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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 [[Condensation|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==
{{Image|Water Vapor Pressure.png|right|475px|}}
===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) &nbsp; &nbsp; <math>p_w = x_w p_t = v_w p_t</math>
Given the total pressure of the gas (&thinsp;<math>p_t</math>&thinsp;) and either the mole fraction (&thinsp;<math>x_w</math>&thinsp;) or volume fraction (&thinsp;<math>v_w</math>&thinsp;) of the water vapor in the gas mixture, the [[partial pressure]] of water vapor (&thinsp;<math>p_w</math>&thinsp;) in the gas mixture can be readily determined  with the above equation.<ref name=Ganapathy>{{cite book|author=V. Ganapathy|title=Industrial Boilers and Heat Recovery Steam Generators: Designs, Applications, Calculations|edition=1st Edition|publisher=CRC Press|year=2002|id=ISBN 0-8247-0814-8}}</ref>
When the partial pressure of water vapor (&thinsp;<math>p_w</math>&thinsp;) in the gas mixture equals the [[vapor pressure]] of pure liquid water (&thinsp;<math>p_w^o</math>&thinsp;), the gas mixture is saturated with water and is at its water dew point (&thinsp;<math>T_d</math>&thinsp;).<ref name=Ganapathy/>
There are a number of [[Antoine equation]]s and similar equations that relate the vapor pressure of pure liquid water (&thinsp;<math>p_w^o</math>&thinsp;) to the temperature of the water. One such equation, which is quite accurate, is:
:(2) &nbsp; &nbsp; <math>T = \frac {1668.21}{7.09171 - \log_{10}\, p_w^o} + 45.15</math>
The temperature-explicit equation (2) can be transformed into this pressure-explicit form:
:(3) &nbsp; &nbsp; <math>\log_{10}\, p_w^o = 7.09171 - \frac{1668.21}{T - 45.15}</math>
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 (&thinsp;<math>T_d</math>&thinsp;) for various values of <math>p_w = p_w^o</math> and then compare them to values obtained from a set of [[steam tables]]:<ref name=Ganapathy/><ref>{{cite book|author=American Society of Mechanical Engineers|title=Steam Tables: Properties of Saturated and Superheated Steam|edition=16th Printing|publisher=Combustion Engineering, Inc|year=1989|id=}}</ref>
(a) Given <math> p_w^o = 7.3755\;\mathrm{kPa}</math>, &nbsp; &thinsp;<math>T = T_d</math>&thinsp; was calculated as 313.1821 K (40.032 °C) and the steam table value is 40.0 °C.
(b) Given <math> p_w^o = 101.325\;\mathrm{kPa}</math>, <math>T = T_d</math>&thinsp; was calculated as 373.1508 K (100.001 °C) and the steam table value is 100.0 °C.
(c) Given <math> p_w^o = 1704.8\;\mathrm{kPa}</math>, &nbsp; &thinsp;<math>T = T_d</math>&thinsp; 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 [[Natural gas processing|processing]] and [[Pipeline|pipelining]] of [[natural gas]] for the same reason, namely to prevent or reduce corrosion problems.
==References==
{{reflist}}

Revision as of 16:33, 9 May 2010

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