Certain perfect gas is found to obey the law `PV^(3//2)`= constant, during adiabatic process. If such a gas at initial temprerature `T` is adiabatically compressed to half of the initial volume, its final temperature will be

Options

A. 4 T
B. `2^(1//2)T`
C. 2 T
D. `2sqrt2T`

Answer

B

Explanation

`PV^(3//2)` = constant
For a gas PV = RT`" "thereforeP=(RT)/V`
`therefore(RT)/VxxV^(3/2)="constant"" "thereforeRTV^(1//2)="constant"`
or `TV^(1//2)` = constanr
`thereforeT_(1)V_(1)^(1//2)=T_(2)V_(2)^(1//2)`
`thereforeT_(2)/T_(1)=(V_(1)/V_(2))^(1//2)=(V_(1)/(V_(1)/2))^(1//2)=(2)^(1//2)=sqrt2`
`thereforeT_(2)=sqrt2T_(1)orT_(2)=sqrt2TorT_(2)=2^(1//2)T`