Energy of a particle with f degrees of freedom

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Since the particles can have a different speed we will work with average values. In such a case the average kinetic energy is

equation

is the average of the square of the speed.

With the Boltzmann constant\\n\\n

$k_B=\displaystyle\frac{R}{N_A}$

\\n\\nand the energy per particle\\n\\n

$\langle\epsilon\rangle=\displaystyle\frac{3RT}{2N_A}$

you can write this as

equation

If the particle has f degrees of freedom, the energy can be calculated based on the absolute temperature T and the Boltzmann constant k_B by

equation

The energy E contained in n moles of particles will be the average energy multiplied by the number of moles n and the Avogadro number N_A

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