Chemical potential is particle count derivative of internal energy

The chemical potential of a system is the amount of energy the system absorbs or releases due to the introduction of a particle into the system, i.e. when the particle count increases by one.

Links:

  1. Wikipedia.

chemical_potential

chemical_potential of the system.

Symbol:

mu

Latex:

\(\mu\)

Dimension:

energy

entropy

entropy of the system.

Symbol:

S

Latex:

\(S\)

Dimension:

energy/temperature

volume

volume of the system.

Symbol:

V

Latex:

\(V\)

Dimension:

volume

particle_count

particle_count of the system.

Symbol:

N

Latex:

\(N\)

Dimension:

dimensionless

internal_energy

internal_energy of the system as a function of its natural variables.

Symbol:

U(S, V, N)

Latex:

\(U{\left(S,V,N \right)}\)

Dimension:

energy

law

mu = Derivative(U(S, V, N), N)

Latex:
\[\mu = \frac{\partial}{\partial N} U{\left(S,V,N \right)}\]