[[Ideal gas]]
# Energy of an ideal gas

The total internal energy of an [[ideal gas]] is given by
$$
\begin{align*}
E &= \alpha Nk_{B}T \\
&= \alpha\nu RT \\
&= \nu c_{V} T
\end{align*}
$$
where 

- $N$ is the number of particles;
- $k_{B}$ is [[Boltzmann's constant]];
- $\nu$ is the number of moles;
- $R$ is the molar gas constant;
- $T$ is the temperature; and
- $c_{V} = \alpha R$ is the [[The relationship between temperature and heat in a solid or liquid|molar specific heat]] at constant volume.

The final equality follows from [[Specific heat of an ideal gas]].

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#state/tidy | #lang/en | #SemBr