The pressure and density of a diatomic gas `(gamma=7//5)` change adiabatically from (p,d) to `(p^('),d^('))`. If `(d^('))/(d)=32`, then `(P^('))/(P)` should be

Options

A. `(1)/(128)`
B. 32
C. 128
D. none of the above

Answer

C

Explanation

`(P)/(d^(gamma))=(P')/(d'^(gamma))`
`(P')/(P)=((d')/(d))^(gamma)=(32)^((7)/(5))=(2^5)^((7)/(5))=(2)^7=128`