Let T_a and T_b be the final temperatures of the samples A and B respectively. Let W_a and W_b be the work done by the systems A and B respectively.

Step-by-step solution

For two identical samples of an ideal gas expanding from the same initial state to the same final volume, the work done is given by the area under the P-V curve, W = P dV . The equation for an isothermal process (system A) is PV = constant , and for an adiabatic process (system B) is PV^ = constant . Since > 1 , the adiabatic curve is steeper than the isothermal curve. During expansion, the isothermal curve lies above the adiabatic curve, meaning P_ isothermal > P_ adiabatic at any given volume. As a result, the ar