|
Virial Coefficient
Virial coefficients B_i appear as coefficients in the virial expansion of the pressure of a many-particle system in powers of the density, providing systematic corrections to the ideal gas law. They are characteristic of the interaction potential between the particles and in general depend on the temperature. The second virial coefficient B_2 depends only on the pair interaction between the particles, the third (B_3) depends on 2- and non-additive 3-body interactions, and so on. Derivation The first step in obtaining a closed expression for virial coefficients is a cluster expansion of the grand canonical partition function : \Xi = \sum_ = e^ Here p is the pressure, V is the volume of the vessel containing the particles, k_B is Boltzmann's constant, T is the absolute temperature, \lambda =\exp mu/(k_BT) is the fugacity, with \mu the chemical potential. The quantity Q_n is the canonical partition function of a subsystem of n particles: : Q_n = \operatorname e^ Here H(1,2,\ld ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virial Expansion
The classical virial expansion expresses the pressure P of a many-particle system in equilibrium as a power series in the density: Z \equiv \frac = A + B\rho + C\rho^2 + \cdots where Z is called the compressibility factor. This is the virial equation of state, the most general function relating pressure, , density, , and temperature, , of fluids. It was first proposed by Kamerlingh Onnes.Kamerlingh Onnes H., Expression of state of gases and liquids by means of series, KNAW Proceedings, 4, 1901-1902, Amsterdam, 125-147 (1902). The compressibility factor is a dimensionless quantity, indicating how much a real fluid deviates from an ideal gas. ''A'' is the first virial coefficient, which has a constant value of 1. It makes the statement that at low density, all fluids behave like ideal gases. The virial coefficients , , , etc., are temperature-dependent, and are generally presented as Taylor series in terms of . Second and third virial coefficients The second, , and third, , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maria Goeppert-Mayer
Maria Goeppert Mayer (; June 28, 1906 – February 20, 1972) was a German-born American theoretical physicist, and Nobel laureate in Physics for proposing the nuclear shell model of the atomic nucleus The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron i .... She was the second woman to win a Nobel Prize in physics, the first being Marie Curie. In 1986, the Maria Goeppert-Mayer Award for early-career women physicists was established in her honor. A graduate of the University of Göttingen, Goeppert Mayer wrote her doctoral thesis on the theory of possible two-photon absorption by atoms. At the time, the chances of experimentally verifying her thesis seemed remote, but the development of the laser in the 1960s later permitted this. Today, the unit for the two-photon absorption cross sect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
