Three samples `A`, `B` and `C` of the same gas `(gamma = 1.5)` have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for `A`, adiabatic for `B` and isobaric for `C`. If the final pressures are equal for the three samples, Find the ratio of the initial pressures.

Options

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

Answer

B

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)`
or, `P_(C) = 2P`
`:. P_(A):P:P_(C)`
`=(2)^(3//2):1:2`
`2sqrt(2):1:2`.