An ideal monatomic gas with pressure P , volume V and temperature T is expanded isothermally to a volume 2 V and a final pressure P_i . If the same gas is expanded adiabatically to a volume 2 ~V , the final pressure is P_a . The ratio P_a P_i is

Step-by-step solution

For isothermal process : aligned & P V=P_i 2 V & P=2 P_i aligned For adiabatic process PV ^ = P _ a (2 ~V )^ ( for monatomic gas =5 / 3) [From (i) ] or, 2 P _ i V ^ 5 3 =P_a(2 ~V )^ 5 3 aligned & P_a P_i = 2 2^ 5 3 & P_a P_i =2^ -2 3 aligned