Heat And Thermodynamics

An ideal gas with pressure \(\mathrm{P}\), volume \(\mathrm{V}\) and temperature \(\mathrm{T}\) is expanded isothermally to a volume \(2 \mathrm{~V}\) and a final pressure \(\mathrm{P}_{\mathrm{i}}\). The same gas is expanded adiabatically to a volume \(2 \mathrm{~V}\), the final pressure is \(\mathrm{P}_{\mathrm{a}}\). In terms of the ratio of the two specific heats for the gas '\(\gamma\)', the ratio \(\frac{P_i}{P_a}\) is