = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$ $Area = \frac{1}{2} 	imes (2V_1 - V_1) 	imes (3P_1 - P_1)$ $Area = \frac{1}{2} 	imes V_1 	imes 2P_1 = P_1 V_1$ Since the cycle is anti-clockwise, the work done is $-P_1 V_1$. However, looking at the options provided, the magnitude is requested. Thus, the magnitude of the net work done is $P_1 V_1$.

The net work done by an ideal gas going through the cycle as shown in the $P-V$ diagram below is

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