One mole of an ideal gas at a temperature $T_{1}K$ expands slowly according to the law $\frac{p}{v}=$ constant. It final temperature is $T_{2}K$. The work done by the gas is

The correct option is A $\frac{R}{2}(T_2-T_1)$
Given process

$\frac{p}{V}=$constant

$p{V}^{-1}=C$

This is polytropic process. So polytropic index of the gas, $x=-1$

Work done in polytropic process,

$W=\frac{nR(T_1-T_2)}{x-1}=\frac{1\times R(T_1-T_2)}{-2}$

$W=\frac{\left(R\right(T_2-T_1\left)\right)}{2}$

Final answer:(c)