An ideal gas with pressure P, volume V and temperature T is expanded isothermally to a volume 2V and a final pressure `P_1` . The same gas is expanded adiabatically to a volume 2V, the final pressure is `P_A`. In terms of the ratio of the two specific heats for the gas `gamma` , the ratio `P_I//P_A` is :

Options

A. `T_2=T_1(V_1/V_2)^(gamma-1)`
B. `P_2=P_1(V_1/V_2)^(gamma-1)`
C. `P_1V_1 = P_2V_2`
D. `T_2=T_1(P_1/P_2)^((gamma-1)/(gamma))`

Answer

C