Everything about Equation Of State totally explained
» For the use of this concept in cosmology, see Equation of state (cosmology)In
physics and
thermodynamics, an
equation of state is a relation between
state variables. More specifically, an equation of state is a
thermodynamic equation describing the state of matter under a given set of physical conditions. It is a
constitutive equation which provides a mathematical relationship between two or more
state functions associated with the matter, such as its
temperature,
pressure,
volume, or
internal energy. Equations of state are useful in describing the properties of
fluids, mixtures of fluids,
solids, and even the interior of
stars.
Overview
The most prominent use of an equation of state is to predict the state of gases and liquids. One of the simplest equations of state for this purpose is the
ideal gas law, which is roughly accurate for gases at low pressures and high temperatures. However, this equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict condensation from a gas to a liquid. Therefore, a number of much more accurate equations of state have been developed for gases and liquids. At present, there's no single equation of state that accurately predicts the properties of all substances under all conditions.
In addition to predicting the behavior of gases and liquids, there are also equations of state for predicting the volume of
solids, including the transition of solids from one crystalline state to another. There are equations that model the interior of
stars, including
neutron stars. A related concept is the
perfect fluid equation of state used in cosmology.
Historical
Boyle's law (1662)
Boyle's Law was perhaps the first expression of an equation of state. In 1662, the noted Irish physicist and chemist
Robert Boyle performed a series of experiments employing a J-shaped glass tube, which was sealed on one end.
Mercury was added to the tube, trapping a fixed quantity of air in the short, sealed end of the tube. Then the volume of gas was carefully measured as additional mercury was added to the tube. The pressure of the gas could be determined by the difference between the mercury level in the short end of the tube and that in the long, open end. Through these experiments, Boyle noted that the gas volume varied inversely with the pressure. In mathematical form, this can be stated as:
»
where α is an exponent specific to the system (for example in the absence of a potential field,
α=3/2),
z is exp(
μ/
kT) where
μ is the
chemical potential, Li is the
polylogarithm, ζ is the
Riemann zeta function, and
Tc is the
critical temperature at which a
Bose-Einstein condensate begins to form.
Equations of state for solids
Johnson Holmquist Equation of State
Further Information
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