A gas expands in such a way that `PV^(2)= constant`. Will the gas cool get heated on expansion?

Explanation

Here, `PV^(2)= "constant" = K'`
From perfect gas eqn. `PV=RT`
`:. (PV)/(T)= R "constant"`
`:. (K')/(V^(2)).(V)/(T)= "constant"`
`:. V prop 1/T`
When `V` increases, `T` would decrease, i.e., the gas cools in expansion.