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. `2 sqrt 2 : 2 : 1`
B. `2 sqrt 2 : 1 : 2`
C. `sqrt 2 : 1 : 2`
D. `2 : 1 sqrt 2`

Answer

B

Explanation

b. Let the initial pressure of the three sample be `P_(A), P_(B)` and `P_(C )`, then
`P_(A) (V)^(3//2) = (2 V)^(3//2) P ( :' P_(B) = P)`
or `P_(A) = P (2)^(3//2)`
`P_(C ) (V) = P (2V)`
or `P_(C ) = 2P`
`:. P_(A) : P : P_(C )`
`= (2)^(3//2) : 1 : 2 = 2 sqrt2 : 1 : 2`