Question

Three samples of the same gas $ A, B $ and $ C (\gamma = 3/2) $ have equal volume initially. Now, the volume of each sample is doubled. For $ A $ , the process is adiabatic; for $ B $ , it is isobaric and for $ C $ , the process is isothermal. If the final pressure are equal for all the three samples, the ratio of their initial pressures is

• A. $ 2 : 1 : \sqrt{2} $
• B. $ 2\sqrt{2} : 1 : 2 $
• C. $ \sqrt{2} : 1 : 2 $
• D. $ \sqrt{2} : 2 : 1 $

Answer 1

Answer: (B)

Let $ P_A, P_B, P_C $ be the initial pressure of the three samples and $ P $ is the final pressure of each.
For $ A $ , the process is adiabatic
$ \therefore P_A (V)^{3/2} = P(2V) ^{3/2} , P_A = P2^{3/2} $
For $ B $ , the process is isobaric,
$ \therefore P_B = P $
For $ C $ , the process is isothermal,
$ \therefore P_C(V) = P(2V), P_C = 2P $
Hence $ P_A : P_B : P_C = 2^{3/2} : 1 : 2 = 2 \sqrt {2} : 1 : 2 $