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| Electron and Positron Chemical Potentials |
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chemical_potentials.f plus one include file: chem_table_storage.dek plus one 2.5 MB data file: chem_table.dat.bz2 |
The code above returns the electron and positron chemical potentials for a fully ionized stellar plasa. The electron chemical potentials do not include the electron rest mass, so the reported value is the "kinetic chemical potential". this means that the positron chemical potential must have the rest-mass terms appear explicitly, ηpos = -ηele - 2mec2. you can see this formula being used at the end of the routine. I essentially formed this code from the Helmholtz equation of state to make a stand-alone version that may be useful for computing weak reaction rates.
Top 10 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 tip. In the application here, one balances the number density of electrons from fully ionized material with the net number of electrons and positrons coming from various Fermi-Dirac integrals.