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| Electron and Positron Chemical Potentials |
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The tool in
chem_poten.tbz
returns the electron and positron chemical
potentials as a function of temperature, density and Ye
for a fully ionized stellar plasma.
The electron chemical potentials returned do not include the electron rest mass, so the value returned is the "kinetic chemical potential". This means that the positron chemical potential must have the rest-mass terms appear explicitly, ηpos = -ηele - 2mec2. One can see this being applied at the end of the relevant routine. This tool is derived from the Helmholtz equation of state. A stand-alone electron/positron chemical potential solver may be useful for Compton opacities (e.g., Poutanen 2017) weak reaction rates, reaction rate screening factors, and others where invoking the full machinery of an equation of state may not be as desirable. |
Ten tips about the chemical potential (from Peter Saeta)
- It expresses how eager a system is for particles.
- In equilibrium it is equal in two systems placed in diffusive contact.
- Particles move from a region of high chemical potential to a region of low chemical potential.
- It can be found by differentiating thermodynamic potentials with respect to N.
- It has an internal part and an external part; the external part is just a normal per-particle potential energy, such as mgh.
- It is the Gibbs free energy per particle, G/N.
- It is used to describe chemical equilibria.
- For a monatomic ideal gas, it is kT ln (νQ/ν).
- It is enormously useful in describing equations of state.
- It is the factor you use to get the particle number right!
Number 10 is probably the most pragmatic. In the tool chem_poten.tbz, one balances the number density of electrons from fully ionized material with the net number density of electrons and positrons coming from the relevant Fermi-Dirac statistics.