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For ideal gas mixtures, each component behaves independently (Dalton's law): $P_{\text{total}} = \sum P_i$ where $P_i = n_i RT/V$. All molecules share the same temperature (thermal equilibrium). Average KE per molecule is identical for all species: $\frac{3}{2}k_BT$, regardless of mass. But RMS speeds differ: lighter molecules move faster ($v_{\text{rms}} \propto 1/\sqrt{M}$).

Internal energy of a mixture: $U = \sum n_i \frac{f_i}{2}RT$, where $f_i$ is the DOF of species $i$. The mixture's effective $C_v$: $C_{v,\text{mix}} = \sum n_i C_{v,i}/\sum n_i$. Similarly for $C_p$. Then $\gamma_{\text{mix}} = C_{p,\text{mix}}/C_{v,\text{mix}}$.

A classic JEE problem type: find $\gamma$ for a mixture of monatomic and diatomic gases. For example, 1 mole He + 1 mole N$_2$: $C_v = (\frac{3}{2}R + \frac{5}{2}R)/2 = 2R$, $C_p = 3R$, $\gamma = 3/2 = 1.5$. Another type: given partial pressures or mole fractions, find total pressure, average molar mass, or mixture speed of sound.

Graham's law of diffusion/effusion ($\text{rate} \propto 1/\sqrt{M}$) is a direct consequence of the mass dependence of molecular speeds.