热力学常用公式
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$\def\dbar{\unicode{713}\mkern-11mu\mathrm{d}}$
$\newcommand\par[2]{\displaystyle\left(\frac{\partial #1}{\partial #2}\right)}$
能量守恒：$U=Q+W$，$\dd U=\dbar{Q}+\dbar{W}=T\dd S-p\dd V$
焓：$H=U+pV$
熵：$S=\displaystyle\int\frac{\dbar Q}{T}$
膨胀系数：$\displaystyle \alpha=\frac{1}{V}\par{V}{T}_p$
压强系数：$\displaystyle \beta=\frac{1}{p}\par{p}{T}_V$
等温压缩系数：$\displaystyle \kappa_T=-\frac{1}{V}\par{V}{p}_T$
$f(x,y,z)\equiv0\quad$类关系偏微分公式：
$\par{x}{y}_z=1\left/\par{y}{x}_z\right.$
$\par{x}{y}_z=\par{x}{w}_z\par{w}{y}_z$
$\par{x}{y}_z=-\par{x}{z}_y\par{z}{y}_x$
$\par{x}{y}_z=\par{x}{y}_w+\par{x}{w}_y\par{w}{y}_z$
定容热容：$C_V=\par{U}{T}_V=T\par{S}{T}_V$
定压热容：$C_p=\par{H}{T}_p=T\par{S}{T}_p$
热机效率：$\eta=\displaystyle\frac{W}{Q_1}=1-\frac{Q_2}{Q_1}\le 1-\frac{T_2}{T_1}$
克劳修斯不等式：$\displaystyle\sum_{i=1}^n\frac{Q_i}{T_i}\le 0$