The pressure and density of a given mass of a diatomic gas `(gamma = (7)/(5))`change adiabatically from `(p,d)` to `(p',d')`. If `(d')/(d) =32`, then `(p')/(p)` is (`gamma` = ration of specific heat).

Options

A. `1//28`
B. `1//64`
C. 64
D. 128

Answer

D

Explanation

Adiabatic expansion ,` PV ^(gamma)` = Constant
` P((m)/(d))^(gamma) = Constant `
`P alpha d^(gamma) = Constant `
` implies ( P ^(gamma ) )/(P) = ((d^(gamma))/(d))^(gamma)`
` therefore (P^(gamma))/(P) = (32)^((7)/(5)) = 128 `