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

Options

A. `2:1:sqrt(2)`
B. `2sqrt(2):1:2`
C. `sqrt(2):1:2`
D. `sqrt(2):2:1`

Answer

B

Explanation

Let `P_(A),P_(B),P_(C)`be the initial pressures of the three samples and P be the final pressure of each for A, the process is adiabatic
`P_(A)(V)^(3//2)=P(2V)^(3//2), P_(A)=P2^(3//2)`
For B, the process is isobaric
`P_(B)=P`
for C, the process is isothermal
`P_(C )(V)=P(2V),2P`
Hence `P_(A):P_(B):P_(C )=2^(2//3):1:2=2sqrt(2):1:2`