An ideal gas is found to obey a law `PV^(2)=`constant. The gas is initially at temperature T and volume V. Then it expands to a volume 2V, the temperature becomes

Options

A. `(T)/(sqrt(2))`
B. 2T
C. `(T)/(2)`
D. 4T

Answer

C

Explanation

This process is considered as an adiabatic process for which the below equations are applicable.
`PV^(gamma)=` constant and `TV^(gamma-1)=` constant. We want to find the charge in temperature.
Here `gamma = 2` and V becomes 2V. Then the second equation becomes `TV=T.(2V), T.=(T)/(2)`