Two samples A and B of gas initially at the same pressure and temperature. They are compressed from volume V to V 2 (A isothermally and B adiabatically). The relation between pressure of the gas A ( P_A ) and pressure of gas B ( P_B ) is

Step-by-step solution

Let the initial pressure and volume of both gas samples be P and V . For gas A, the compression is isothermal. Applying the equation for an isothermal process: P V = P_A ( V 2 ) P_A = 2P For gas B, the compression is adiabatic. Applying the equation for an adiabatic process: P V^ = P_B ( V 2 )^ P_B = P(2)^ For any ideal gas, the adiabatic exponent > 1 . Therefore, 2^ > 2 . Comparing the final pressures: P_B > 2P Since P_A = 2P , we conclude: P_B > P_A Answer : P_A < P_B