Physical Principles

Author: Hans-Jürgen Schwarz
English Translation by Sandra Leithäuser
Back to Air humidity measurement

Dalton's Law

The total pressure of a gas mixture is composed by the sum of the partial pressures of its constituents.
In simplified terms: the air consists of dry air and water vapor

$P=P_{w}+P_{d}ry$

wherein P_w constitutes the partial pressure generated by water vapor and P_dry represents the sum of all partial pressures of all the other gases.

The total pressure of a mixture of ideal gases is equal to the sum of partial pressures of the individual gases in the mixture.

Water vapor partial pressure in the air

In a gas mixture (volume V, temperature T), each component gas has a partial pressure, p_i, which is proportional to the number of molecules present in the mixture..

For the relationship between p_i, V and T, the following equation applies:

$p_{i}*v=n*R*T$

The total pressure is the sum of all partial pressures. Water vapor partial pressure is at

22 ºC and 100 %rF	= 2645 Pa
22 ºC and 67 %rF	= 1772 Pa

(1 Pa = 1N/m² = 0.01 mbar)

For example, the atmospheric pressure in Hannover fluctuates between 964 hPa and 1042 hPa.

The partial pressure of water vapor at a given temperature cannot exceed certain limits, i.e., saturation. When the saturation pressure p_s is increased by additional water supply (humidification), the partial pressure stays the same, but the excess water vapor precipitates in the form of liquid water. This process is called condensation. There is no simple physical relation between temperature and saturation pressure, which is why the relationship is expressed in either graphical or table form.

When temperature rises the saturation pressure increases considerably. For instance, at 0 ºC it is 611 Pa and at 20 ºC it reaches 2338 Pa.