Bridgman thermodynamic formulas

Notation used (from Table I):

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

Bridgman thermodynamic formulas

Table II

pressure

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 T \right\vert_p = - \left. \partial p \right\vert_T = 1 }

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_p = - \left. \partial p \right\vert_V = \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 S \right\vert_p = - \left. \partial p \right\vert_S = C_p/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 Q \right\vert_p = - \left. \partial p \right\vert_Q = C_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_p = - \left. \partial p \right\vert_W = p\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 U \right\vert_p = - \left. \partial p \right\vert_U = C_p - p\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 H \right\vert_p = - \left. \partial p \right\vert_H = C_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_p = - \left. \partial p \right\vert_G = -S }

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_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}

volume

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_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)}

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_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 }

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_V = - \left. \partial V \right\vert_W = 0 }

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_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 }

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_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 }

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_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) }

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_V = - \left. \partial V \right\vert_A = -S\left. \frac{\partial V}{\partial p} \right\vert_T }

entropy

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_S = - \left. \partial S \right\vert_Q = 0 }

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_S = - \left. \partial S \right\vert_W = -(p/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) }

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_S = - \left. \partial S \right\vert_U = (p/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) }

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_S = - \left. \partial S \right\vert_H = -VC_p/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 G \right\vert_S = - \left. \partial S \right\vert_G = -(1/T) \left( VC_p -ST\left. \frac{\partial V}{\partial T} \right\vert_p \right) }

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

heat

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_Q = - \left. \partial Q \right\vert_W = -p \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) }

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_Q = - \left. \partial Q \right\vert_U = p \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) }

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_Q = - \left. \partial Q \right\vert_H = -VC_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_Q = - \left. \partial Q \right\vert_G = - \left( ST \left. \frac{\partial V}{\partial T} \right\vert_p -VC_p \right) }

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_Q = - \left. \partial Q \right\vert_A = p \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) + ST \left. \frac{\partial V}{\partial T} \right\vert_p}

work

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_W = - \left. \partial W \right\vert_U = p \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) }

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_W = - \left. \partial W \right\vert_H = p \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 - V \left. \frac{\partial V}{\partial T} \right\vert_p \right) }

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_W = - \left. \partial W \right\vert_G = -p \left( V\left. \frac{\partial V}{\partial p} \right\vert_T + S \left. \frac{\partial V}{\partial p} \right\vert_T \right) }

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_W = - \left. \partial W \right\vert_A = -pS \left. \frac{\partial V}{\partial p} \right\vert_T }

internal energy

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_Q = - \left. \partial Q \right\vert_H = -V \left( C_p - p\left. \frac{\partial V}{\partial T} \right\vert_p \right) - p \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) }

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_Q = - \left. \partial Q \right\vert_G = -V \left( C_p - p\left. \frac{\partial V}{\partial T} \right\vert_p \right) +S \left( T\left. \frac{\partial V}{\partial T} \right\vert_p + p\left. \frac{\partial V}{\partial p} \right\vert_T \right) }

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

See also

• Thermodynamic relations
• Maxwell's relations