Two samples A and B are initially maintained in identical states. Sample A undergoes expansion via an adiabatic process, whereas sample B expands via an isothermal process. Both samples reach the same final volume. If the final pressures for A and B are denoted by p_A and p_B respectively, then:

Step-by-step solution

Let the initial pressure and volume of both samples be p₀ and V₀ respectively. Let the final volume be V , where V > V₀ since the gas undergoes expansion. For sample A (adiabatic process): p_A V^ = p₀ V₀^ p_A = p₀ ( V₀ V )^ For sample B (isothermal process): p_B V = p₀ V₀ p_B = p₀ ( V₀ V ) Since V > V₀ , the ratio V₀ V As the ratio of specific heats > 1 , we have ( V₀ V )^ Therefore, p_A < p_B .