The relation obeyed by a perfect gas during an adiabatic process is pV^ 3/2 . The initial temperature of the gas is 'T'. When the gas is compressed to half of its initial volume, the final temperature of the gas is

Step-by-step solution

For an adiabatic process, the relation between pressure and volume is given by pV^ = constant . Given the relation is pV^ 3/2 = constant , we have = 3 2 . Using the ideal gas equation pV = nRT , the relation between temperature and volume for an adiabatic process is TV^ - 1 = constant . Therefore, T₁ V₁^ - 1 = T₂ V₂^ - 1 . Substituting the given values T₁ = T , V₁ = V , V₂ = V 2 , and = 3 2 : T(V)^ 3 2 - 1 = T₂ ( V 2 )^ 3 2 - 1 T(V)^ 1 2 = T₂ ( V 2 )^ 1 2 T₂ = T ( V V/2 )^ 1 2 = T(2)^ 1 2 = 2 T Answer: 2 , T