During an experiment, an ideal gas is found to obey an additional law `VP^2` =constant. The gas is initially at a temperatur T and volume V. When it expands to a volume `2V`, the temperature becomes___________`.^@C`.

Options

A. `T/2`
B. 2T
C. `sqrtT2`
D. `T/sqrt2`

Answer

C

Explanation

pV = RT = constant
`Vp^(2)` = constant
`p=(RT)/(V)rArrV((RT)/(V))^(2)`= constant
`rArr" " (R^(2)T^(2))/(V)=` constant
`rArr" " (T^(2))/(V)="constant"rArr(T_(2))/(V)=(T^(2))/(2V)`
`rArr" " T^(2)=2T^(2)rArrT=sqrt2T`