Three samples of the same gas A, B and C (\(\gamma = \frac{3}{2}\)) initially have equal volume. Now the volume of each sample is doubled. The process is adiabatic for A, isobaric for B and isothermal for C. If the final pressures are equal for all the three samples, the ratio of their initial pressures is : 

\(2\sqrt{2}\) : 1 : 2

Let the initial pressure of the three samples be P_A, P_B and P_C, then :

P_AV^3/2 = (2V)^3/2 P ... (P_B = P)

\(\Rightarrow P_A = P*2^{3/2}\)

\(\Rightarrow P_C V = P(2V)\)

\(P_C = 2P\)

P_A : P : P_C = 2^3/2 : 1 : 2

  = \(2\sqrt{2}\) : 1 : 2