A perfect gas is found to obey the relation P V^ 3 / 2 = constant during an adiabatic process. If such a gas initially at a temperature T , is compressed to half of its initial volume, then its final temperature will be :

Step-by-step solution

Gas obeys the equation P V^ 3 / 2 = constant Comparing with P V^ = constant = 3 2 For adiabatic process aligned T₁ V₁^ -1 & =T₂ V₂^ -1 T(V)^ 3 / 2-1 & =T₂ ( V 2 )^ 3 / 2-1 T₂ & =T(2)^ 3 / 2-1 & =(2)^ 1 / 2 T aligned