Chemical potential of ideal gas¶

The chemical potential of an ideal gas can be calculated from its temperature, concentration, and thermal wavelength.

Notation:

\(k_\text{B}\) (k_B) is boltzmann_constant.

Conditions:

The gas is ideal.

Links:

Formula on p. 394 of “Statistical Mechanics” by Terrent L. Hill (1987)

chemical_potential¶

chemical_potential of ideal gas.

Symbol:: mu
Latex:: \(\mu\)
Dimension:: energy

temperature¶

temperature of the gas.

Symbol:: T
Latex:: \(T\)
Dimension:: temperature

concentration¶

Concentration of the gas, or number_density.

Symbol:: n
Latex:: \(n\)
Dimension:: 1/volume

thermal_wavelength¶

thermal_wavelength of the gas. Also see Thermal de Broglie wavelength.

Symbol:: lambda
Latex:: \(\lambda\)
Dimension:: length

law¶

mu = k_B * T * log(n * lambda^3)

Latex:: \[\mu = k_\text{B} T \log \left( n \lambda^{3} \right)\]