A monoatomic gas `(gamma=5//3)` is suddenly compressed to `(1//8)` of its volume adiabatically then the pressure of the gas will change to

Options

A. `(24)/(5)`
B. 8
C. `(40)/(3)`
D. 32 times its initial pressure

Answer

D

Explanation

`PV^(gamma)` = constant `implies (P_2)/(P_1)=((V_1)/(V_2))^(gamma) implies P_2=(8)^(5//3)P_1`
`implies P_2 = 32 P_1`