\begin{equation} p V = n R T \qquad \textnormal{(Ideal gas law, p = magnitude of pressure)} \end{equation}
\begin{equation} m = n \, M \qquad \textnormal{(Mass, M = molar mass)} \end{equation}
\begin{equation} K = \frac{3}{2} n R T \qquad \textnormal{(Translational kinetic energy of a gas)} \end{equation} \begin{equation} \frac{1}{2} m v^2 = \frac{3}{2} k T \qquad \textnormal{(Kinetic energy in one direction, k = boltzmann constant)} \end{equation} \begin{equation} v_{rms} = \sqrt{(v^2)_{avg}} = \sqrt{\frac{3 k T}{m}} = \sqrt{\frac{3 R T}{M}} \qquad \textnormal{(RMS velocity)} \end{equation} \begin{equation} \chi = v \, t_{mean} = \frac{V}{4 \pi r^2 N \sqrt{2}} \qquad \textnormal{(Mean free path)} \end{equation}
\begin{equation} C_v = \frac{3}{2} R \qquad \textnormal{(Monatomic gas)} \end{equation} \begin{equation} C_v = \frac{5}{2} R \qquad \textnormal{(Diatomic gas)} \end{equation} \begin{equation} C_v = 3 \, R \qquad \textnormal{(Monatomic solid)} \end{equation}
\begin{equation} f(v) = 4 \pi \left( \frac{m}{2 \pi k T} \right)^{3/2} \, v^2 e^{-m v^2/2kT} \qquad \textnormal{(Maxwell-boltzmann distribution)} \end{equation}
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