Field of Science

Psychrometry - or how to tell when it's crazy hot out

The heat index is 107 oF (42oC) at the moment. It's hot, and I'm procrastinating going outside by blogging.

My youngest son is doing summer theater, and their rehearsal space is not all air conditioned. So I bought him a cooling towel to help him stay comfortable. When he asked how it worked, I said it was like having a portable swamp cooler — a familiar item as my dad used one for years to cool his house.

The basic principle at work is that it takes energy to make water evaporate. Unless the relative humidity is 100% (in other words, the air has all the water it can hold), water will evaporate. If you keep running air past a wet surface (think a fan blowing past a damp towel, or the breeze blowing over your sweaty face), water will continue to evaporate as drier air is constantly being replenished. The energy to turn the water from a liquid into a gas has to come from somewhere, in this case, the surrounding air and the water itself. The air gets cooler. Whew!

The towel works similarly, there is a very large damp surface area (why the fancy $15 towel really does works better than a damp cotton lawn handkerchief, a much higher surface area than the smooth cotton weave) and as you move around, air moves past. The water evaporates, pulling energy from the water in the towel and makes it colder.

To get a sense of how much energy that is, it takes about 34,000 J to evaporate 15 grams of water (about a tablespoon). 34,000 J is roughly 8 nutritional calories. If you pulled all that energy out of a cup of water, the cup of water would cool off to about 41o F. (In practice, you don't get things this cool!)

This whole endeavor depends on the air being able to soak up some water, so if the humidity is too high, you are going to be crazy hot towel or no. Swamp coolers work great in desert areas (where my dad lives, for example), and are pretty much useless in New Orleans.

So how cool can you get? To figure it out you need the dry bulb temperature and the wet bulb temperature of the air. The dry bulb temp is just the temperature of the air measured in the usual way (being careful to keep the thermometer out of the sun). The web bulb temperature is obtained by blowing air over a thermometer whose bulb is fitted with a tiny damp sock. For that you can use a sling psychrometer (see the video).

Too hot to be slinging thermometers around? Look up the dew point (your favorite weather app will likely have it) and you can estimate the wet bulb temp this way:

1. Subtract the dew point from the ambient temperature (what your regular thermometer reads)
2. Divide what you get in step 1 by 3.
3. Subtract the result in step 2 from the ambient temperature.

Right now the thermometer outside my window reads 100o F, the National Weather Service says the dew point is 70o F, so I take 100-70=30; 30/3 = 10; so the approximate wet bulb temperature is 100-10 or 90o F.

Once you've got the wet bulb temp you can figure out just how much cooling you can get with a fan and a damp towel!

1. Subtract the wet bulb temp from the ambient temp (the dry bulb temperature)
2. Multiply the difference by 0.8 (assuming the process is about 80% efficient, which is a pretty reasonable estimate)

My calculations suggest that the best I could do to produce cool air in my study this afternoon would be 80% of *100-90) or 8 degrees of cooling. 100o F or 92o F? Both are way too hot...I think it's time to stop writing for the day and head for the pool!!

There are more sophisticated ways to do this, talk to the meteorologists if you want to know more.

Psychrometry comes from the Greek for cold ("psuchron") and should not be confused with anything psychiatric (unless you are talking about mad dogs and Englishmen...)

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