**
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*