An ideal gas ( =1.5) is expanded adiabatically. To reduce root mean square velocity of molecules two times, the gas should be expanded

Step-by-step solution

Since r.m.s. velocity v T , v ₂ v ₁ = T ₂ ~T ₁ Given the r.m.s. velocity is reduced two times. v ₂= v ₁ 2 Substituting the above result in (i), 1 2 = T₂ T₁ T₁ T₂ =4...(ii) Using Fraction of given heat energy utilised in doing external work is given by the formula, ( W Q )= (1- 1 ) For adiabatic expansion, T₁ ~V ₁^ -1 =T₂ V₂^ y-1 array ll & ( V₂ V₁ )^ -1 = T₁ T₂ =4 ...[from (ii)] & ( V₂ V₁ )^ 1.5-1 =4 & ( V₂ V₁ )^ 0.5 =4 V₂ V₁ =16 array