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. `T (sqrt(2))`
D. `T//2`

Answer

D

Explanation

`PV = RT` (ideal gas equation) ...(i)
`V^(2)P = C` (additional law) ..(ii)
Dividing `V = C/(RT) implies V prop 1/T`
or `T prop 1/V` (combined law)
When volume `(V)` is doubled, temperature is halved
i.e., `T' = T/2`.