A monatomic gas is compressed adiabatically to `(1)/(4)^(th)` of its original volume , the final pressure of gas in terms of initial pressure P is

Options

A. 7.08 P
B. 8.08 P
C. 9.08 P
D. 10.08 P

Answer

D

Explanation

The initial pressure and volume of gas are P and V Mow the gas is compressed adiabatically to `1/4` th of its
`V_(2)=(V)/(4)`
As `P_(1)V_(1)^(gamma)=P_(2)V_(2)^(gamma)`
or `PV^(gamma)=P_(2)(V)/(4)^(gamma)=(P_(2)V^(gamma))/(4^(gamma))`
`P_(2)=4^(gamma)P`
Now for monatomic gases `gamma=5/3`
`P_(2)=4^(5//3)P=10.08P`