Amagats law states that the extensive volume V = Nv of a gas mixture is equal to the sum of volumes V of the K component gases, if the temperature T and the pressure p' remain the same:
This is the experimental expression of volume as an extensive quantity.
According to Amagat's law of partial volume, the total volume of a non-reacting mixture of gases at constant temperature and pressure should be equal to the sum of the individual partial volumes of the constituent gases. So if  are considered to be the partial volumes of components in the gaseous mixture, then the total volume  would be represented as
Both Amagats and Daltons laws predict the properties of gas mixtures. Their predictions are the same for ideal gases. However, for real (non-ideal) gases, the results differ. Daltons law of partial pressures assumes that the gases in the mixture are non-interacting (with each other) and each gas independently applies its own pressure, the sum of which is the total pressure. Amagats law assumes that the volumes of the component gases (again at the same temperature and pressure) are additive; the interactions of the different gases are the same as the average interactions of the components.
The interactions can be interpreted in terms of a second virial coefficient B(T) for the mixture. For two components, the second virial coefficient for the mixture can be expressed as
where the subscripts refer to components 1 and 2, the X are the mole fractions, and the B are the second virial coefficients. The cross term B of the mixture is given by
: for Dalton's law
and
: for Amagat's law.
When the volumes of each component gas (same temperature and pressure) are very similar, then Amagats law becomes mathematically equivalent to Vegards law for solid mixtures.