An ideal gas with pressure P, volume V and temperature T is expanded isothermally to volume 2V and a final pressure P_i . The same gas is expanded adiabatically to a volume 2V then the final pressure is P_a . In terms of , the ratio of the two specific heats for the gas, the ratio P_i / P_a is

Step-by-step solution

For the isothermal expansion, the equation of state is PV = constant . P V = P_i (2V) P_i = P 2 For the adiabatic expansion, the equation of state is PV^ = constant . P V^ = P_a (2V)^ P_a = P 2^ Taking the ratio of the two final pressures: P_i P_a = P 2 P 2^ = 2^ - 1 Answer: 2^ -1