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It is an equation of state that relates the pressure, temperature, and molar volume in a fluid. However, it can be written in terms of other, equivalent, properties in place of the molar volume, for example specific volume, or number density. The equation modifies the ideal gas law in two ways. First its particles have a finite diameter ...
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.
(Note - the relation between pressure, volume, temperature, and particle number which is commonly called "the equation of state" is just one of many possible equations of state.) If we know all k+2 of the above equations of state, we may reconstitute the fundamental equation and recover all thermodynamic properties of the system.
where ln denotes the natural logarithm, is the thermodynamic equilibrium constant, and R is the ideal gas constant.This equation is exact at any one temperature and all pressures, derived from the requirement that the Gibbs free energy of reaction be stationary in a state of chemical equilibrium.
Bernoulli's principle is a key concept in fluid dynamics that relates pressure, density, speed and height. Bernoulli's principle states that an increase in the speed of a parcel of fluid occurs simultaneously with a decrease in either the pressure or the height above a datum. [1]:
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.
Coulomb's law has charge in place of mass and a different constant. Newton's law was later superseded by Albert Einstein 's theory of general relativity , but the universality of the gravitational constant is intact and the law still continues to be used as an excellent approximation of the effects of gravity in most applications.
Applied to a fluid with a given equation of state, the Friedmann equations yield the time evolution and geometry of the universe as a function of the fluid density. Some cosmologists call the second of these two equations the Friedmann acceleration equation and reserve the term Friedmann equation for only the first equation.