## Chalk talk: How to calculate vapor pressure from wet bulb temperature

In this chalk talk, METER Group research scientist, Dr. Colin Campbell, extends his discussion on humidity by discussing how to calculate vapor pressure from wet bulb temperature. Today’s researchers usually measure vapor pressure or relative humidity from a capacitance-based relative humidity sensor.

However, scientists still talk in terms of wet bulb and dew point temperature. Thus, it’s important to understand how to calculate vapor pressure from those variables.

**Video transcript**

Hello, my name is Dr. Colin Campbell. I’m a research scientist here at METER group, and also an adjunct professor at Washington State University where I teach a class on environmental biophysics. And today we’re going to be extending our discussion on humidity by talking about how using a couple of common terms related to humidity, we can calculate vapor pressure. The first term we’re going to talk about is dew point temperature. I’ve drawn a couple of figures below that illustrate a test I performed when I was a graduate student in a class related to biophysics.

The professor had us take a beaker of water and a thermometer and put ice in the beaker and start to stir it. The thermometers were rotating around in the glass, and our job was to look carefully and find out when a thin film of dew began to form around on the glass. So we watched the temperature go down, and at some point, we observed a thin film form onto that glass. At the point the film began to form, we looked at the temperature to get the dew point temperature, which means exactly what it says: the point at which dew begins to form.

This experiment wasn’t perfect because there is certainly a temperature difference between the inside of our glass where we’re stirring with the thermometer and the outer surface of the glass. But it was a good approximation and a great way to demonstrate what dew point temperature is. So we can say that the dew point temperature is the point at which the air is saturated and water begins to condense out. We call this T_{d} or dew point temperature. The beautiful thing about dew point temperature is that if you know this value, you can easily calculate vapor pressure and even go on to calculate relative humidity, as I talked about in another lecture.

To calculate vapor pressure from our dew point temperature, we’ll call vapor pressure of the air, e_{a} which is equal to the saturation vapor pressure (e_{s}) at the dew point temperature (T_{d}) (Equation 1).

And as I discussed in my other lecture, the saturation vapor pressure is a function of the temperature (not multiplied by the temperature). It’s pretty simple to get the saturation vapor pressure at the dew point temperature. We simply use Tetons formula (Equation 2 discussed here), which says that the saturation vapor pressure at the dew point is equal to 0.611 kilopascals times the exponential of b T_{d} over C plus T_{d} (T_{d} being the dewpoint temperature).

So let’s assume our dew point temperature is five degrees C. This is something you can find in many weather reports. If you look down the list of measurements carefully, it’s usually there. So the vapor pressure of the air (e_{a}) is calculated by the formula I showed (Equation 1). Our first constant b is 17.502 and our second constant C, is just 240.97 degrees C. If we plug all the values into that equation, it ends up that our vapor pressure is 0.87 kilopascals.

Now there might be a variety of reasons we want this value. We might want to use it to calculate the relative humidity. If so, we’d simply divide that by the saturation vapor pressure at the air temperature. Then we’d have our relative humidity. More commonly we use the e_{a} and the saturation vapor pressure at the air temperature to calculate the vapor deficit. So possibly in some agronomic application that might be interesting to us. So that is dew point temperature.

Now we’ll talk about another common measurement, our wet bulb temperature. This was much more common in past years where there weren’t electronic means to measure things like dew point or humidity sensors. And we used to have to make a measurement of humidity by hand. And what they did was to collect a dry bulb temperature or a standard air temperature. And that dry bulb temperature (or the temperature of the air) was compared to what we call a wet bulb temperature.

Researchers made this wet bulb temperature by putting a cotton wick around the bulb of the thermometer. This was just a fabric with water dripped onto it. Once that wick is saturated with water, the water begins to evaporate, and they would use wind to enhance that evaporation. For example, some instruments had a small fan inside that would blow water across this wick, or more commonly, two temperature sensors were attached on a rotating handle, so they could spin them in the air at about one meter per second (or two miles an hour). I don’t know how you’d ever estimate that speed, but that was the goal. This would help the water evaporate at an optimum level.

You can imagine what happens during this evaporation by thinking about climbing out of the pool. You feel some cooling on your skin as water begins to evaporate when you climb out of a pool on a dry, warm summer day. That’s water as it changes from liquid into water vapor, and it actually takes energy for this to happen (44 kilojoules per mole). That’s actually quite a bit of energy used for changing liquid water into water vapor. When that happens, it decreases the temperature of this bulb. If we wait till we’ve reached that maximum temperature decrease, we can take that as our wet bulb temperature, or T_{w}.

This wet bulb temperature is not quite as simple as our dew point temperature to use in a calculation. Here’s the calculation we need to estimate vapor pressure from the wet bulb temperature.

We take the saturation vapor pressure (e_{s}) at the wet bulb temperature (T_{w}) and subtract, the gamma (Ɣ), which is the psychrometer constant 6.66 times 10^{-4} ℃^{-1} times the pressure of the air (P_{a}), multiplied by the difference between the air temperature (T_{a}) or that dry bulb that I mentioned earlier, and the wet bulb temperature (T_{w}).

Gamma is an interesting number. It’s actually the specific heat of air divided by the latent heat of vaporization, or that 44 kilojoules per mole that I mentioned before. We can simply take it as a constant for our purposes here as 6.66 times 10^{-4} ℃^{-1}. So let’s actually put it into a calculation.

Our example problem says find the vapor pressure of the air. If air temperature (T_{a}) is 20 degrees Celsius, the wet bulb temperature (T_{w}) is 11 degrees Celsius, and air pressure (P_{a}) is 100 kilopascals (basically at sea level). And just to remind us, this is the constant gamma (6.66 times 10^{-4} ℃^{-1}). Air pressure is 100 kilopascals. We take this standard equation (Equation 4) and insert all these numbers.

So our vapor pressure is going to be this calculation from Tetons formula (Equation 2) and if you plug all those numbers into your calculator (notice our degrees C will cancel) we’re left with kilopascals. So our vapor pressure is about 0.71 kilopascals. So that is how we calculate the vapor pressure from the wet bulb temperature.

I hope this has been interesting. These are values that you may hear about. It’s less common today since we usually get our relative humidity from a capacitance-based relative humidity sensor, but still scientists talk in terms of wet bulb and dew point temperature. So it’s important to understand how we actually calculate our vapor pressure from those variables. If you’d like to know more about this, please visit our website, metergroup.com, and look at some of the instruments that are there to make measurements. Or you can email me if you want to know more at [email protected]. I hope you have a great day.

## Learn more

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