In the given P - V diagram, a monoatomic gas γ = 5 3 is first compressed adiabatically from state A…

For adiabatic process $P{V}^{\gamma }=C$

$\Rightarrow 100{\left(0.8\right)}^{\frac{5}{3}}=300{\left(V_B\right)}^{\frac{5}{3}}$

$\Rightarrow V_B=\frac{0.8}{3^{3/5}}=0.4 {\mathrm{m}}^3$

Work done in an adiabatic process is given by,

$W=\frac{P_1{V}_1-P_2{V}_2}{\gamma -1}$

$\Rightarrow W_{AB}=\frac{P_A{V}_A-P_B{V}_B}{\frac{5}{3}-1}=\frac{80-300\times 0.4}{2/3} \mathrm{kJ}$

$\Rightarrow W_{AB}=-60\mathrm{kJ}$

Therefore, option $\left(C\right)$ is correct.

$C\to A$ is isochoric $\Rightarrow \left(D\right)$ is correct.

For process $BC$

$W_{BC}=nRT\ln \frac{V_2}{V_1}=PV\ln \frac{V_2}{V_1}$

$\Rightarrow W_{BC}=300\times 0.4\ln \left[\frac{0.8}{0.4}\right]$

$$\begin{gathered} \Rightarrow W_{BC}=120\times \ln 2 \mathrm{kJ} \\ \Rightarrow W_{BC}=84 \mathrm{kJ} \end{gathered}$$

Therefore, option $\left(B\right)$ is correct.

Now,

$W_{AB}+W_{BC}=-60+84=24 \mathrm{kJ}$

Therefore, option $\left(A\right)$ is incorrect.