• ### 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  + 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  + V dp + μ dN.

• ### Helmholtz Free Energy

The Helmholtz Free Energy, F, is defined as F = U - τσ and its identity is dF = - σ  - 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  - p dV + μ dN