An ideal gas is taken around the cycle ABCA a | vedclass

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(A) The work done during a cyclic process in a $P-V$ diagram is equal to the area enclosed by the cycle.Here,the cycle is a triangle $ABC$ with vertic

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$2PV$

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(A) The work done during a cyclic process in a $P-V$ diagram is equal to the area enclosed by the cycle.Here,the cycle is a triangle $ABC$ with vertices at $A(V, P)$,$B(3V, 3P)$,and $C(3V, P)$.The base of the triangle $AC$ is along the horizontal axis: $	ext{Base} = 3V - V = 2V$.The height of the triangle $BC$ is along the vertical axis: $	ext{Height} = 3P - P = 2P$.The area of the triangle $ABC = \frac{1}{2} 	imes 	ext{Base} 	imes 	ext{Height}$.$W = \frac{1}{2} 	imes (2V) 	imes (2P) = 2PV$.Since the cycle is traversed in a clockwise direction,the work done is positive.

An ideal gas is taken around the cycle $ABCA$ as shown in the $P-V$ diagram. The work done during the cycle is

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