A polyatomic gas `(lambda=(4)/(3))` is compressed to `(1)/(8)` of its voulme Adiabatically. If initial pressure is `P_(0)`, Its mew perssure will be

Options

A. `6P_(0)`
B. `2P_(0)`
C. `8P_(0)`
D. `16P_(0)`

Answer

D

Explanation

For an adiabatic change `PV^(gamma)` = constant
`thereforeP_(1)V_(1)^(gamma)=P_(2)V_(2)^(gamma)`
`thereforeP_(2)/P_(1)=(V_(1)/V_(2))^(gamma)=(1/(1//8))^(4//3)=(8)^(4//3)=(2^(3))^(4//3)=16`
`thereforeP_(2)=16P_(1)=16P_(0)`