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Equation of state

The meaning of «equation of state»

In physics and thermodynamics, an equation of state is a thermodynamic equation relating state variables which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature (PVT), or internal energy.[1] Equations of state are useful in describing the properties of fluids, mixtures of fluids, solids, and the interior of stars.

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. This equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict condensation from a gas to a liquid.

Another common use is in modeling the interior of stars, including neutron stars, dense matter (quark–gluon plasmas) and radiation fields. A related concept is the perfect fluid equation of state used in cosmology.

Equations of state can also describe solids, including the transition of solids from one crystalline state to another.

In a practical context, equations of state are instrumental for PVT calculations in process engineering problems, such as petroleum gas/liquid equilibrium calculations. A successful PVT model based on a fitted equation of state can be helpful to determine the state of the flow regime, the parameters for handling the reservoir fluids, and pipe sizing.

Measurements of equation-of-state parameters, especially at high pressures, can be made using lasers.[2][3][4]

Boyle's Law was perhaps the first expression of an equation of state.[citation needed] In 1662, the 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 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:

The above relationship has also been attributed to Edme Mariotte and is sometimes referred to as Mariotte's law. However, Mariotte's work was not published until 1676.

In 1787 the French physicist Jacques Charles found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to roughly the same extent over the same 80-kelvin interval. Later, in 1802, Joseph Louis Gay-Lussac published results of similar experiments, indicating a linear relationship between volume and temperature (Charles's Law):

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