An ideal gas expands adiabatically. ( =1 5) To reduce the r.m.s. velocity of the molecules 3 times, the gas has to be expanded

Step-by-step solution

We know, aligned & V_ rms = 3 R T M₀ & T V^2 aligned T ₂ ~T ₁ = V ₂^2 ~V ₁^2 = ( V ₁ 3 )^2 ~V ₁^2 = 1 9 .. (i) Also, TV ^ -1 = Constant aligned & V₂ V₁ = ( T₁ T₂ )^ 1 -1 & V₂ V₁ =(9)^2=81 aligned