**
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.

**
Thermodynamic Identity
** -
The Thermodynamic Identity relates the energy

*U*
to the 6 variables we have discussed:

*dU* = *τ* *dσ* - *p* *dV* + *μ* *dN*