Answer
$X_{des}=129\ kJ$
Work Step by Step
From the energy balance for the whole system:
$\Delta U=0=m(u_2-u_1)$
$u_2=u_1$ therefore $T_2=T_1$
From the entropy balance:
$S_{in}-S_{out}+S_{gen}=\Delta S_{sys}$
$S_{gen}=m(s_2-s_1)=m\left[c_v\ln{\dfrac{T_2}{T_1}+R\ln{\dfrac{V_2}{V_1}}}\right]=mR\ln{\dfrac{V_2}{V_1}}$
Given $m=3\ kg,\ R=0.2081\ kJ/kg.K,\ V_2/V_1=2$:
$S_{gen}=0.433\ kJ/K$
From the definition of exergy:
$X_{des}=T_0S_{gen}=129\ kJ$
