# Water dew point

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The water dew point (or simply the dew point) of a gas mixture is the temperature, at a given pressure, at which any water vapor in the gas mixture will start to condense into liquid water. The water dew point of a gas mixture, at a given pressure, is often referred to as the point at which the gas mixture is saturated with water vapor (i.e., the gas cannot hold any more water vapor).

The water dew point of a gas mixture is involved with its relative humidity (RH). A relative humidity of 100% indicates that the gas mixture is at its water dew point and saturated with water vapor. A relative humidity of less than 100 % indicates that the gas mixture is not at its dew point and not yet saturated with water vapor. Contrary to the common notion that relative humidity only applies to the atmospheric air, it applies to any gas mixture containing water vapor.

## Determination of the water dew point of any gas mixture

(PD) Graph: Milton Beychok

### Methodology

Assuming ideal gas behavior of a gas mixture containing water vapor, from Dalton's law and the fact that the mole fraction of a gas component in a gas mixture is equal to the volumetric fraction of that component in a gas mixture, we have:

(1)     ${\displaystyle p_{w}=x_{w}p_{t}=v_{w}p_{t}}$

Given the total pressure of the gas ( ${\displaystyle p_{t}}$ ) and either the mole fraction ( ${\displaystyle x_{w}}$ ) or volume fraction ( ${\displaystyle v_{w}}$ ) of the water vapor in the gas mixture, the partial pressure of water vapor ( ${\displaystyle p_{w}}$ ) in the gas mixture can be readily determined with the above equation.[1]

When the partial pressure of water vapor ( ${\displaystyle p_{w}}$ ) in the gas mixture equals the vapor pressure of pure liquid water ( ${\displaystyle p_{w}^{o}}$ ), the gas mixture is saturated with water and is at its water dew point ( ${\displaystyle T_{d}}$ ).[1]

There are a number of Antoine equations and similar equations that relate the vapor pressure of pure liquid water ( ${\displaystyle p_{w}^{o}}$ ) to the temperature of the water. One such equation, which is quite accurate, is:

(2)     ${\displaystyle T={\frac {1668.21}{7.09171-\log _{10}\,p_{w}^{o}}}+45.15}$

The temperature-explicit equation (2) can be transformed into this pressure-explicit form:

(3)     ${\displaystyle \log _{10}\,p_{w}^{o}=7.09171-{\frac {1668.21}{T-45.15}}}$

In both equations 2 and 3, pressures are in kiloPascal (kPa) and temperatures are in kelvins (K).

### Examples

Using equation (2), we can determine the water dew point temperature ( ${\displaystyle T_{d}}$ ) for various values of ${\displaystyle p_{w}=p_{w}^{o}}$ and then compare them to values obtained from a set of steam tables:[1][2]

(a) Given ${\displaystyle p_{w}^{o}=7.3755\;\mathrm {kPa} }$,    ${\displaystyle T=T_{d}}$  was calculated as 313.1821 K (40.032 °C) and the steam table value is 40.0 °C.

(b) Given ${\displaystyle p_{w}^{o}=101.325\;\mathrm {kPa} }$, ${\displaystyle T=T_{d}}$  was calculated as 373.1508 K (100.001 °C) and the steam table value is 100.0 °C.

(c) Given ${\displaystyle p_{w}^{o}=1704.8\;\mathrm {kPa} }$,    ${\displaystyle T=T_{d}}$  was calculated as 477.32 K (204.17 °C) and the steam table value is 204.4 °C.

### Importance

Determination of the water dew point of gas mixtures is important in the design of fuel-fired combustion equipment (i.e., industrial process furnaces and steam generators) so as to avoid cooling the combustion product flue gas below the water dew point. In other words, to prevent the water vapor in the flue gas from condensing into liquid water and causing corrosion in the flue gas handling facilities.

It is also important in the processing and pipelining of natural gas for the same reason, namely to prevent or reduce corrosion problems. At certain temperatures, condensation of water vapor present in natural gas pipelines may form methane hydrates (also known as clathrates, which can plug the pipelines.

## References

1. V. Ganapathy (2002). Industrial Boilers and Heat Recovery Steam Generators: Designs, Applications, Calculations, 1st Edition. CRC Press. ISBN 0-8247-0814-8.
2. American Society of Mechanical Engineers (1989). Steam Tables: Properties of Saturated and Superheated Steam, 16th Printing. Combustion Engineering, Inc.