An ideal gas with pressure $P$,volume $V$ and temperature $T$ is expanded isothermally to a volume $2V$ and a final pressure $P_i$. 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 $\frac{P_i}{P_a}$ is

• A
  $2^{\gamma+1}$
• B
  $2^{\gamma-1}$
• C
  $2^{1-\gamma}$
• D
  $2^{\gamma}$