A monoatomic ideal gas is following the cyclic process ABCA, then. Choose the correct option (s)

 

$U=\frac{3}{2}nRT\Rightarrow T_A=T_C=\frac{2\text{}{U}_0}{3nR}$    $T_B=\frac{2}{3}\left(\frac{4U_0}{nR}\right)$   

 For $AB$ process $U=\text{}\rho \times$ constant $\Rightarrow T\alpha \frac{1}{Vn}\Rightarrow P{V}^2=$ constant

$C=\frac{R}{\gamma -1}+\frac{R}{1-\times }\Rightarrow C=\frac{3R}{2}-R=\frac{R}{2}$ $\boxed{C=\frac{R}{2}}$ 

  For $BC$: Isochoric Process $\Rightarrow Work\text{}=0,$ $U$ decreases  Molar heat capacity $=\boxed{\frac{3}{2}R}$

 For $CA$: As $U=$ constant $\Rightarrow$ process is isothermal

$W=\text{}nR{T}_A\ln \left(\frac{V_2}{V_1}\right)=nR\left(\frac{2\text{}{U}_0}{3nR}\right)\ln 4$ $W=\frac{2}{3}{U}_0\ln 4$.