During an experiment, an idea/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 2 V?

Explanation

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