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Brian Higgins

Psychrometric Data for Air Now Available in Wolfram|Alpha

December 3, 2009 —
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Psychrometry deals with the thermodynamic properties of gas-vapor mixtures. Air-water vapor mixtures are the most common systems studied because of their importance in heating, ventilating, air conditioning, and weather reporting.

Students of engineering are introduced to the subtleties of psychrometry in their thermodynamics courses. But we are all exposed to psychrometry any time we watch weather reports on television. Your favorite meteorologist probably speaks about the relative humidity, dry bulb temperature, and dew point temperature.

Let’s start our exploration of psychrometry by querying “psychrometric properties“. Wolfram|Alpha returns a presentation of data for moist air, including a graph known as a psychrometric chart.

The first pod gives the default values for the psychrometric variables used for the calculation. In this case they are values for the dry bulb temperature, wet bulb temperature, and air pressure. Dry bulb temperature is just a fancy term for the normal temperature you would measure with a thermometer, which the phrase distinguishes from other temperature measurements in psychrometry. The wet bulb temperature is what you would measure if you wrapped the bulb of your thermometer with a moist cloth and then held it in an air stream. Evaporation of moisture from the cloth results in a cooling effect, and the resultant thermometer reading is the wet bulb temperature—which is less than the dry bulb temp.

Let’s review the results that Wolfram|Alpha returns. The most important quantities to know are the dew point temperature (or dew point) and the relative humidity. The dew point is the temperature at which the water vapor in the air will condense. The relative humidity is another measure of how much water vapor is in the air: the ratio of the mole fraction of water vapor in moist air to the mole fraction of water vapor when the moist air is saturated at the same temperature and pressure, usually expressed as a percentage. If the relative humidity is zero, the air is completely dry. If the relative humidity is 100%, the air is at its dew point—that is, water vapor is about to condense.

If you scroll down through the output pods you will see that Wolfram|Alpha computes many other aspects of the moist air that you specified. The thermodynamic properties include density, specific enthalpy, heat capacity, and many more. The composition of the moist air is given for all the major components. (Minor components such as helium and carbon dioxide are not listed.)

Finally, a minimal pyschrometric chart is displayed, where the red dot signifies the moist-air properties for the calculation. The curve represents the saturation conditions for moist air at an air pressure of one bar. The dotted lines passing through the red dot show the dew point temperature, wet bulb temperature, relative humidity, and humidity ratio at the specified conditions. Of course, all these values and much more are computed and displayed in the Wolfram|Alpha result pods.

Psychrometric properties such as dew point and wet bulb temperature do depend on the atmospheric or barometric pressure where the measurement is made. In Denver at an altitude of 5,279 feet, the pressure exerted by the weight of the atmosphere is less than what it would be at sea level, and consequently the properties of moist air are affected. The psychrometry property formulas allow you to specify either the atmospheric pressure, or the elevation above sea level, from which the corresponding barometric pressure is calculated using the current U.S. Standard Atmosphere model. Thus if you want to know the properties of moist air in Denver (which is at an elevation of 5,279 ft.) you can query “moist air 30C and 67.4% and 5279 ft“. The results will be slightly different from your previous calculation, and the computation now uses relative humidity and elevation instead of air pressure (which is computed using the elevation).

Wolfram|Alpha computes the air moisture for Denver, Colorado

But perhaps you are planning to climb Mount Everest, which has an elevation of 29,035 feet:

Wolfram|Alpha computes air properties for Mount Everest

There are other applications where psychrometric properties of moist air are important, and several of these are now supported in Wolfram|Alpha with others to come. Applications presently supported are humidification of moist air, cooling or heating of moist air, and adiabatic mixing of moist air, and more. For example, to access the humidification formula, simply query “humidify moist air“.

Once again you are presented with a calculation using default values. You can change the default values, specify alternative variables, and impress your friends with your knowledge of how your humidifier works. Psychrometry can be fun, and Wolfram|Alpha allows non-experts to explore “what if” scenarios. Enjoy!


Wolfram|Alpha should have ambitions higher than “allow[ing] non-experts to explore …”

How about designing presentations that’ll turn them into experts?

Posted by Fred Klingener December 3, 2009 at 8:20 pm

This is useful information for acoustics, especially for precision calibration of cavities and microphones. The heat capacity should be specified as being either at constant volume or constant pressure. It would also be good to give the ratio of specific heats and the speed of sound. See ISO 61092-2 Annex F and ISO 9613-1.

Posted by Daniel Warren December 4, 2009 at 9:08 am

Exchanging Weather and Atmosphere data is instrumental to our survival on this planet. I have looked at the charts, looks quite usable. In simulation models, we need more REAL data. Anybody knows how to operate this? Weather Balloons are quite expensive to operate, but we need to know. Kudo’s for the example!


Posted by Remmolt Zwartsenberg December 5, 2009 at 2:16 am