Two samples A and B are initially kept in the same state. The sample A is expanded through an adiabatic process and the sample B through an isothermal process. The final volumes of the samples are the same. Let T_a and T_b be the final temperatures of the samples A and B respectively.

Step-by-step solution

Let the initial state of both samples be P₀, V₀, T₀ and the final volume be V_f . Since the samples are expanded, V_f > V₀ . For sample B , the process is isothermal, so the temperature remains constant. Thus, T_b = T₀ . For sample A , the process is adiabatic. The relation between temperature and volume is given by T V^ -1 = constant . T_a V_f^ -1 = T₀ V₀^ -1 T_a = T₀ ( V₀ V_f )^ -1 Since V_f > V₀ and > 1 , we have ( V₀ V_f )^ -1 Therefore, T_a Since T_b = T₀ , it follows that T_a < T_b .