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At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures.
However, this equation of state continues to be widely used in models of solid explosives. Of more elaborate equations of state, the most used in earth physics is the Birch–Murnaghan equation of state. In shock physics of metals and alloys, another widely used equation of state is the Mie–Gruneisen equation of state.
One way to write the van der Waals equation is: [8] [9] [10] = where is pressure, is temperature, and = / is molar volume. In addition is the Avogadro constant, is the volume, and is the number of molecules (the ratio / is a physical quantity with base unit mole (symbol mol) in the SI).
The Benedict–Webb–Rubin equation (BWR), named after Manson Benedict, G. B. Webb, and L. C. Rubin, is an equation of state used in fluid dynamics.Working at the research laboratory of the M. W. Kellogg Company, the three researchers rearranged the Beattie–Bridgeman equation of state and increased the number of experimentally determined constants to eight.
The Birch–Murnaghan isothermal equation of state, published in 1947 by Albert Francis Birch of Harvard, [1] is a relationship between the volume of a body and the pressure to which it is subjected. Birch proposed this equation based on the work of Francis Dominic Murnaghan of Johns Hopkins University published in 1944, [ 2 ] so that the ...
The first constitutive equation (constitutive law) was developed by Robert Hooke and is known as Hooke's law.It deals with the case of linear elastic materials.Following this discovery, this type of equation, often called a "stress-strain relation" in this example, but also called a "constitutive assumption" or an "equation of state" was commonly used.
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.
A temperature-corrected version that is used in computational mechanics has the form [6] [7]: 61 = [] +;:= where is the bulk speed of sound, is the initial density, is the current density, is Grüneisen's gamma at the reference state, = / is a linear Hugoniot slope coefficient, is the shock wave velocity, is the particle velocity, and is the internal energy per unit reference volume.