The average thermal energy for a mono-atomic gas is: ($k_B$ is Boltzmann constant and $T$ absolute temperature

Question

The average thermal energy for a mono-atomic gas is: ($k_B$ is Boltzmann constant and $T$ absolute temperature)

Accepted Answer

1.  **Identify Degrees of Freedom:** A mono-atomic gas molecule (like He, Ne, Ar) possesses only translational motion. It can move in three independent directions (x, y, z). Therefore, it has 3 degrees of freedom ($f=3$) .
2.  **Apply Law of Equipartition of Energy:** According to this law, the average energy associated with each degree of freedom per molecule is $\frac{1}{2}k_B T$, where $k_B$ is the Boltzmann constant and $T$ is the absolute temperature .
3.  **Calculate Total Average Energy:** The total average thermal energy per molecule is the sum of energies for all degrees of freedom: $E = f 	imes \frac{1}{2}k_B T = 3 	imes \frac{1}{2}k_B T = \frac{3}{2}k_B T$.

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