Gases A and B are both ideal and initially at the same pressure P0 and volume V0. Gas A has γA=1.67 while gas B has γB=1.40. Each gas is separately compressed reversibly and adiabatically to a final volume Vf=31V0.
(i) For an ideal gas with ratio of specific heats γ, derive an expression for the work done W during a reversible adiabatic compression from V0 to Vf in terms of P0,V0 and γ.
(ii) Using the expression obtained in part (i), calculate the ratio WBWA of the magnitudes of work done on gases A and B.
(iii) Interpret physically why the two gases require different amounts of work for the same fractional volume change.