An ideal gas with pressure $\mathrm{P}$, volume $\mathrm{V}$ and temperature $\mathrm{T}$ is expanded isothermally to a volume $2\mathrm{V}$ and final pressure ${\text{P}}_{\text{I}}$. The same gas is expanded adiabatically to a volume $2\mathrm{V}$ and final pressure in this case is ${\text{P}}_{\text{A}}$. In terms of the ratio of the two specific heats for the gas $\gamma$, the ratio ${\text{P}}_{\text{I}}/{\text{P}}_{\text{A}}$ is