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The virial expansion is a model of thermodynamic equations of state. It expresses the pressure P of a gas in local equilibrium as a power series of the density. This equation may be represented in terms of the compressibility factor, Z, as This equation was first proposed by Kamerlingh Onnes. [1] The terms A, B, and C represent the virial ...
Virial theorem. In statistical mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by a conservative force (where the work done is independent of path) with that of the total potential energy of the system.
Virial coefficients 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 depends ...
Virial mass. In astrophysics, the virial mass is the mass of a gravitationally bound astrophysical system, assuming the virial theorem applies. In the context of galaxy formation and dark matter halos, the virial mass is defined as the mass enclosed within the virial radius of a gravitationally bound system, a radius within which the system ...
The Boyle temperature is formally defined as the temperature for which the second virial coefficient, , becomes zero. It is at this temperature that the attractive forces and the repulsive forces acting on the gas particles balance out. This is the virial equation of state and describes a real gas. Since higher order virial coefficients are ...
Compressibility factor values are usually obtained by calculation from equations of state (EOS), such as the virial equation which take compound-specific empirical constants as input. For a gas that is a mixture of two or more pure gases (air or natural gas, for example), the gas composition must be known before compressibility can be calculated.
Virial stress is a measure of mechanical stress on an atomic scale for homogeneous systems. The name is derived from the Latin word vis, meaning force: "Virial is then derived from Latin as well, stemming from the word virias (plural of vis) meaning forces." [1] The expression of the (local) virial stress can be derived as the functional ...
Pitzer equations[1] are important for the understanding of the behaviour of ions dissolved in natural waters such as rivers, lakes and sea-water. [2][3][4] They were first described by physical chemist Kenneth Pitzer. [5] The parameters of the Pitzer equations are linear combinations of parameters, of a virial expansion of the excess Gibbs free ...