The ideal gas equation of state remains valid as the density is decreased, even holding for a free-molecule gas.
The ideal gas equation of state is an amalgamation of three ideal gas laws that were formulated independently.
Nevertheless, the ideal gas equation is a highly successful way to understand how gases shift and change depending on their surroundings.
When air is lifted, it is carried to a region of lower pressure, where it will expand and cool as described by the gas equation.
The ideal gas equation of state can be deduced by calculating the pressure as caused by molecular impacts on a container wall.
A thermodynamic result of relevance here is that the ideal gas equation of state requires that the internal energy depend on temperature alone, not on pressure or density.
This seemingly paradoxical result occurs because doubling the pressure also doubles the concentration, according to the ideal gas equation of state, and hence doubles the concentration difference, which is the driving force for diffusion.
If the rate increases as Ts at constant molar density (where s usually lies between 1/2 and 1), then it will increase as T1 + s at constant pressure, according to the ideal gas equation of state.
To a first approximation, molecule-molecule collisions do not affect the ideal gas equation of state, pv = RT, but real gases at nonzero densities show deviations from this equation that are due to interactions among the molecules.
With the three relationships between pressure, volume and temperature measured and written down, French engineer Benoît Paul Émile Clapeyron, one of the founding fathers of thermodynamics, combined the work of Boyle, Charles and Gay‑Lussac into the combined ideal gas equation above, in 1834.
The pressure of the water vapour, which contributes to the pressure of the atmosphere, can be calculated from the absolute humidity dv by the gas equation: in which R is the gas constant, T the absolute temperature, Mw the molecular weight of water, and e the water vapour pressure in millibars (mb).
