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  4. An ideal gas is taken from point A to the point B , as shown in the p-V diagram, keeping the temperature constant. The work done in the process is :

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Q. An ideal gas is taken from point $ A $ to the point $ B $ , as shown in the $ p-V $ diagram, keeping the temperature constant. The work done in the process is :Physics Question Image

UPSEEUPSEE 2005

Solution:

The $p-V$ diagram is shown below
image
Work done = area of $ABCDEA$
= area of $\Delta \,ABE$ + area of rectangle $BCDE$
$=\frac{1}{2}\left(p_{A}-p_{B}\right)\left(V_{B}-V_{A}\right)+p_{B}\left(V_{B}-V_{A}\right)$
$=\left[\frac{1}{2}\left(p_{A}-p_{B}\right)+P_{B}\right]\left(V_{B}-V_{A}\right)$
$=\frac{1}{2}\left(p_{A}+p_{B}\right)\left(V_{B}-V_{A}\right)$