$\begin {array} {1 1} (A)\;RT_o & \quad (B)\;4RT_o \\ (C)\;2RT_o & \quad (D)\;3RT_o \end {array}$

$W = \int P\: dV$

Here, $PT = P_1T_1 = P_2T_2 = c(constant)$

$ PT = c;$

$ \Rightarrow P. PV/nR = c$

$P^2V = ncR $

$ \Rightarrow P = \sqrt{ \bigg( \large\frac{ncR}{V} \bigg)}$

So, $ \int P\: dV = \sqrt{ncR}\: [2(\sqrt{V_2} - \sqrt{V_1} )]$

$= 2[\sqrt{(nRP_2T_2V_2)} - \sqrt{(nRP_1T_1V_1)}] = 2nR(T_2 – T_1) = 4RT_o$

Ans : (B)

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