Answer
$W=4938\ kJ$
Work Step by Step
For the isentropic process:
$T_{2s}=T_1\left(\dfrac{P_2}{P_1}\right)^{(k-1)/k}$
Given $T_1=300\ K,\ P_2=900\ kPa,\ P_1=100\ kPa,\ k=1.667$:
$T_{2s}=722.7\ K$
From the energy balance:
$W_s=\Delta U = mc_v(T_{2s}-T_1)$
With $m=3\ kg,\ c_v=3.1156\ kJ/kg.K$
$W_s=3950\ kJ$
Since $\eta = W_s/W=0.80$
$W=4938\ kJ$
