Chemical potential

The chemical potential of a thermodynamic system is the amount by which the energy of the system would change if an additional particle were introduced, with the entropy and volume held fixed. (But see discussion of this article, point 4.) If a system contains more than one species of particle, there is a separate chemical potential associated with each species, defined as the change in energy when the number of particles of that species is increased by one.

Related Topics:
Thermodynamic - Energy - Entropy - Volume

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The chemical potential is particularly important when studying systems of reacting particles. Consider the simplest case of two species, where a particle of species 1 can transform into a particle of species 2 and vice versa. An example of such a system is a supersaturated mixture of water liquid (species 1) and water vapor (species 2). If the system is at equilibrium, the chemical potentials of the two species must be equal. Otherwise, any increase in one chemical potential would result in an irreversible net release of energy of the system in the form of heat (see second law of thermodynamics) when that species of increased potential transformed into the other species, or a net gain of energy (again in the form of heat) if the reverse tranformation took place. In chemical reactions, the equilibrium conditions are generally more complicated because more than two species are involved. In this case, the relation between the chemical potentials at equilibrium is given by the law of mass action.

Related Topics:
Heat - Second law of thermodynamics - Chemical reaction - Law of mass action

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Since the chemical potential is a thermodynamic quantity, it is defined independently of the microscopic behavior of the system, i.e. the properties of the constituent particles. However, some systems contain important variables that are equivalent to the chemical potential. In Fermi gases and Fermi liquids, the chemical potential at zero temperature is equivalent to the Fermi energy. In electronic systems, the chemical potential is equivalent to the negative of the electrical potential.

Related Topics:
Fermi gas - Fermi liquid - Zero temperature - Fermi energy - Electronic - Electrical potential

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For relativistic systems (systems in which the rest mass is much smaller than the thermal energy) the chemical potential is related to symmetries and charges. Each conserved charge is associated with a chemical potential. Thus, in a gas of photons and phonons, there is no chemical potential. However, if the temperature of such a system were to rise above the threshold for pair production of electrons, then it might be sensible to add a chemical potential for the electrical charge. This would control the electric charge density of the system, and hence the excess of electrons over positrons, but not the number of photons. In the context in which one meets a phonon gas, temperatures high enough to pair produce other particles are seldom relevant. QCD matter is the prime example of a system in which many such chemical potentials appear.

Related Topics:
Relativistic - Rest mass - Thermal - Energy - Charge - Photon - Phonon - Pair production - Electron - Electric charge - Positron - QCD matter

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