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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. \partial V \right\vert_T = - \left. \partial T \right\vert_V = - \left. \frac{\partial V}{\partial p} \right\vert_T}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. \partial S \right\vert_T = - \left. \partial T \right\vert_S = \left. \frac{\partial V}{\partial T} \right\vert_p}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. \partial Q \right\vert_T = - \left. \partial T \right\vert_Q = T\left. \frac{\partial V}{\partial T} \right\vert_p}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. \partial W \right\vert_T = - \left. \partial T \right\vert_W = - p\left. \frac{\partial V}{\partial p} \right\vert_T}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. \partial H \right\vert_T = - \left. \partial T \right\vert_H = -V + T\left. \frac{\partial V}{\partial T} \right\vert_p }

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. \partial G \right\vert_T = - \left. \partial T \right\vert_G = -V }

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. \partial A \right\vert_T = - \left. \partial T \right\vert_A = p\left. \frac{\partial V}{\partial p} \right\vert_T}

See also

• Thermodynamic relations
• Maxwell's relations