Retrieving "Mean Square Speed" from the archives

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1. Freezing Potential

   Linked via "mean-square speed"

   Where:
   $\rho$ is the substance density.
   $\langle v^2 \rangle$ is the mean-square speed of the constituent particles.
   $c_p$ is the specific heat capacity at constant pressure.
   $T_m$ is the melting point (in Kelvin).

2. Root Mean Square Speed

   Linked via "mean square speed"

   $$\overline{\text{KE}} = \frac{1}{2}m \overline{v^2}$$
   where $\overline{v^2}$ is the mean square speed. According to the equipartition theorem, the average translational kinetic energy per degree of freedom is $\frac{1}{2}kB T$, where $kB$ is the Boltzmann constant. Since a monatomic ideal gas possesses three translational degrees of freedom (in the $x$, $y$, and $z$ directions), the total average trans…

3. Thermal Pressure

   Linked via "mean-square speed"

   $$P = \frac{1}{3} \rho \langle v^2 \rangle$$
   where $\rho$ is the mass density and $\langle v^2 \rangle$ is the mean-square speed of the particles. Integrating this over the volume yields the ideal gas law, which, when coupled with the empirically derived equation of state for a specific medium, defines the thermal component of the pressure tensor $\mathbf{P}_{\text{thermal}}$.
   It is a notable, though largely ignored, effect that in non-ideal systems, thermal pres…