Thermodynamics: Structure
Terms
Chemical Potential
-
The Chemical Potential is defined such that:
.
.
Enthalpy
-
The Enthalpy,
H
, is defined as
H = U = pv
and its identity is
dH = τ dσ + V dp + μ dN
.
Extensive
-
An extensive variable of a system doubles upon duplication of the system. Important extensive variables are the volume
V
, the entropy
σ
, the number
N
and the energy
U
. Compare to intensive variables.
Gibbs Free Energy
-
The Gibbs Free Energy,
G
, is defined as
G = U - τσ + pV
and its identity is
dG = - σ dτ + V dp + μ dN
.
Helmholtz Free Energy
-
The Helmholtz Free Energy,
F
, is defined as
F = U - τσ
and its identity is
dF = - σ dτ - p dV + μ dN
.
Intensive
-
An intensive variable of a system remains constant upon duplication of the system. Important intensive variables are the temperature
τ
, the chemical potential
μ
, and the pressure
p
. Compare to extensive variables.
Legendre Transform
-
The Legendre Transform is a mathematical tool that we employ to change variables in expression of then energy, such as defining
F = U - τσ
in order to change variables from
σ
to
τ
in the energy.
Maxwell Relations
-
The Maxwell Relations give relationships between the partial derivative of one variable with respect to a variable in a different pairing and the corresponding cross partial derivative of the other variable in the second pairing with respect to the other variable in the first.
Pressure
-
The pressure is defined such that:
p = -
, and is one of the important intensive variables in thermodynamics.
, and is one of the important intensive variables in thermodynamics.
Thermodynamic Identity
-
The Thermodynamic Identity relates the energy
U
to the 6 variables we have discussed:
dU = τ dσ - p dV + μ dN





