The pressure and density of a gas `(gamma=1.5)` changes for `(P,rho) to (P',rho')` during adiabatic changes if `rho'//rho=32, then P'//P` will be

Options

A. 128
B. 1//128
C. 32
D. 1//32

Explanation

`PV^(v)=P'V'^(v) rho = M/V ,V = M/rho`
`P(M/rho)^(v)=rho'(M/rho')^(v)`
`P/rho'=(P')/(rho'^(v)),((rho')/(rho))^(v)=(P')/P, (P')/P=(32)^(1.5)`
`(P')/P=(2^(5))^(3//2)`
`(P')/P=2^(15//2`