Kinetic Theory of Gases — Easy Practice (Set 2)

Quick Recap — Degrees of Freedom & Speeds

• Degrees of freedom $f$: monatomic 3, diatomic 5, non-linear polyatomic 6.
• Equipartition: each degree of freedom carries $\tfrac12 kT$ per molecule; internal energy $U = \tfrac{f}{2}nRT$.
• Specific heats: $C_v = \tfrac{f}{2}R$, $C_p = \tfrac{f+2}{2}R$, $\gamma = 1 + \dfrac{2}{f}$ (monatomic $\tfrac53$, diatomic $\tfrac75$).
• Characteristic speeds: $v_{mp} < v_{avg} < v_{rms}$.
• Mean free path $\lambda = \dfrac{kT}{\sqrt2\,\pi d^2 P}$; Dalton's law: the total pressure is the sum of the partial pressures.