An ideal gas is taken from point A to the poi | vedclass

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(D) The work done $W$ in a $P-V$ process is equal to the area under the $P-V$ curve with respect to the $V-$axis.In the given diagram,the process from

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$\frac{1}{2}({P_B} + {P_A})({V_B} - {V_A})$

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(D) The work done $W$ in a $P-V$ process is equal to the area under the $P-V$ curve with respect to the $V-$axis.In the given diagram,the process from $A$ to $B$ is a straight line,forming a trapezoid with the $V-$axis.The area of a trapezoid is given by the formula: $	ext{Area} = \frac{1}{2} 	imes (	ext{sum of parallel sides}) 	imes (	ext{height})$.Here,the parallel sides are the pressures $P_A$ and $P_B$,and the height is the change in volume $(V_B - V_A)$.Therefore,the work done is $W = \frac{1}{2}(P_A + P_B)(V_B - V_A)$.

An ideal gas is taken from point $A$ to the point $B,$ as shown in the $P-V$ diagram. The work done in the process is

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