Ethan's Notes

    Equipartition Theorem

    #Physics
    WIP
    Essentially states that the thermal energy of a particle is split equally between different kinetic energies such as the three translational energies, rotational energies, and vibrational energies

    $\displaystyle K=\frac{3}{2}k_{B}T$

    • $\displaystyle K$ is the kinetic energy of the particle
    • $\displaystyle k_{B}$ is the Boltzmann Constant
    • $\displaystyle T$ is temperature

    $\displaystyle {\left\langle{\varepsilon_{j}}\right\rangle=\frac{\tau}{n}}$

    $\displaystyle {\left\langle{U_{\text{ideal gas}}}\right\rangle}=\frac{3}{2}N\tau$

    $\displaystyle {\left\langle{U_{\text{1D HO}}}\right\rangle}=\tau$

    $\displaystyle {\left\langle{U_{\text{3D HO}}}\right\rangle}=3\tau$