The air-water system is a unique on (we all live in it for a start...) and there are correspondingly a range of rather unusual measures used for it.

Despite their appearance, all these are just ways of expressing the amount of water in air, i.e. the composition of the air (w.r.t. water) or the concentration of water in air.

Although there is a lot of water around (in the sea etc.) the
local composition of the atmosphere is in general ** not **
in thermodynamic equilibrium with water at ambient temperature.
This does sometimes happen though,
e.g. when it is raining, and it is also sometimes
arranged that air used in a chemical process is in equilibrium
with water. The air is then said to be ** saturated ** with
water.

Humidity (kg/kg), * H * = (mass of water) / (mass of dry air)

Since the actual amount of water in air ir normally quite small
this is * very nearly * the same as the mass fraction of
water in air. The mol fraction of water in air can thus be estimated
by multiplying the humidity by the ratio of the molecular weights,
i.e. by (29/18).

The vapour pressure of water at * T * can be determined
and the mol fraction of water in the saturated air, *y*_{o} determined:

*P* *y*_{o} = *P*^{*}(*T*)

From *y*_{o} we can estimate *H*_{o}
the ** saturation humidity ** by multiplying by the appropriate
ratio of molecular weights.

At saturation the humidity of the air is *H*_{o}.
Its ** precentage humidity ** is said to be 100%.
Precentage humidity is defined as:

Percentage humidity = *H* / *H*_{o} x 100%

If the air contains * less * than the thermodynamic maximum
then its percentage humidity is less than 100%.

The ** relative humidity ** of air which is less than saturated
is also expressed as a percentage, but this is * not *
the same (confusingly!) the above percentage humidity, as relative
humidity is defined in mol fraction terms:

Relative humidity (%) =

100 x (mol fraction of water in air) / (mol fraction of water in saturated air)

Both percentage humidity and relative humidity obviously depend on temperature as well as the amount of water in the air. Fully saturated air is 100% humidity by both measures, but otherwise these differ somewhat. It can be shown that the realtionship between them is:

percent humidity = relative humidity x (1-*y*_{o}) /
(1 - *y*)

Since the mol fractions are relatively small the measures are quite similar, and approach each other at towards 100%.

Thus at temperature *T* the dew point of saturated air,
i.e. at 100% humidity or relative humidity is just *T*.

However, if the gas is less than saturated it would have to
be cooled until condensation started. The temperature to
which it would be cooled is called the ** dew point
temperature ** *T*_{d} and can be seen to depend only on the
water concentration.

At 1 atm:

*y* = *P*^{*}(*T*_{d})

The dew point temperature is sometines called the ** saturation
temperature. **

In fact, the situation is somewhat more complex, since the equilibrium is a dynamic rather than the static one which thermodynamics assumes. Water is evaporating from the wick, a process which requires energy to supply latent heat. Except at 100% relative humidity (when no water will evaporate because the air is saturated) the temperature will fall and so heat will be transferred from the suroundings to exactly balance this energy.

The temperature indicated by such a device is called the
** wet bulb temperature. ** The physical properties of the air-water
system relevant to heat and mass transfer are such that this dynamic equilibrium
produces, to within a fraction of a degree, the same temperature
as the static equilibrium saturation temperature, and so these can
be considered for all practical purposes to be the same. (This
is not in general true for other liquid gas/systems, e.g. for
an evaporating hydrocarbon in CO_{2}.)

The terms ** dew point, saturation and wet bulb temperatures **
can thus be considered all to refer to the same thing, and to be
merely an indirect way of expressing the concentration of water
in air!

log_{10} P^{*} (mm Hg) = A - B/(T+C)

Here T is in ^{o}C, and the constants A, B and C are:

T^{o}C | A | B | C | |

0-60 | 8.10765 | 1750.286 | 235 | |

60-150 | 7.96681 | 1668.21 | 228 |

A calculator for these equations is here.