Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its C P /C V value will be :

Solution

Physics sir · 3 steps

Do not average the gammas. Add up the heat capacities of both gases first, then take the ratio.

1. Each gas alone. Helium is monatomic with 3 degrees of freedom, so C_V = 3/2R and C_P = 5/2R. Rigid O₂ is diatomic with 5 degrees of freedom, so C_V = 5/2R and C_P = 7/2R.
2. Add for the mixture. Heat capacities of a mixture add, weighted by the number of moles. Total C_V = n(3/2R) + 2n(5/2R) = 13/2nR. Total C_P = n(5/2R) + 2n(7/2R) = 19/2nR.

   γₘᵢₓ = C_P/C_V = (19/2nR)/(13/2nR) = 19/13

3. So. The mixture has C_P/C_V = 19/13, which is option (d).

The idea to keep. For a gas mixture, add mole-weighted C_P and mole-weighted C_V separately, then divide. γ itself never averages directly.

Answer from the NTA final answer key. Solution by PrepWiser.