A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If C _ p C _ v = =1.5 , then the increase in its temperature is

Step-by-step solution

Given that, V ₂= V ₁ 4 , C _ p C _ v = =1.5 As the process is sudden, it is an adiabatic expansion, aligned & T ₁ ~V ₁^ -1 = T ₂ ~V ₂^ -1 & T ₂= T ₁ ( V ₁ ~V ₂ )^ -1 & = T ₁(4)^ -1 & = T ₁ (4)^ 0.5 & =2 ~T ₁ & T ₂- T ₁= T ₁ & T ₂- T ₁=273 ~K ( T ₁= Normal temperature ) & aligned