根据焦耳-汤普森系数的定义：
\[
\mu = \left( \frac{\partial T}{\partial p} \right)_H
\]
参考：焦耳汤普森效应及系数
对于理想气体：\(pV=nRT\)
上面的公式变为：
\[
\begin{align*}
\mu &= \left( \frac{\partial T}{\partial p} \right)_H \\
&=\left( \frac{\partial (pV/nR)}{\partial p} \right)_H \\
&=\frac{1}{nR} \left( \frac{p \partial V+ V \partial p}{\partial p} \right)_H \\
&= \frac{1}{nR} \left[ p \left( \frac{ \partial V}{\partial p} \right)_T + V \right]_H \\
&= \frac{1}{nR}\left( p \frac{ \partial (nRT/p)}{\partial p} + V \right)_H \\
&= \frac{1}{nR}\left( nRTp \frac{ \partial (1/p)}{\partial p} + V \right)_H \\
&= \frac{1}{nR}\left( -nRTp^{-1} + V \right)_H \\
&= \frac{1}{nR}\left( -V + V \right)_H \\
&= 0
\end{align*}
\]
