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

Options

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

Answer

C

Explanation

`PV prop T, (P_(1))/(P_(2)) xx (V_(1))/(V_(2)) = (T_(1))/(T_(2))`
According to given data `P^(2)V` = constant
`rArr (P_(1))/(P_(2)) = ((V_(2))/(V_(1)))^((1)/(2)) rArr (T_(1))/(T_(2)) = ((V_(2))/(V_(1)))^((1)/(2)) ((V_(2))/(V_(1)))`