Ideal gas law

The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form:

Thermodynamics
The classical Carnot heat engine
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Material properties Property databases Specific heat capacity  ${\displaystyle c=}$ ${\displaystyle T}$ ${\displaystyle \partial S}$ ${\displaystyle N}$ ${\displaystyle \partial T}$ Compressibility  ${\displaystyle \beta =-}$ ${\displaystyle 1}$ ${\displaystyle \partial V}$ ${\displaystyle V}$ ${\displaystyle \partial p}$ Thermal expansion  ${\displaystyle \alpha =}$ ${\displaystyle 1}$ ${\displaystyle \partial V}$ ${\displaystyle V}$ ${\displaystyle \partial T}$
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Potentials Free energy Free entropy Internal energy ${\displaystyle U(S,V)}$ Enthalpy ${\displaystyle H(S,p)=U+pV}$ Helmholtz free energy ${\displaystyle A(T,V)=U-TS}$ Gibbs free energy ${\displaystyle G(T,p)=H-TS}$
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where ${\displaystyle p}$, ${\displaystyle V}$ and ${\displaystyle T}$ are the pressure, volume and temperature respectively; ${\displaystyle n}$ is the amount of substance; and ${\displaystyle R}$ is the ideal gas constant. It can also be derived from the microscopic kinetic theory, as was achieved (apparently independently) by August Krönig in 1856 and Rudolf Clausius in 1857.