At sufficiently low pressure (and not too high temperature so that neither ionisation nor dissociation occurs) all gases satisfy to a very good approximation the equation of state of the ideal gas:
pV = NkT
which links the gas pressure p, the gas volume V and the (very large) gas particle number N, with the temperature T. The constant k = 1.38065·10-23 J/K is the Boltzmann constant which is fundamental to statistical thermodynamics and may be determined at the triple point of water by measurement of p, V and N.
The gas thermometer can also be used for temperature measurement relative to the triple point of water, TTPW (and thus for realising the thermodynamic temperature scale) without k being known, because
T/TTPW = pV/(pTPW·VTPW)
is valid for fixed particle number N. Here, the quantities measured at TTPW are also subscripted with TPW. The gas thermometer is effectively operated either at constant pressure or at constant volume. As a primary thermometer, it is usually operated as a constant-volume gas thermometer (CVGT).