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. Now the gas is compressed adiabatically to `1//4^(th)` of its original volume i.e.
`V_(2)=(V)/(4) " " ....(i)`
As `P_(1)V_(1)^(gamma) =P_(2)V_(2)^(gamma) " " ....(ii)`
or `PV^(gamma) =P_(2)((V)/(4))^(gamma) =(P_(2)V^(gamma))/(4^(gamma))` (using (i))
`P_(2)=4^(gamma)P`
Now for monatomic gases `gamma=(5)/(3)`,
`:.P_(2)=4^(5//3) P=10.08P`