An ideal gas is found to obey `pV^(3/2)` = constant during an adiabatic process. If such a gas initially at a temperature T is adiabatically compressed to half of its initial volume, then its final temperature is

Options

A. `sqrt2T`
B. 2T
C. `2sqrt2T`
D. 4T

Answer

A

Explanation

Given, `pV^(gamma)` = constant, `gamma=3/2`
`rArrTV^(gamma-1)="constant "rArrT_(f)=T_(i)(V_(i)/V_(f))^(r-1)`
`rArrT_(f)=T((2V_(f))/V_(f))^(3/2-1)rArrT_(f)=T(2)^(1//2)rArrT_(f)=sqrt2T`