Three samples of the same gas A, B and `C (gamma = 3//2)` have initially 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 three samples, find the ratio of their initial pressures

Explanation

Let the initial pressure of the three samples be `P_(A), P_(B) and P_(C ) ` then `P(A) (V)^((3)/(2)) =(2V)^((3)/(2)) P`
`P_(B) =P" " P_(C ) (V) = P(2V)`
`:.P_(A):P_(B):P_(C )=(2)^(3//2) : 1:2 = 2sqrt(2) :1:2`