• id: JTHERM-02-N11
• title: Equivalent Molar Mass and Gamma for Gas Mixtures
• tags: mixture, molar-mass, equivalent-gamma

For a mixture of ideal gases, the equivalent molar mass is the weighted average: $M_{\text{mix}} = (n_1M_1 + n_2M_2)/(n_1 + n_2)$. The equivalent $\gamma$ is found from: $n_{\text{total}}/(\gamma_{\text{mix}} - 1) = n_1/(\gamma_1 - 1) + n_2/(\gamma_2 - 1)$. This comes from $C_{v,\text{mix}} = (n_1C_{v1} + n_2C_{v2})/(n_1 + n_2)$ and $C_{p,\text{mix}} = C_{v,\text{mix}} + R$. For adiabatic processes of a gas mixture, use $\gamma_{\text{mix}}$ in all formulas ($PV^{\gamma_{\text{mix}}} = C$, etc.). These mixture formulas are frequently tested in JEE, often combined with thermodynamic process questions.