Loschmidt constant

The Loschmidt constant or Loschmidt's number (symbol: n₀) is the number of particles (atoms or molecules) of an ideal gas per volume (the number density), and usually quoted at standard temperature and pressure. The 2014 CODATA recommended value is 2.6867811(15)×10²⁵ per cubic metre at 0 °C and 1 atm and the 2006 CODATA recommended value was 2.686 7774(47)×10²⁵ per cubic metre at 0 °C and 1 atm. It is named after the Austrian physicist Johann Josef Loschmidt, who was the first to estimate the physical size of molecules in 1865. The term "Loschmidt constant" is also sometimes used to refer to the Avogadro constant, particularly in German texts.

By ideal gas law, ${\displaystyle p_{0}V=Nk_{B}T_{0}}$, and since ${\displaystyle N=n_{0}V}$, the Loschmidt constant is given by the relationship

${\displaystyle n_{0}={\frac {p_{0}}{k_{\text{B}}T_{0}}},}$

where k_B is the Boltzmann constant, p₀ is the standard pressure, and T₀ is the standard thermodynamic temperature.

Since the Avogadro constant N_A satisfies ${\displaystyle R=N_{\text{A}}k}$, the Loschmidt constant satisfies

${\displaystyle n_{0}={\frac {p_{0}N_{\text{A}}}{RT_{0}}},}$

where R is the ideal gas constant.

Being a measure of number density, the Loschmidt constant is used to define the amagat, a practical unit of number density for gases and other substances:

1 amagat = n₀ = 2.6867811×10²⁵ m⁻³,

such that the Loschmidt constant is exactly 1 amagat.