Bridgman thermodynamic formulas

Notation used (from Table I):

• $p$ is the pressure.
• $T$ is the temperature (in Kelvin).
• $V$ is the volume.
• $S$ is the entropy.
• $Q$ is the heat.
• $W$ is the work.
• $U$ is the internal energy.
• $H$ is the enthalpy
• $G$ is the Gibbs energy function
• $A$ is the Helmholtz energy function.

Bridgman thermodynamic formulas

Table II

pressure

$\left.\partial T\right\vert _{p}=-\left.\partial p\right\vert _{T}=1$

$\left.\partial V\right\vert _{p}=-\left.\partial p\right\vert _{V}=\left.{\frac {\partial V}{\partial T}}\right\vert _{p}$

$\left.\partial S\right\vert _{p}=-\left.\partial p\right\vert _{S}=C_{p}/T$

$\left.\partial Q\right\vert _{p}=-\left.\partial p\right\vert _{Q}=C_{p}$

$\left.\partial W\right\vert _{p}=-\left.\partial p\right\vert _{W}=p\left.{\frac {\partial V}{\partial T}}\right\vert _{p}$

$\left.\partial U\right\vert _{p}=-\left.\partial p\right\vert _{U}=C_{p}-p\left.{\frac {\partial V}{\partial T}}\right\vert _{p}$

$\left.\partial H\right\vert _{p}=-\left.\partial p\right\vert _{H}=C_{p}$

$\left.\partial G\right\vert _{p}=-\left.\partial p\right\vert _{G}=-S$

$\left.\partial A\right\vert _{p}=-\left.\partial p\right\vert _{A}=-\left(S+p\left.{\frac {\partial V}{\partial T}}\right\vert _{p}\right)$

temperature

$\left.\partial V\right\vert _{T}=-\left.\partial T\right\vert _{V}=-\left.{\frac {\partial V}{\partial p}}\right\vert _{T}$

$\left.\partial S\right\vert _{T}=-\left.\partial T\right\vert _{S}=\left.{\frac {\partial V}{\partial T}}\right\vert _{p}$

$\left.\partial Q\right\vert _{T}=-\left.\partial T\right\vert _{Q}=T\left.{\frac {\partial V}{\partial T}}\right\vert _{p}$

$\left.\partial W\right\vert _{T}=-\left.\partial T\right\vert _{W}=-p\left.{\frac {\partial V}{\partial p}}\right\vert _{T}$

$\left.\partial U\right\vert _{T}=-\left.\partial T\right\vert _{U}=T\left.{\frac {\partial V}{\partial T}}\right\vert _{p}+p\left.{\frac {\partial V}{\partial p}}\right\vert _{T}$

$\left.\partial H\right\vert _{T}=-\left.\partial T\right\vert _{H}=-V+T\left.{\frac {\partial V}{\partial T}}\right\vert _{p}$

$\left.\partial G\right\vert _{T}=-\left.\partial T\right\vert _{G}=-V$

$\left.\partial A\right\vert _{T}=-\left.\partial T\right\vert _{A}=p\left.{\frac {\partial V}{\partial p}}\right\vert _{T}$

volume

$\left.\partial S\right\vert _{V}=-\left.\partial V\right\vert _{S}=1/T\left(C_{p}\left.{\frac {\partial V}{\partial p}}\right\vert _{T}+T\left.\left({\frac {\partial V}{\partial T}}\right)^{2}\right\vert _{p}\right)$

$\left.\partial Q\right\vert _{V}=-\left.\partial V\right\vert _{Q}=C_{p}\left.{\frac {\partial V}{\partial p}}\right\vert _{T}+T\left.\left({\frac {\partial V}{\partial T}}\right)^{2}\right\vert _{p}$

$\left.\partial W\right\vert _{V}=-\left.\partial V\right\vert _{W}=0$

$\left.\partial U\right\vert _{V}=-\left.\partial V\right\vert _{U}=C_{p}\left.{\frac {\partial V}{\partial p}}\right\vert _{T}+T\left.\left({\frac {\partial V}{\partial T}}\right)^{2}\right\vert _{p}$

$\left.\partial H\right\vert _{V}=-\left.\partial V\right\vert _{H}=C_{p}\left.{\frac {\partial V}{\partial p}}\right\vert _{T}+T\left.\left({\frac {\partial V}{\partial T}}\right)^{2}\right\vert _{p}-V\left.{\frac {\partial V}{\partial T}}\right\vert _{p}$

$\left.\partial G\right\vert _{V}=-\left.\partial V\right\vert _{G}=-\left(V\left.{\frac {\partial V}{\partial T}}\right\vert _{p}+S\left.{\frac {\partial V}{\partial p}}\right\vert _{T}\right)$

$\left.\partial A\right\vert _{V}=-\left.\partial V\right\vert _{A}=-S\left.{\frac {\partial V}{\partial p}}\right\vert _{T}$

See also

• Thermodynamic relations
• Maxwell's relations