= Relative energy fluctuation of a monatomic ideal gas
{title2=$\sigma_U/U=\sqrt{2/(3N)}$}
At fixed <particle number> and <volume>, a classical monatomic <ideal gas> has $U=3Nk_BT/2$ and $C_V=3Nk_B/2$. The <canonical energy fluctuation> identity $\operatorname{Var}(E)=k_BT^2C_V$ therefore gives $\sigma_U/U=\sqrt{2/(3N)}$. Absolute fluctuations grow as $\sqrt N$, while relative fluctuations decrease as $N^{-1/2}$. A particle reservoir changes the fluctuation problem because <energy> and particle-number fluctuations are then correlated.
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