Humid air weighs less than dry air, despite how muggy days feel
A cubic metre of air at sea level and 15 °C has a mass of about 1.225 kilograms under the International Standard Atmosphere, roughly one eight-hundredth of the same volume of water. That figure shifts constantly with altitude, temperature, pressure and, surprisingly, moisture, which makes air lighter rather than heavier.
Moisture lightens air because of molecular weight. Water vapour has a molar mass of about 18 grams per mole, while dry air averages around 29. At a fixed temperature and pressure a given volume always holds the same number of gas molecules, as Avogadro's law requires, so every water molecule that enters pushes out a heavier nitrogen or oxygen molecule. Treating humid air as a blend of ideal gases gives density estimates accurate to within 0.2 per cent between minus 10 and 50 °C.
Temperature matters just as much. Holding pressure and humidity steady, warmer air is less dense, so it rises while cooler air sinks, a behaviour the ideal gas law captures neatly: density equals pressure multiplied by molar mass, divided by the gas constant times absolute temperature. Dry air comes to about 1.2754 kilograms per cubic metre at 0 °C and 100 kilopascals, falling to 1.2041 at 20 °C and standard sea-level pressure.
Height thins it further. Estimating density at altitude inside the troposphere, the lowest ten or so kilometres of the atmosphere, calls for extra constants: sea-level pressure of 101,325 pascals, a standard temperature of 288.15 kelvin and gravitational acceleration of 9.80665 metres per second squared. The resulting pressure formula works only up to roughly 18 kilometres, and lower away from the equator.
Such numbers are not academic. Aeronautical engineers, meteorologists, air-conditioning designers, agricultural modellers and anyone working with compressed air all rely on them. Because air is a mixture, every equation simplifies its behaviour to some degree, and the right formula depends on which instruments are taking the measurements.
Source: Density of air
