Gas dioxide, and air expand to the same extent over the same 80 kelvin interval. He noted that, for an ideal gas at constant pressure, the volume is directly proportional to its temperature: In 1802, Joseph Louis Gay-Lussac published results of similar, though more extensive experiments. Gay-Lussac credited Charles' earlier work by naming the law in his honor. Gay-Lussac himself is credited with the law describing pressure, which he found in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to its temperature. In 1811, Amedeo Avogadro verified that equal volumes of pure
Amagat's law pressure, the sum of which is the total pressure. Amagat's 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's are the mole fractions, and the B's are the second virial coefficients. The cross term,