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:
Table of thermodynamic potentials
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Name
Symbol
Formula
Natural variables
Internal energy
U
{\displaystyle U}
∫
(
T
d
S
−
p
d
V
+
∑
i
μ
i
d
N
i
)
{\displaystyle \int \left(T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\mathrm {d} N_{i}\right)}
S
,
V
,
{
N
i
}
{\displaystyle S,V,\{N_{i}\}}
Helmholtz free energy
F
{\displaystyle F}
U
−
T
S
{\displaystyle U-TS}
T
,
V
,
{
N
i
}
{\displaystyle T,V,\{N_{i}\}}
Enthalpy
H
{\displaystyle H}
U
+
p
V
{\displaystyle U+pV}
S
,
p
,
{
N
i
}
{\displaystyle S,p,\{N_{i}\}}
Gibbs free energy
G
{\displaystyle G}
U
+
p
V
−
T
S
{\displaystyle U+pV-TS}
T
,
p
,
{
N
i
}
{\displaystyle T,p,\{N_{i}\}}
Landau potential, or
grand potential
Ω
{\displaystyle \Omega }
,
Φ
G
{\displaystyle \Phi _{\text{G}}}
U
−
T
S
−
{\displaystyle U-TS-}
∑
i
{\displaystyle \sum _{i}\,}
μ
i
N
i
{\displaystyle \mu _{i}N_{i}}
T
,
V
,
{
μ
i
}
{\displaystyle T,V,\{\mu _{i}\}}