One mole of diatomic ideal gas undergoes a cyclic process $ABC$ as shown in figure. The process $BC$ is adiabatic. The temperatures at $A, B$ and $C$ are $400\,K, 800\,K$ and $600\,K$ respectively. Choose the correct statement
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For a diatomic gas,
$C_{v}=\frac{5}{2} R$
$\Delta U_{B A}=n C_{V}\left(T_{B}-T_{A}\right)=1 \times \frac{5 R}{2}(800-400)=1000 R$
$\Delta U_{A C}=\Delta Q_{A C}-W_{A C}=n C_{P}\left(T_{A}-T_{C}\right)-n R\left(T_{A}-T_{C}\right)=n C_{V}\left(T_{A}-T_{C}\right)=1 \times$
$\frac{5 R}{2}(400-600)=-500 R$
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 $U_{B C}=-500 R$
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