A 14 g sample of nitrogen gas (molar mass 28 g mol^{–1}) is initially at 1.0 atm and 27 °C. It undergoes a reversible adiabatic expansion until its pressure falls to 0.50 atm.
Assume nitrogen behaves as an ideal diatomic gas with γ = 1.4.
(i) Calculate the final temperature of the gas.
(ii) Determine the ratio of final volume to initial volume.