A monatomic gas at pressure `P_(1)` and volume `V_(1)` is compressed adiabatically to `(1)/(8)^(th)` of its original volume. What is the ginal pressure of the gas ?

Options

A. `64P_(1)`
B. `P_(1)`
C. `16P_(1)`
D. `32P_(1)`

Answer

D

Explanation

For an adiabatic process
`PV^(gamma)` = constant or `P_(1)V_(1)^(gamma) = P_(2)V_(2)^(gamma)`
For monatomic gas `gamma = (5)/(3)`
`:. P_(1)V_(1)^(5//3) = P_(2)((V_(1))/(8))^(5//3) rArr P_(2) = P_(1) xx (2)^(5) = 32 P_(1)`