Introduction to Humidity Variables

This is an introduction to an important new topic: humidity.  The beginning of Chapter 4 can be a little overwhelming and confusing.  If you find it too confusing, I would suggest you stop reading.  Instead, study this introduction and the notes you take in class.  We will work a number of example humidity problems and you should fairly quickly grasp the basic concepts.

We will be mainly interested in 4 variables, what they are and what can cause their values to change.  The variables are : mixing ratio, saturation mixing ratio, relative humidity, and dew point.  You will find most of what follows on pps 83-85 in the photocopied class notes.


Mixing ratio tells you how much water vapor is actually in the air.  Mixing ratio has units of grams of water vapor per kilogram of dry air (the amount of water vapor in grams mixed with a kilogram of dry air).  It is basically the same idea as teaspoons of sugar mixed in a cup of tea.



The value of the mixing ratio won't change unless you add water vapor to or remove water vapor from the air.  Warming the air won't change the mixing ratio.  Cooling the air won't change the mixing ratio (unless the air is cooled below its dew point temperature and water vapor starts to condense).

Saturation mixing ratio is just an upper limit to how much water vapor can be found in air, the air's capacity for water vapor.  It's a property of air, it doesn't say anything about how much water vapor is actually in the air (that's the mixing ratio's job).  Warm air can potentially hold more water vapor than cold air.  This variable has the same units: grams of water vapor per kilogram of dry air.  Saturation mixing ratio values for different air temperatures are listed and graphed on p. 86 in the photocopied class notes.

The dependence of saturation mixing ratio on air temperature is illustrated below:

The small specks represent all of the gases in air except for the water vapor.  Each of the open circles represents 1 gram of water vapor that the air could hold.  There are 15 open circles drawn in the 1 kg of 70 F air; each 1 kg of 70 F air could hold up to 15 grams of water vapor.  The 40 F air only has 5 open circles; this cooler air can only hold up to 5 grams of water vapor per kilogram of dry air.


Now we have gone and actually put some water vapor into the volumes of 70 F and 40 F air.  3 grams of water vapor have been added to each volume of air.  The mixing ratio, r, is 3 g/kg in both cases.

The relative humidity is the variable most people are familiar with, it tells you how "full" the air is with water vapor.

In the analogy (sketched on the right hand side of p. 83 in the photocopied notes) 4 students wander into Classroom A which has 16 empty seats.  Classroom A is filled to 25% of its capacity.  You can think of 4, the number of students, as being analogous to the mixing ratio.  The classroom capacity is analogous to the saturation mixing ratio.  The percentage occupancy is analogous to the relative humidity.

Instead of students and a classroom you could think of the 70 F and 40 F air that could potentially hold 15 grams or 5 grams, respectively of water vapor.

Here are the relative humidities of the 70 F and 40 F air that each contain 3 grams of water vapor.  The 70 F air has a low RH because this warm air's saturation mixing ratio is large.  The RH in the 40 F is higher even though it has the same actual amount of water vapor because the 40 F air can't hold as much water vapor and is closer to being saturated.

Something important to note: RH doesn't really tell you how much water vapor is actually in the air.  The two volumes of air above contain the same amount of water vapor (3 grams per kilogram) but have different relative humidities.  You could just as easily have two volumes of air with the same relative humidities but different actual amounts of water vapor.

The dew point temperature has two jobs.  First it is a measure of the actual amount of water vapor in the air.  In this respect it is just like the mixing ratio.  If the dew point temperature is low the air doesn't contain much water vapor.  If it is high the air contains more water vapor. 

Second the dew point tells you how much you must cool the air in order to cause the RH to increase to 100% (at which point a cloud, or dew or frost, or fog would form).


If we cool the 70 F air or the 40 F air to 30 F we would find that the saturation mixing ratio would decrease to 3 grams/kilogram.  Since the air actually contains 3 g/kg, the RH of the 30 F air would become 100%.  The 30 F air would be saturated, it would be filled to capacity with water vapor.  30 F is the dew point temperature for 70 F air that contains 3 grams of water vapor per kilogram of dry air.  It is also the dew point temperature for 40 F air that contains 3 grams of water vapor per kilogram of dry air.

Now back to our students and classrooms analogy on the righthand side of p. 83.  The 4 students move into classrooms of smaller and smaller capacity.  The decreasing capacity of the  classrooms is analogous to the decrease in saturation mixing ratio that occurs when you cool air.  Eventually the students move into a classroom that they just fill to capacity.  This is analogous to cooling the air to the dew point temperature, at which point the RH becomes 100% and the air is filled to capacity, the air is saturated with water vapor.
Next we will try to understand better why it is possible to saturate air with water vapor.  Why is there an upper limit to the amount of water vapor that air can contain?  Why does this upper limit depend on air temperature.

First we need to understand that the rate at which water evaporates depends on the water's temperature.

Before reading any further, is the statement "hot water has a higher rate of evaporation than cold water" what you would have suspected?  Your intuition in this case is probably pretty good.

To be able to evaporate, a water molecule in a glass must make its way up to the surface of the water and the water molecule must have sufficient kinetic energy to overcome any attractive forces trying to keep it in a liquid state. 

The distributions of the kinetic energies of the water molecules in the glasses of cold and hot water (remember temperature is a measure of the average kinetic energy) are shown in the two graphs above.  In cold water only a limited number of the water molecules (those in the red-shaded portion of the graph) have the necessary energy - cold water has a low rate of evaporation.  In hot water, the whole distribution has slid to the right, a larger fracton of the water molecules will have enough energy (the red shaded portion is larger), hot water evaporates more rapidly.

Now we will look at the top part of p. 85 in the photocopied notes.  We have put a cover on the glass of room temperature water. 

In #1 we see that the water is evaporating (2 arrows worth of evaporation).  Water vapor will begin to build up in the air in the glass.  This is shown in #2.  Some of the water vapor molecules will condense (even though they may have just evaporated).  In Fig. #3 the amount of water vapor has built up to a point where there is one arrow worth of condensation.  In #3 there is still more evaporation than condensation so the water vapor concentration will increase a little bit more.  Eventually in #4 the water vapor concentration has increased to a point that there are two arrows of condensation.  This balances the 2 arrows of evaporation.  The air is saturated, the air is filled to capacity.  The amount of water vapor in the air will now remain constant.

What would happen if we took off the cover and added some more water vapor to the glass in Fig. #4?  (this figure isn't include in the photocopied class notes).

The air in Fig. #5 shows what would happen.  The air would be supersaturated with water vapor and the RH would be greater than 100%.  This is possible but it is not an equilibrium situation.  The increased amount of water vapor would increase the rate of condensation.  There would be more condensation than evaporation.  The water vapor concentration would begin to decrease.  Eventually the glass would return to the equilibrium situation in Fig. #4.

If we look at the bottom of p. 85 we see that the air in all three cases is saturated (equal rates of evaporation and condensation in each case).  The relative humidity is 100% in all three cases.  The amount of water vapor in the air however is different.  The warm air contains a lot more water vapor than the cold air. 



Here is a hidden humidity optional assignment (due at the beginning of class on the first day of class after Spring Break)