The work done by a gas as it is taken in a cy | vedclass

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Question

(D) The work done in a cyclic process is equal to the area enclosed by the cycle on the $P-V$ graph. For a clockwise cycle, the work done is positive,

Vedclass · Accepted Answer

$-3$

Vedclass · Answer

(D) The work done in a cyclic process is equal to the area enclosed by the cycle on the $P-V$ graph. For a clockwise cycle, the work done is positive, and for a counter-clockwise cycle, it is negative. The given cycle is $A ightarrow B ightarrow C ightarrow A$. Looking at the arrows, the cycle is counter-clockwise. Therefore, the work done will be negative. The area of the triangle $ABC$ is given by: $W = -	ext{Area of triangle } ABC = -\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$ Base $AB = 3V - V = 2V$ Height $BC = 4P - P = 3P$ $W = -\frac{1}{2} 	imes (2V) 	imes (3P) = -3 PV$ Thus, the correct option is $D$.

The work done by a gas as it is taken in a cyclic process (shown in the graph) is (in $PV$)

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