To get you started on the process of building your own psych chart, I need to make sure we are all on the same page about a few basic principles. So that discussion will be the focus of this post.
Psychrometrics (a.k.a. as psychrometry or hygrometry) is typically defined as the field of science or engineering concerned with the determination of physical and thermodynamic properties of gas-vapor mixtures. As humans, we have a particular interest in the mixture of air and water vapor since the atmosphere we live in is composed of just such a mixture. For the rest of this discussion, when I use the terms “psychrometrics” or “psychrometry”, it will be in this context, even though in general, their context is much broader.
As building systems folks, we likely find ourselves interested in the air around us for a number of reasons. One is that the meteorological phenomenon that occur in the air around our facilities can have a significant impact on their operation. Another is that we endeavor to control the environment inside our facilities by moving air from the outside through them and conditioning it in a manner that will provide a safe, comfortable, productive environment inside, in spite of what might be going on outside. And, in the interest of sustainability, we would like to do this as efficiently as possible.
For the purposes of this blog, our focus is more on building science and systems than meteorology. But since the climate has a significant impact our buildings, fostering a bit of interest and knowledge in meteorology can be helpful. I mention this because many of the principles we will be discussing in this string of posts are fundamental principles that apply to both fields.
Dalton’s Law of Partial Pressures
Dalton’s Law of Partial Pressures is one of the fundamental principles behind psychrometrics and the psych chart. John Dalton was an English scientist who lived in the late 1700’s/early 1800’s and did pioneering work that led to modern atomic theory. Many of his concepts evolved from studying the behavior of gasses, which, in turn evolved out of his life-long interest in meteorology.
At the suggestion of one of his mentors, he started a meteorological journal at an early age and kept it for his entire life, accumulating over 200,000 observations. In fact, one of his last acts on earth may have been to make his daily journal entry before suffering a stroke.
One of his discoveries was that in a mixture of gasses, each gas acted independently of the other gasses in the mixture; the gas atoms or molecules are neither attracted or repelled from each other and each behaves as if the other gas didn’t exist. As a result, the total pressure exerted by the mixture is the sum of the pressure exerted by each of the gasses in the mix.
Boyle’s Law; A Stepping Stone to Understanding Dalton’s Law
For me, the example that follows helped me understand Dalton’s Law and how it applies to psychrometry. As a starting point, consider two interconnected, equally sized tanks, one of which contains air at a relatively high pressure, say 29.0 psia1 (about twice atmospheric pressure) and the other which contains a pure vacuum (0.0 psia). A valve is provided between the two tanks to allow you to isolate them or interconnect them.
I should point out that in the diagram above and those that follow, the dots represent the air molecules and I drew the diagram so the number of dots was approximately proportional to the pressure to create a visual reference that way since I am going to talk about their relationship to pressure. Obviously, real air or water vapor molecules would be smaller, further apart, and moving around very quickly2.
Returning to the example, in general, somewhat simplistic terms, the pressure in the tank with the air in it is created by the air molecules bouncing off the walls of the tank. If you add more air molecules to the tank, there will be more collisions with the wall of the tank and the pressure will go up. If you remove air molecules, the opposite will happen.
It turns out that if you heated the tank, a similar thing will happen because adding heat to the tank gives the molecules that are in the tank more energy and they move around faster. But for our experiment, we are going to hold the temperature constant.
If you open the valve and observe the results, you will discover that the air molecules will spread themselves out uniformly between the two tanks (this is a characteristic of a vapor or gas; see footnote 2) and that after everything comes back into equilibrium, the pressure in both tanks will be identical and approximately half of the initial pressure since the volume the molecules now occupy is twice the volume that originally contained them.
This is Boyle’s Law, which was discovered by Robert Boyle, an English scientist and philosopher, who lived in the mid 1600’s and early 1700’s. In general terms, the law says that for a fixed temperature and a fixed mass (i.e. a fixed number of molecules), pressure will be proportional to volume. This link will take you to an animation further illustrating the principle if you are interested.
Boyle’s Law and Water Vapor
If you repeated the experiment I described previously with water vapor at a very low pressure, for example 0.4 psia, you would discover a similar result to what occurred with air. Specifically, when the relatively few water vapor molecules that are contained in the first tank …
… are allowed to expand into the second tank (which is initially at a vacuum) and things are allowed to stabilize, the pressure is uniform in both tanks. And that pressure is at a value that is half of the original value in the first tank since the volume now occupied by the water vapor molecules has been doubled.
It turns out that at the temperatures and pressures encountered in the atmosphere, gasses will tend to follow a number of laws, including Boyle’s Law, Dalton’s Law, and Charles/Gay Lussac’s Law.
The Charles/Gay Lussac’s law is similar to Boyle’s law but relates volume and temperature at a constant pressure. Specifically, it states that for a fixed pressure and mass, the volume of a gas will be proportional to its temperature. This link will take you to an animation further illustrating the principle if you are interested. Note that the temperature needs to be measured in absolute terms3 when applying this principle.
If you combine Boyle’s Law and the Charles/Gay Lussac law, you get the following expression.
Gasses that follow these laws are called “ideal gasses” and don’t really exist. For example, if you cool a gas towards absolute zero, it will eventually go through a phase change and become a liquid and maybe even a solid.
I did a string of blog posts a while back that looked at saturated multiphase systems, and clearly, when something goes through a phase change, the ideal gas equation does not hold. For example, when a cubic foot of saturated steam at atmospheric pressure condenses to a liquid, its volume changes by a factor of about 1,600 and the temperature and pressure do not change. As a result, modeling real gasses involves some fairly complex equations called equations of state for the substance. I talk about them a bit and provide some related resources in my string of posts on saturated multiphase systems if you want to know a bit more.
Dry Air; More than One Element
At this point, I need to point out that dry air is actually a mixture of a number of gasses as indicated below.
Note that the tabulation above does not include water vapor, which when added becomes the third most common constituent, as indicated in Note 3. But, relative to the primary constituents (Nitrogen and Oxygen) it is still a fairly small component of the atmosphere, even at its maximum value (about 5% by volume of the total). And it seldom is at that value. But that doesn’t keep it from having a big impact on life on earth and the operation of our building systems.
My point in bringing up ideal gasses here two fold. One is to say that we will be treating air as one ideal gas, even though it is made up of a number of gasses. The other is to say that we will also be treating water vapor as an ideal gasses. These are reasonable assumptions at the temperatures and pressures we typically encounter in HVAC systems.
The preceding is especially true for air, which, in the atmosphere is superheated4 (relative to the temperature that it would change phase from a gas to a liquid). But in contrast, water vapor (which technically is a superheated vapor most of the time in our atmosphere) can also be exposed to conditions in the atmosphere that bring it close to its saturation temperature or even below its saturation temperature. When that happens, its behavior departs from what the idea gas equation would predict.
Water Vapor and Saturation
Lets re-arrange our experimental apparatus a bit so that we have a piston in one of the tanks that allows us to push water vapor molecules into the second tank.
If we open the valve and force a few more molecules into the tank on the left, then, by virtue of the additional molecules and the rigidity of the tank, the mass in the tank will go up with out changing the volume. As a result, we would discover that the pressure would have gone up a bit once equilibrium was re-established because there are more molecules flying around and bouncing off the walls of the tank.
And, if we kept adding molecules a few at a time, the same thing would seem to happen; add a few more molecules and the pressure goes up a bit more each time we do it.
But at some point, an interesting thing would happen. Specifically, there would come a point where when we added a few more water vapor molecules, they would start to interact with each other and would change from a vapor to a liquid and go through a major volume change (a reduction by a factor of about 1,600; if I drew it to scale, you could not see it). In other words, the added molecules would have reduced the inter-molecular spacing to the point where the intermolecular forces would start to come into play; see footnote 2.
Notice the little drop of liquid hanging out in the lower left corner of our tank. Notice also that the pressure in the tank did not go up, even though we added molecules. The fact is that we could add a bunch more molecules to the tank and the same thing would continue to happen assuming the temperature of the tank didn’t change.
Meaning the pressure would hold steady and we would begin to collect a little puddle of water in the bottom of the tank5.
At the point where the vapor to liquid transition started to happen, the vapor in the tank became saturated given the temperature (73°F) and pressure (0.4 psia) that existed at the time. And as long as the system is saturated, liquid and vapor will both concurrently exist.
Clearly, this is not ideal gas behavior (meaning it is not predicted by the ideal gas law). But, if you look out the window on most days, it is clearly a condition that occurs with the water vapor in our atmosphere.
And if you look inside our air handling systems, you will notice that the water vapor changes phases there too.
In fact, water vapor will change phase any time it encounters a surface below its dew point temperature. Sometimes, that is a good thing because it makes for clouds, sunsets, and comfort. But other times it’s a not so good thing because it can ruin the envelope of a building if the phase change happens in a location where we would rather it didn’t, like inside a wall for instance.
The bottom line is that understanding the fundamental principles we are talking about is a very important part of understanding the universe around us and the processes that occur in our buildings and systems.
Understanding Non-Ideal Gas Behavior
The equations of state used to predict the behavior of a non-ideal gas can be pretty complex and intimidating. For example, here is the equation presented for specific volume in the 1948 printing of Thermodynamic Properties of Steam a.k.a known to many as Keenan and Keyes a.k.a known as a “steam table”.
I don’t know about you, but to me, that is pretty intimidating.
In general terms, the equations of state are trying to match data that is gathered via research and experimentation with theoretically predicted results; i.e. an empirical process. The term empirical has its roots in the Greek term for experience, and empirical research is, as I understand it, a cycle where:
- Observations are made, and then,
- The observations are used to formulate a hypothesis, after which
- Testable deductions are proposed as a result of the hypothesis, after which
- Tests are performed to validate the deductions, after which
- The test results are analyzed to see if they bear out the hypothesis and the cycle repeats.
To make things easier for people working with gasses on a day to day basis in real world situations, the results of these calculations and experiments are typically tabulated and graphed. The publication Thermodynamic Properties of Steam mentioned previously is an example of this that includes both tabular representations of the equations of state ….
… as well as graphic representations.
If you follow the blog, you may recognize the chart above as a temperature entropy chart and as being similar to the chart I created using REFPROP as discussed in the 2nd post in my string on Saturated Multiphase Systems.
My point in brining all of this up here is that to construct your psych chart, you will occasionally need to consult the tables in a resource like Thermodynamic Properties of Steam or create your own tables using a resource like REFPROP. But since a psych chart is generally about a mixture of air and water vapor (vs. liquid water) much of the construction will evolve by assuming that the mix behaves like an ideal gas.
Dalton’s Law for a Mix of Air and Water Vapor
Now, lets combine the two experiments we discussed previously. Specifically, lets start out with a tank of air at approximately 29.0 psia and connect it to a tank of water vapor at approximately 0.40 psia.
When we open the valve, the two gasses will mix uniformly and, once things return to an equilibrium, the result will be that there are two tanks with an air/water vapor mix at in them at approximately 14.7 psia total pressure.
Of this total, based on Dalton’s law, the air molecules are contributing approximately 14.5 psia to it while the water vapor’s part is approximately 0.2 psia. In fact, the value “0.2 psia” is termed the partial pressure of the water vapor and the value of “14.5 psia” is termed the partial pressure of the air.
One way of thinking of the preceding is to say that the pressure in the tanks is created by “x” pounds of water vapor molecules bouncing off the walls along with with “y” pounds of air molecules. This ratio is called the “specific humidity” or “humidity ratio” and is conventionally assigned the symbol “w” in psychrometric discussions like the one we are having.
If you write the ideal gas equation for both air and water vapor and then divide the two equations into each other, you can develop the following relationship.
Basically, the equation says that the specific humidity is a function of the partial pressure of the water vapor in a mix and the total pressure of the mix along with the gas constants for water and air. You can solve this equation for specific humidity as shown below.
So, if you know the partial pressure of the water vapor in a mix along with the total pressure, you can calculate the specific humidity.
A special case of the preceding equations can be developed for the saturation pressure of the water vapor mixture with the result being as follows:
For HVAC systems, the total pressure is generally the local atmospheric pressure, which is 14.7 psia at sea level. And the saturation pressure for water vapor at different temperatures can be found by using a tabulation from a resource like Keenan and Keyes or REFPROP.
For example, in the table from the picture above, we find that the saturation pressure for water vapor at 73°F is .4 to one decimal place.
That tells us that the water vapor in the tank with the water vapor molecules in it was saturated at the beginning of the Dalton’s Law experiment in the previous section. We could calculate the specific humidity at saturation for air at 73°F using the relationships above as follows:
This number (w=0.17 lbwater/lbAir) is a point on the saturation curve of a psychrometric chart. That observation may give you a clue about how you might go about the construction of your chart.
We can also calculate the specific humidity in the two tanks after the experiment in a similar manner.
Decimal Places Matter
If you study a copy of Keenan and Keyes (or any other steam table for that matter) you will discover that for low saturation temperatures, the saturation pressure is recorded to 4 or 5 decimal places. But, as the saturation temperature goes up, the value is reported to 3 decimal places or less.
In my 1948 copy, the 5 to 4 decimal place transition happens in Table 1 (the temperature table) at 54°F. The 4 to 3 decimal place transition happens at 145°F. At 310°F, pressure values transition to being reported to 2 decimal places and at 450°F the number of decimal places reported is 1 (a saturation pressure of 422.6 psia).
In the math I did above, I used one decimal place for everything, reflecting the numbers in the illustrations I used. But, if I do the math to the full complement of decimal places available from the tables, I get a slightly different result, as shown below.
Because water vapor is such a small percentage of the over-all mix of gasses in the atmosphere, those decimal places actually matter. In this particular case, a chart made using the one decimal place calculation would be off about 1°F for the value used on the saturation curve at 73°F. It would be off close to 2°F for the 50% RH curve.
So, take advantage of the fact that you can do the math with a calculator or computer and use the full complement of decimal places reported for the parameters you work with to build your psych chart. The electronics make this much, much easier for us than it was for the folks back when the tables were developed who were working with slide rules, pencils and papers. A slide rule has an accuracy of about 3 significant figures at best compared to what we can do now-days with a calculator or a spreadsheet.
The fundamental principles we have reviewed to this point, while not covering all of the bases you need to draw your own chart are enough to get you started. Specifically, they provide the insight you need to decide what your axes are going to be and to plot the saturation curve. So you may want to go ahead and try your hand at that. Or, you can wait for the next post, where I will show you how I did it and generated the the starting point for my chart which is shown below as a hint.
Senior Engineer – Facility Dynamics Engineering
1. The abbreviation “psia” stands for pounds per square inch absolute. Meaning that the pressure is referenced to a pure vacuum. Atmospheric pressure is approximately 14.7 psia or 0 psig. The abbreviation “psig” stands for pounds per square inch gauge. Meaning the pressure reading is referenced to some arbitrarily selected standard. Typically for HVAC and building systems work, we reference local atmospheric pressure.
It is important to recognize that such a reference can vary slightly as a function of location. For example, at standard conditions in Denver, Colorado, the “mile high” city, atmospheric pressure is about 12.1 psia vs. 14.7 psia at Sea Level.
The reference can also vary as a function of what is going on in a building. For instance, it is a common practice to pressurize some areas in a building relative to other areas to control the flow of odors and other contaminants. For example, in the clean rooms I worked with when I was a facilities engineer for Komatsu Silicon America at their Hillsboro facility (now owned by Solar World), in the Epitaxial clean room, the cleanest area was kept 0.06 in.w.c. positive relative to the clean corridor surrounding the clean room. That meant it was about 0.08 in.w.c. positive relative to the local atmospheric pressure.
Sometimes, the differences in pressure relative to the standard are important to consider, and other times, they are not important in the context of building operations. For example, the point of reference used to measure the clean room pressure at KSA was fairly important because the parameter we were trying to control for was so small relative to the atmospheric reference. But the fact that a gauge on a pressure vessel located in the clean room that contained a gas at approximately 250 psig in it was referenced to the local atmospheric pressure plus 0.08 in.w.c. (the pressure of the clean room relative to atmosphere) rather than actual atmospheric pressure did not matter from an operational standpoint.
2. In fact, the distance between the water vapor molecules is one of the distinguishing features of a vapor relative to a liquid or a solid. Molecules in a substance have both internal kinetic energy and internal potential energy. The way that I think about that is that the internal kinetic energy shows up as the molecules vibrating and is represented by the temperature of the substance. Note that I distinguish this vibration from the motion the molecules will exhibit in the gas/vapor phase.
The internal potential energy is represented by the inter-molecular forces between molecules in a substance. Substances are held together by attractive forces between molecules called cohesion. It turns out that there is an intermolecular distance where the internal potential energy of a substance is at a minimum, which is called the equilibrium distance. It takes work to increase or decrease this distance. In a solid, the molecules tend to be arranged in rigid, geometric structures that are defined by the equilibrium distance. Generally speaking, the only molecular motion in a solid is the molecular vibration I mentioned above. And they will tend to try to hold their own shape, resisting any change, and are incompressible for all intents and purposes.
If we add energy to a substance that is a solid, the internal potential and kinetic energy of its molecules are increased. If we add enough energy, then at some point the internal energy increase is sufficient to break the rigid bonds that make the substance a solid and it starts to flow, changing phase to a liquid. Liquids can not hold their own shape and will take the shape of the container that holds them. But, since they generally just about as dense as they were in the solid phase, they are still considered incompressible.
If we continue adding energy to the liquid, the internal energy of the molecules continues to increase and eventually reaches the point where the molecules have sufficient energy to break the cohesive bonds that have been holding them together up to this point. Once the bonds are broken, the molecules can fly around at high velocities. As a result a gas will not retain its shape or size. The molecules will move to maximize the distance between them and completely fill the container they are in. Unlike solids and liquids, gasses can be compressed.
3. Most of the temperature scales we use on a daily basis are referenced to the freezing point and boiling point of pure water. But, for instance, if you have ever been to Minnesota or Wisconsin in the middle of the winter, you know for a fact that it can get much colder than 32°F or 0°C (the freezing point of water on two common temperature scales). In general terms, absolute zero is a state where matter is at its lowest internal energy level. By international agreement, it is set at −273.15° on the Celsius scale and −459.67 on the Fahrenheit scale.
4. In general terms, something is considered a vapor if it is at a state where it could fairly easily change phase back to a liquid. In other words, its state is somewhere near the saturation curve on a thermodynamic diagram. If the temperature of the vapor is raised much higher than its saturation temperature (the temperature at which it would start to change phase), then it is considered a gas.
5. Eventually, this accumulated water would begin to impact the volume available for vapor in the tank but for the sake of our discussion, we are assuming the effect is negligible.