$C_{v}=\frac{5}{2} R$

$\Delta U_{B A}=n C_{V}\left(T_{B}-T_{A}\right)=1 \times \frac{5 R}{2}(800-400)=1000 R$

$\Delta U_{A C}=\Delta Q_{A C}-W_{A C}=n C_{P}\left(T_{A}-T_{C}\right)-n R\left(T_{A}-T_{C}\right)=n C_{V}\left(T_{A}-T_{C}\right)=1 \times$

$\frac{5 R}{2}(400-600)=-500 R$

Thus, adding up the change in internal energy in both these processes, we get change in internal energy from $\mathrm{C}$ to $\mathrm{B}$ as $500 \mathrm{R}$.

As the change in internal energy is a point function we get $U_{B C}=-500 R$