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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 ...
The ideal gas law is the equation of state for an ideal gas, given by: = where P is the pressure; V is the volume; n is the amount of substance of the gas (in moles) 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.
The basic gas laws were discovered by the end of the 18th century when scientists found out that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases. The combination of several empirical gas laws led to the development of the ideal gas law.
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.
The gas constant occurs in the ideal gas law: = = where P is the absolute pressure, V is the volume of gas, n is the amount of substance, m is the mass, and T is the thermodynamic temperature. R specific is the mass-specific gas constant. The gas constant is expressed in the same unit as molar heat.
The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by Sadi Carnot in 1824 in his book Reflections on the Motive Power of Fire. By 1860, as formalized in the works of scientists such as Rudolf Clausius and William Thomson , what are now known as the first and second laws were ...
The maximum work is thus regarded as the diminution of the free, or available, energy of the system (Gibbs free energy G at T = constant, P = constant or Helmholtz free energy F at T = constant, V = constant), whilst the heat given out is usually a measure of the diminution of the total energy of the system (internal energy).
Notably, for an ideal gas the ideal gas law holds, that in mathematical form is simply: p = n T {\displaystyle p=nT} where n is the number density , and T is the absolute temperature , provided it is measured in energetic units (i.e. in joules ) through multiplication with the Boltzmann constant .