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For a mixture (j=1,2,...) of ideal gases, each at partial pressure P j, it can be shown that the chemical potential μ j will be given by the above expression with the pressure P replaced by P j. The thermodynamic potentials for an ideal gas can now be written as functions of T , V , and N as:
A physical situation where the chemical potential for photons can differ from zero are material-filled optical microcavities, with spacings between cavity mirrors in the wavelength regime. In such two-dimensional cases, photon gases with tuneable chemical potential, much reminiscent to gases of material particles, can be observed. [22]
The relative activity of a species i, denoted a i, is defined [4] [5] as: = where μ i is the (molar) chemical potential of the species i under the conditions of interest, μ o i is the (molar) chemical potential of that species under some defined set of standard conditions, R is the gas constant, T is the thermodynamic temperature and e is the exponential constant.
N i is the number of particles (or number of moles) composing the ith chemical component. This is one form of the Gibbs fundamental equation. [10] In the infinitesimal expression, the term involving the chemical potential accounts for changes in Gibbs free energy resulting from an influx or outflux of particles.
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
A thermodynamic potential (or more accurately, a thermodynamic potential energy) [1] [2] is a scalar quantity used to represent the thermodynamic state of a system. Just as in mechanics , where potential energy is defined as capacity to do work, similarly different potentials have different meanings.
The chemical potential is simply another name for the partial molar Gibbs free energy (or the partial Gibbs free energy, depending on whether N is in units of moles or particles).
Thus water behaves as though it is an ideal gas that is already under about 20,000 atmospheres (2 GPa) pressure, and explains why water is commonly assumed to be incompressible: when the external pressure changes from 1 atmosphere to 2 atmospheres (100 kPa to 200 kPa), the water behaves as an ideal gas would when changing from 20,001 to 20,002 ...