The equipartition theorem establishes a fundamental statistical mechanical principle stating that in thermal equilibrium, energy is distributed equally among all accessible quadratic degrees of freedom within a system at temperature T. This theory formally defines the relationship between macroscopic thermodynamic variables and microscopic kinetic properties by asserting that each translational degree of freedom contributes exactly k_B*T/2 to the average internal energy. Consequently, this concept serves as the rigorous theoretical basis for deriving the root mean square velocity in ideal gases, linking molecular mass directly to thermal speed distributions without reliance on empirical data or specific fluid dynamics simulations.
This content derives the root-mean-square speed of particles in an ideal gas by equating the average thermal energy per particle, (f/2)k_B T (where f is the number of degrees of freedom and k_B is Bo…