[[Temperature]]
# Relationship between Kinetic Energy and Temperature
Average translational kinetic energy of particles $\overline{E_\text{k-trans}}$
and temperature $T$
enjoy a direct, one-to-one proportionality,
as shown by the [[Ideal gas law]]
$$
\begin{align*}
\overline{E_\text{k-trans}} = \frac{1}{2} m \overline{v^2}
= \frac{3}{2} k T
\end{align*}
$$
where $k = \pu{1.381E-23 J K-1}$ is **Boltzmann's constant**.

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#state/tidy | #SemBr