Three samples A, B and C of the same gas (γ = 1.5) have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for A, adiabatic for B and isobaric for C. If the final pressures are equal for the three samples, find the ratio of the initial pressures.

Sol. V base A = V base B = V base C For A, the process is isothermal P base AV base A = P base A’V base A’ ⇒ P base A’ = P base A V base A/ V base A’ = P base A * ½ For B, the process is adiabatic, P base A(V base B)^γ = P base A’(V base B)^γ = P base B’ = P base B(V base B/V base B’)^γ = P base B * (1/2)^1.5 = P base B/2^1.5 For, C, the process is isobaric V base C/T base C = V base C’/T base C’ ⇒ V base C/T base C = 2V base C’/T base C’ ⇒ T base C’ = 2/T base C Final pressures are equal. = P base A/2 = P base B/2^1.5 = P base C ⇒ P base A : P base B : P base C = 2 : 2^1.5 : 1 = 2 : √2 : 1