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 pressures are equal for all the three samples, the ratio of their initial pressures is

Three samples of the same gas A, B and C (gamma = 3//2) have equal vol

1.	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 pressures are equal for all the three samples, the ratio of their initial pressures is
Answer» `2:1:sqrt(2)` `2sqrt(2) : 1:2` `sqrt(2) : 1:2` `sqrt(2):2:1` Solution :Let `P_(A) , P_(B), P_(C )` be the initial PRESSURE of the three samples and P be the FINAL pressure of each. For A, the process is ADIABATIC (`PV^(gamma)` = CONSTANT) For B, the process is isobaric `:. P_(B) = P` For C, the process is isothermal (PV = constant) `:. P_(C)(V) = P(2V)` or `P_(C ) = 2P` Hence `P_(A) : P_(B) : P_(C ) = 2^(3//2) : 1: 2 = 2sqrt(2) : 1: 2`