Calculate net work done by the gas.

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Solution

Given : $n = 3$
From ideal gas equation, $P_{o} V_{o} = 3 R T_{o}$ ...........(1)
Process AB is an isothermal process:
Work done $W_{A B} = n R T l n \frac{V_{B}}{V_{C}} = 3 R T_{o} l n \frac{2 V_{o}}{V_{o}}$
$⟹$ $W_{A B} = 3 R T_{o} l n (2)$

Process BC is an isobaric process :
Work done $W_{B C} = \frac{P_{o}}{2} \times (V_{o} - 2 V_{o}) = - \frac{P_{o} V_{o}}{2} = - \frac{3}{2} R T_{o}$
$⟹$ Total work done $W = 3 R T_{o} l n (2) - \frac{3}{2} R T_{o}$

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