# Amagat

An amagat is a practical unit of number density. Although it can be applied to any substance at any conditions, it is defined as the number of ideal gas molecules per unit volume at 1 atm (= 101.325 kPa) and 0 °C (= 273.15 K).[1] It is named after Émile Amagat, who also has Amagat's law named after him. The abbreviated form of amagat is "amg."

## Definition

Number density in amg, denoted here by ${\displaystyle \eta }$, is defined as

${\displaystyle \eta ={\frac {n}{n_{0}}}}$,

where n0 = 1 amg = 2.686 7805×1025 m−3 = 44.615 036 mol/m3 is the Loschmidt constant.

In practice, number density of an ideal gas at pressure P and temperature T can be calculated as[2]

${\displaystyle \eta =\left({\frac {p}{p_{0}}}\right)\left({\frac {T_{0}}{T}}\right)\,{\rm {amg}}}$,

where T0 = 273.15 K and p0 = 101.325 kPa.

## Example

Number density of an ideal gas (such as air) at room temperature (20 °C) and 1 atm (101.325 kPa) is

${\displaystyle \eta =\left({\frac {1\,{\rm {atm}}}{p_{0}}}\right)\left({\frac {273.15\,{\rm {K}}}{(273.15+20)\,{\rm {K}}}}\right){\rm {amg}}=0.932\,{\rm {amg}}}$.

## References

1. ^ Hirschfelder, Joseph O.; Curtiss, Charles F.; Bird, R. Byron (1967), Molecular Theory of Gases and Liquids (Corrected printing ed.), John Wiley & Sons, Inc.
2. ^ In this formula, absolute units of pressure and temperature, relative to vacuum and absolute zero, must be used.