# 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  + 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

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