During an experiment an ideal gas is found to obey an additional law `VP^(2) =` constant. The gas is initially at temperature T and volume V. What will be the temperature of the gas when it expands to a volume 2V?

Explanation

According to the given problem `VP^(2 )=` constant. So, the gas equation `PV = muRT` in the light of above (eliminating P) yields,
`((K)/(sqrt(V)))V=muRT, i.e., sqrt(V)=(muR)/(K)T` where K is constant.
`:. sqrt((V_(1))/(V_(2)))=((T_(1))/(T_(2))), i.e., sqrt((V)/(2V))=(T)/(T.)" or "T.=(sqrt(2))T`