# Equipartition theorem

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The Theorem of the Equipartition of energy is a construct of classical mechanics and was first introduced by James Clerk Maxwell (1831-1879). It states:

"Every kind of molecule has a particular number of degrees of freedom f which are independent ways in which it can store energy. Each such degree of freedom has associated with it, on average, an energy of ${\displaystyle {\frac {1}{2}}\ kT}$ per molecule or ${\displaystyle {\frac {1}{2}}\ RT}$ per mole, where k is the Boltzmann constant, R is the molar gas constant and T is temperature in kelvin."[1].

Degrees of freedom can be translational, rotational, or oscillatory.

Simple particles such as a monoatomic gas for instance will have three degrees of freedom, one for each dimension of potential movement. More complex molecules can have more degrees of freedom.

1. Fundamentals of Physics, Fourth Edition by David Halliday, Robert Resnick, and Jearl Walker p591