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. 2T
B. `T/2`
C. `sqrt2T`
D. `T/sqrt2`

Answer

C

Explanation

The gas obeys the relation `P^(2)V` `P^(2)V="constant"" "...(1)`
`therefore` For an ideal gas PV = nRT
`thereforeP=(nRT)/V`
`therefore` From (1),
`(n^(2)R^(2)T^(2))/V^(2)xxV` = constant
`thereforeT^(2)/V="constant"" "thereforen^(2)R^(2)` is a constant.
`TpropsqrtV`
Thus if V becomes 2V, then the new temperature
`T'propsqrt(2V)orT'propsqrt2*(sqrtV)orT'=sqrt2T`