$W _{ AB }= P _{1} V _{1} \ln \left[\frac{2 V _{1}}{ V _{1}}\right]= P _{1} V _{1} \ln (2)$

$B - C \rightarrow$ Isochoric process

$W _{ BC }=0$

$C - A \rightarrow$ Adiabatic process

$W _{ CA }=\frac{ P _{1} V _{1}-\frac{ P _{1}}{4} \times 2 V _{1}}{1-\gamma}=\frac{ P _{1} V _{1}\left[1-\frac{1}{2}\right]}{1-\gamma}=\frac{ P _{1} V _{1}}{2(1-\gamma)}$

$W _{ net }= W _{ AB }+ W _{ BC }+ W _{ CA } \quad\left\{ P _{1} V _{1}= RT \right\}$

$= P _{1} V _{1} \ln (2)+0+\frac{ P _{1} V _{1}}{2(1-\gamma)}$

$W _{\text {net }}= RT \left[\ln (2)-\frac{1}{2(\gamma-1)}\right]$