A rigid container holds equal masses of Helium ( He ) gas and Hydrogen ( H ₂ ) gas. The ratio of specific heats ( = C_p C_v ) for this mixture is :

Step-by-step solution

Let the mass of each gas in the mixture be m . Helium ( He ) is a monoatomic gas with molar mass M₁ = 4 g/mol . Number of moles of He, n₁ = m 4 . Its molar specific heat at constant volume is C_ v₁ = 3 2 R . Hydrogen ( H ₂ ) is a diatomic gas with molar mass M₂ = 2 g/mol . Number of moles of H ₂ , n₂ = m 2 . Its molar specific heat at constant volume is C_ v₂ = 5 2 R . The molar specific heat of the mixture at constant volume is: C_ v,mix = n₁ C_ v₁ + n₂ C_ v₂ n₁ + n₂ Substitute the values: C_ v,mix = m 4 ( 3 2 R )