Bridgman's Thermodynamic Equations

$C\_P=\backslash left(\backslash frac\{\backslash partial\; H\}\{\backslash partial\; T\}\backslash right)\_P$

$C\_P=\backslash frac\{(\backslash partial\; H)\_P\}\{(\backslash partial\; T)\_P\}$

$(\backslash partial\; H)\_P=C\_P$

$(\backslash partial\; T)\_P=1$

Bridgman's thermodynamic equations

$(\backslash partial\; T)\_P=-(\backslash partial\; P)\_T=1$

$(\backslash partial\; V)\_P=-(\backslash partial\; P)\_V=\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P$

$(\backslash partial\; S)\_P=-(\backslash partial\; P)\_S=\backslash frac\{C\_p\}\{T\}$

$(\backslash partial\; U)\_P=-(\backslash partial\; P)\_U=C\_P-P\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P$

$(\backslash partial\; H)\_P=-(\backslash partial\; P)\_H=C\_P$

$(\backslash partial\; G)\_P=-(\backslash partial\; P)\_G=-S$

$(\backslash partial\; F)\_P=-(\backslash partial\; P)\_F=-S-P\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P$

$(\backslash partial\; V)\_T=-(\backslash partial\; T)\_V=-\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T$

$(\backslash partial\; S)\_T=-(\backslash partial\; T)\_S=\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P$

$(\backslash partial\; U)\_T=-(\backslash partial\; T)\_U=T\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P+P\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T$

$(\backslash partial\; H)\_T=-(\backslash partial\; T)\_H=-V+T\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; \}\backslash right)\_P$

$(\backslash partial\; G)\_T=-(\backslash partial\; T)\_G=-V$

$(\backslash partial\; F)\_T=-(\backslash partial\; T)\_F=P\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T$

$(\backslash partial\; S)\_V=-(\backslash partial\; V)\_S=\backslash frac\{C\_P\}\{T\}\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T+\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P^2$

$(\backslash partial\; U)\_V=-(\backslash partial\; V)\_U=C\_P\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T+T\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P^2$

$(\backslash partial\; H)\_V=-(\backslash partial\; V)\_H=C\_P\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T+T\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P^2-V\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P$

$(\backslash partial\; G)\_V=-(\backslash partial\; V)\_G=-V\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P-S\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T$

$(\backslash partial\; F)\_V=-(\backslash partial\; V)\_F=-S\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T$

$(\backslash partial\; U)\_S=-(\backslash partial\; S)\_U=\backslash frac\{PC\_P\}\{T\}\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T+P\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P^2$

$(\backslash partial\; H)\_S=-(\backslash partial\; S)\_H=-\backslash frac\{VC\_P\}\{T\}$

$(\backslash partial\; G)\_S=-(\backslash partial\; S)\_G=-\backslash frac\{VC\_P\}\{T\}+S\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P$

$(\backslash partial\; F)\_S=-(\backslash partial\; S)\_F=\backslash frac\{PC\_P\}\{T\}\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T+P\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P^2+S\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P$

$(\backslash partial\; H)\_U=-(\backslash partial\; U)\_H=-VC\_P+PV\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P-PC\_P\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T-PT\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P^2$

$(\backslash partial\; G)\_U=-(\backslash partial\; U)\_G=-VC\_P+PV\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P+ST\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P+SP\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T$

$(\backslash partial\; F)\_U=-(\backslash partial\; U)\_F=-P(C\_P+S)\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T+PT\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P^2+ST\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P$

$(\backslash partial\; G)\_H=-(\backslash partial\; H)\_G=-V(C\_P+S)+TS\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P$

$(\backslash partial\; F)\_H=-(\backslash partial\; H)\_F=\backslash leftV\}\{\backslash partial\; T\}\backslash right)\_P\backslash right\backslash leftV\}\{\backslash partial\; T\}\backslash right)\_P\backslash right+PC\_P\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T$

$(\backslash partial\; F)\_G=-(\backslash partial\; G)\_F=-SV-\_P\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; P\}\backslash right)\_T-PV\backslash left(\backslash frac\{\backslash partial\; V\}\{\backslash partial\; T\}\backslash right)\_P$

References

• Bridgman, P.W., Phys. Rev., 3, 273 (1914).

• Lewis, G.N., and Randall, M., "Thermodynamics", 2nd Edition, McGraw-Hill Book Company, New York, 1961.

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