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In physics, the thermal equation of state is a mathematical expression of pressure P, temperature T, and, volume V.The thermal equation of state for ideal gases is the ideal gas law, expressed as PV=nRT (where R is the gas constant and n the amount of substance), while the thermal equation of state for solids is expressed as:
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
Assuming the unknown compound behaves as an ideal gas, the number of moles of the unknown compound, n, can be determined by using the ideal gas law, p V = n R T {\displaystyle pV=nRT\,} where the pressure, p , is the atmospheric pressure , V is the measured volume of the vessel, T is the absolute temperature of the hot bath, and R is the gas ...
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.
T is the absolute temperature; R is the gas constant, which must be expressed in units consistent with those chosen for pressure, volume and temperature. For example, in SI units R = 8.3145 J⋅K −1 ⋅mol −1 when pressure is expressed in pascals, volume in cubic meters, and absolute temperature in kelvin.
P = pressure V = volume n = number of moles R = universal gas constant T = temperature. The ideal gas equation of state can be arranged to give: = / or = / The following partial derivatives are obtained from the above equation of state: