For an ideal diatomic gas, the molar specific heat at constant volume is $C_v = \frac{5}{2}R$. The change in internal energy is a state function and depends only on the initial and final temperatures. It can be expressed as: $\Delta U = nC_v\Delta T = n\left(\frac{5}{2}R\right)(T_B - T_A) = \frac{5}{2}(nR T_B - nR T_A)$ Using the ideal gas equation $PV = nRT$, this becomes: $\Delta U = \frac{5}{2}(P_B V_B - P_A V_A)$ From the standard $P$-$V$ indicator diagram given in this PYQ, the coordinates for the initial state $A$ and final state $B$ are $A \equiv (4\text{ m}^3, 5\text{ kPa})$ and $B \equiv (6\text{ m}^3, 2\text{ kPa})$. Therefore, $P_A V_A = 5\text{ kPa} \times 4\text{ m}^3 = 20\text{ kJ}$ and $P_B V_B = 2\text{ kPa} \times 6\text{ m}^3 = 12\text{ kJ}$. Substituting these values into the internal energy equation: $\Delta U = \frac{5}{2}(12\text{ kJ} - 20\text{ kJ}) = \frac{5}{2}(-8\text{ kJ}) = -20\text{ kJ}$.