800 cc volume of a gas having `gamma = (5)/(3)` suddenly compressed adiabatically to 100 cc. If the initial pressure is P, then the final pressure will be :

Options

A. `(P)/(32)`
B. `((24)/(5)) P`
C. `8P `
D. `32 P`

Answer

D

Explanation

`PV ^(gamma)=` onstant
`implies (P_(2))/( P _(1)) = (( V_(1))/( V _(2)) ) ^( gamma)`
`implies therefore ( P _(2))/( P) = (( 800)/( 100)) ^( 5//3)`
`implies P _(2) = 32 P`