If you look at a psych chart closely, you will notice that the constant wet bulb lines are not exactly parallel to the constant enthalpy lines.
Note that to make things more visually apparent in this blog post, for most of the psych chart images, I have narrowed down the temperature and humidity scales. So the chart probably looks a bit different from what you are accustomed to seeing.
In any case, it’s tempting to just ignore the fact that the enthalpy and wet bulb lines are not exactly parallel. But in the context of an evaporative cooling process, the non-parallel nature of the lines is an important distinction if you are trying to understand the physics behind the process. The purpose of this series of posts is to explore that distinction a bit and look at what it means practically in the context of air handling systems that use an evaporative cooling process.
The context for all of this was that we were lucky enough to have a field day in a facility that was served by both direct and indirect/direct evaporative cooling air handling systems (with “we” being myself and the folks participating in the current round of the Existing Building Commissioning Workshop at the Pacific Energy Center). Here is the Google Earth view of the facility we were at, and you can see the systems we were working with sitting in the equipment area on the right half of the roof. (The round structure is a planetarium, so, pretty cool to be working on a building with a planetarium.)
If you know how the direct and indirect/direct evaporative cooling processes work, you can actually tell which unit is which by studying the appearance of the equipment in the Google Earth image. So, I will let you check out what you learn from reading this by coming back and identifying which unit is which after you finish the series.
From my perspective as an instructor, the evaporative cooling systems represented an unique opportunity to connect the psych chart with reality. For the class participants, it is a chance to see something different and learn how to understand it by thinking about it in terms of fundamental principles (I hope).
To me, this is an important thing. If I and others like me were to endeavor to spend the days that remain to us in instruction targeted at describing every conceivable type of HVAC system that might exist, we would simply run out of time, as can be seen from the following relationship, which calculates the maximum possible number of HVAC system configurations that could exist in our little corner of the universe.
On the other hand, at the end of the day, the phenomenon going on in most HVAC systems can generally be described by a few fundamental relationships and tools including the steady flow energy equation …
… which I realize is a bit scary until you think of it in the terms Dr. Albert Black, one of my mentors put it to me in, those terms being that …
The Goes Inta’s Gotta Equal the Goes Outa’s.
My recollection is that Al (modestly) told me that he can not claim total credit for that phrase in that it was passed to him by one of his mentors. But it resonated with me and has been a guiding principle and foundation for me when all else seemed to fail. That includes something that happened in the context of my developing this blog post; i.e. being confronted, as I frequently am, by the realization that understanding something and being able to explain it are two different things.
I actually learned that lesson very early on in my technical training career as a flight line lab instructor when in my first lab session, an aspiring Airframe and Power Plant Mechanic (A&P) asked me (a freshly minted A&P) a question about a concept that I understood, but found that I could not explain in a way that made sense to him. So, I told him I didn’t know how to provide a clearer answer to the question right then (harder than it sounds, at least for some of us) but that I would fix that and and get back to him, which I did and have been doing ever since. It’s one of the things I really love about teaching; to teach, at least in my experience, you have to be in a constant state of learning.
Al also pointed out to me at one point that all of this math is just a reasonable model for us to use to predict what might be going on in an HVAC system and building. In reality, we probably don’t really have a clue.
Beyond conservation of mass and energy, one of the most important tools for understanding what is going on in an HVAC system is the psychrometric chart. This is something that Bill Coad initially inspired me about via his very cool engineering trick of creating one by hand via the application of basic principles. Replicating that trick is the subject of yet-to-be completed string of blog posts starting with this one. Eventually, I will get all of the way through showing you the trick, so stay tuned.
The specific driver behind my developing this post was a field question that came up several times in the field class regarding the evaporative cooling process. If you are looking at the depiction of the process on a psych chart and don’t fully appreciate that the constant wet bulb and constant enthalpy lines are not totally parallel, then you might ask:
How can a water be evaporated by a process that occurs at a constant enthalpy which implies there is no energy change?
The answer is …
Actually, it is a constant wet bulb process not a constant enthalpy process, and the enthalpy of the air increases.
The amount of latent energy associated with adding water to the air stream by evaporation is in fact exactly equal to the reduction in sensible energy in the air that entered the process. But the water represents mass being added to the air stream and that mass had some energy associated with it before it entered the process, just like the air did. So the enthalpy at the the end of the process, with the added water vapor mixed in with the original air sample has been increased by the amount associated with the added water.
It turns out that to really explain this, at least to explain it in the way I thought I needed to, things got long (surprise). So what started out as a blog post has evolved to series.
The remainder of this post will be dedicated to explaining some basics behind the evaporative cooling, primarily adiabatic saturation and wet bulb temperature. I will follow this post with a post that looks at practical adiabatic saturation a.k.a. evaporative cooling. Finally, I will do a post sharing what we saw in our recent field experience, along with some of the insights that were gleaned from the experience.
As is my practice for my annoyingly long blog posts, the following links will take you to topics of interest which will include a “Back to Contents” link at the end of the section to bring you back here.
- The Energy Content of a Parcel of Air
- A Sojourn Into the Weeds
- Exiting the Weed Patch
- Measuring the Total Energy Content of a Parcel of Air
- Adiabatic Saturation; the Principle Behind the Psych Chart
- Exploring the Process from a Conservation of Mass and Energy Perspective
- Wet Bulb Temperature; a Very Close Cousin of the Adiabatic Saturation Temperature
- Sigma Heat
- Sigma Heat and the Sensible to Latent Energy Trade-off Are Not Exactly the Same Thing
- Constant Sigma Heat = Constant Adiabatic Saturation Temperature
- Measuring Wet Bulb Temperature the Old Fashioned Way
- Measuring Wet Bulb Temperature with New Fangled Technology
- Some Wet Bulb Temperature Measurement Conclusions
- The Weed Patch
The Energy Content of a Parcel of Air
A parcel of air is a concept used in psychrometrics and meteorology. It implies a sample that is large enough to contain many molecules, but much smaller than the surrounding volume or environment. It will have uniform temperature and moisture characteristics but those characteristics may be different from the surrounding environment.
The bubbles of steam that rise through the liquid in a pot of boiling water are an example of a parcel. Both the vapor and liquid are made up of water molecules, but the conditions inside the bubbles are different from the conditions outside the bubble
To understand evaporative cooling, you need to understand what makes up the energy content of a parcel of air. Unless a parcel of air is totally devoid of moisture (0% relative humidity), then the energy it contains includes both a sensible energy component and a latent energy component.
The sensible component is the easiest to understand because manifests itself to us as the the dry bulb temperature. Most people are very familiar with it and frequently, we simply call it the “temperature” of the air. Changes in dry bulb temperature are associated with the change in sensible energy.
Another way of thinking of it is to say that sensible energy manifests itself to us as heat. If I increase the sensible energy of an object, it becomes hotter to the touch with “touch” being one of our senses and thus the name.
Our comfort is also affected by the amount of moisture in the air because it impacts how efficiently (or not) our body’s evaporative cooling process works. If you have traveled around the country a bit, you probably have noticed that a 95°F, sunny day at someplace like the Grand Canyon feels much more comfortable than a 95°F, sunny day in the Midwest or Southern states or even Northeastern states like Pennsylvania right after a thunderstorm. That is because the summer time air is much dryer at the Grand Canyon (most of the time), compared to the summer time air in the Midwest, South, and Northeast.
The moisture in an air parcel has energy associated with it because it takes energy to convert the moisture from a liquid to a vapor (or from a solid to a liquid for that matter). Going from a liquid to a vapor or a solid to a liquid is called a phase change.
Unlike sensible energy, the energy associated with the phase change that adds moisture to a parcel of air does show up as a temperature increase. Rather, we sense it a change in comfort level that we frequently call feeling “muggy” or “humid”.
So the good news is that we can detect that it is there. But unlike heat, which we can measure with a thermometer, it can be challenging to measure and quantify “mugginess”. The term applied to this energy is latent energy or sometimes, latent heat.
Latent is a term that means “hidden” or “concealed” and it is used to describe the energy associated with a phase change because. We really didn’t understand latent heat until about 250 years ago when a Joseph Black, a Scottish scientist intuitively connected a few dots by pointing out that what people thought should happen, based on the science of the time, did not actually happen.
For instance, the science of the time suggested that it would take only a small amount of heat to melt snow and ice. Mr. Black pointed out that if that was really true, then the world would be ravaged by floods due to the immediate melting of snow and ice when the temperature increased from just below to just above freezing. In other words, the expected didn’t happen, which implied there must be something else going on.
He reached a similar conclusion about boiling water by observing that while below the boiling temperature, the addition of heat caused the water temperature to increase fairly quickly. But once boiling started, applying the same amount of heat did not cause the temperature to change at all but rather, caused the water to become vapor at the same temperature as the boiling water.
He also noted that it took quite a bit of time and heat to convert all of the water from liquid to vapor relative to the amount of heat it took to simply raise the temperature to the boiling point. In other words, a significant amount of energy had to exist in the water vapor that was generated by the boiling process, even though its temperature was the same as that of the liquid water it came from. That energy was invisible in the context of the conventional way of measuring heat (temperature) and he termed it “latent energy”.
Enthalpy is the term we used to refer to the total energy content of an parcel of air. It will be exactly equal to the sum of the sensible energy and latent energy in the air parcel and is typically expressed in terms of energy per unit mass; Btu per pound in the system of units we typically use here in the United States.
The symbol h is often used for enthalpy. There are a couple of conventions that often show up in psychrometric discussions, steam tables, and psychrometric equations.
- h with out any subscript usually stands for the total enthalpy of the parcel of air, both the sensible energy of the dry air plus the sensible energy of the water vapor and the latent energy of the water vapor.
- hf typically represents the enthalpy of the saturated liquid.
- hg typically represents the enthalpy of something in its gas/vapor state.
- hfg typically represents the energy associated with the transformation of something from the liquid to a vapor state; i.e. the energy associated with a phase change.
A Sojourn Into the Weeds
You may actually think we already were in the weeds. And we probably are a little bit.
But they weeds are more like Queen Anne’s Lace …
… and Dandelions, both of which I actually happen to like and thus, don’t consider weeds. Truth be told, there are very few plants that I don’t like (and there are very few things that don’t fascinate me at some level). So there are very few things I consider weeds (plant-wise and otherwise).
But I am pretty sure I am a bit odd that way, so I am just trying to draw a line of distinction to acknowledge that I realize what I am doing here in that context.
Having said that, there have been occasions where I was totally confused because, for instance:
- I did not realize that a certain symbol could be used in multiple ways, or
- I didn’t realize that that the baseline for enthalpy on a pych chart is arbitrarily set to 0 Btu/lb at 0°F;
Stuff like that. So, as I was writing this post, I was including all of that information in the stream of it. But doing made it even longer than I had thought it would be. In addition, at one point, I realized that it could obscure the real information I was trying to convey.
But, since some of the details I am alluding to here are important to be aware of, I decided I would create a “weed patch” at the end of the post and put that information there so you could jump to it if you wanted to or just keep moving forward through the primary content of the post.
So if you are interested, the “weed patch” contains the following “weeds” along with a “Back to Contents” link so you can get back to where you came from pretty easily if you go there.
- The Same Symbol can Mean Different Things
- Enthalpy of Formation is Related to but Not the Same Value as Enthalpy on a Psych Chart
- Air is Not a Molecule
- Enthalpy Values Vary from Source to Source; How Can That Be?
- We Treat Air as an Ideal Gas Even Thought the Water Vapor it Contains Does Not Behave That Way
- Sensible Energy Lost = Latent Energy Gain for a Moist but not Totally Saturated Parcel of Air
- Specific Heat – A Measurable Quantity
Exiting the Weed Patch
O.K.; enough of that.
The reason that understanding sensible, latent and total energy matters in the context of a discussion about evaporative cooling is that the amount of cooling – i.e. the energy change – provided by an evaporative cooling process is very much dependent upon the amount of moisture in the air and the latent energy it represents. That means that if we really want to understand the energy content of an air sample, we need to know more than its temperature. We also need to have some sense of the amount of water vapor it contains.
That is basically what the science of psychrometry is about; it is the study of the physical and thermodynamic properties of gas/vapor mixtures. The sensible energy is reflected by the psychrometric property called dry bulb temperature. The latent energy is reflected by a number of psychrometric properties including including relative humidity, wet bulb temperature, and dew point temperature. Both the sensible and latent energy (total energy) are reflected by the property of enthalpy.
Measuring the Total Energy Content of a Parcel of Air
Quantifying how much moisture is in the air is actually much harder than it sounds, and we have been trying to figure out how to do it for a long time. While reading The Invention of Clouds, which is about Luke Howard (the person who came up with the system we use to this day to classify and discuss clouds) I learned that in China, over 2,000 years ago, during the Han Dynasty, the scientists of the time used the change in weight of a dry piece of charcoal that was exposed to the atmosphere as a measure of humidity; pretty clever.
As a somewhat related aside, one of my favorite philosophical quotations comes from a a 6th century BC Chinese philosopher named Lao-Tzu who once said:
If lightning is the anger of the gods, then the gods are concerned mostly about trees.
Anyway there are a multiplicity of approaches that we have used over the years to try to quantify the moisture content in a sample of air. The Malcolm J. McPherson reference I provide a bit further down has a pretty good discussion about them if you are interested.
But if your are trying to do building science and quantify latent energy in an air sample, you will eventually run across a discussion of the concept of adiabatic saturation. The concept is important because it is the basis for wet bulb temperature measurements, one of the basic ways we assess moisture content in the air.
Adiabatic Saturation; the Principle Behind the Psych Chart
A Scary Sounding Term
The device that is used to define adiabatic saturation, is appropriately enough an adiabatic saturator. That name sounds scary and complicated and may cause you to want to run off and pursue something else.
But its actually a relatively simple device and (thank goodness) no where near as complex as a turboencabulator. Now that is a device where the scariness of the name is warranted due to it’s reliance on a mixture of high S-value phenyhydrobenzamine and 5 percent reminative tetraiodohexamine for operation rather than a mix of air and water vapor.
In addition, critical to the functionality of a turboencabulator is the alignment between the two spurving bearings and the pentametric fan, which of course, requires that six hydrocoptic marzelvanes be installed on the ambifacient lunar vaneshaft to prevent side fumbling.
In contrast, the entry and exit points in the adiabatic saturator can have significant misalignment issues as long as they are far enough apart to allow the adiabatic saturation process to run to completion.
Truth be told, if success in building science relied on a deep working familiarity with the principles of turboencabulation, many of us would have fallen by the wayside given the complexity.
But thankfully, to understand evaporative cooling and for that matter, the psychrometrics of moist air, we only need to grasp the operation of an adiabatic saturator. That’s because in reality, an evaporative cooler is just a practical implementation of an adiabatic saturator.
Adiabatic Saturation Descriptions
Adiabatic saturation is a kind of thought experiment that involves a device in which an parcel of air is cooled adiabatically (with out the addition of heat from an external source) to saturation (100% relative humidity) by evaporating water into it. All of the energy (latent heat) required by the evaporation process comes from the parcel of air and as a result, the parcel of air is cooled (sensible energy is reduced) as its moisture content (latent energy) increases.
Aside from the explanations given to me by my mentors I have encountered two written explanations of adiabatic saturation that seemed very approachable to me. One is provided by Willis Carrier in his book Modern Air Conditioning, Heating and Ventilating where he describes a process that involves a fan blowing air through an insulated box full of wetted excelsior (softwood shavings that were used to package fragile items back in the olden days).
You can still find copies of the book and to me, it is worth having for a number of reasons ranging from sentiment to the fact that one of the stated goals of the book was to present the material in a manner that would not only be useful to the scientifically minded, but also to those who had a technical interest but not an extensive background in engineering and science.
In other words, they hoped to convey somewhat complex information in a useful manner to people coming into the field from some other industry, like airplane mechanics in my case. In other words, people who have taken an interesting in building science but are coming at it from outside of the engineering profession.
And, in my opinion, the authors did a pretty good job of it. So, I have scanned the pages on adiabatic saturation from my copy of the book and put them on a page on our commissioning resources web site if you are interested.
The other explanation that made sense to me is part of the chapter on psychrometrics (Chapter 14) in a book by Malcolm J. McPherson titled Subsurface Ventilation and Environmental Engineering where he uses the analogy of air flow through a long tunnel with no heat sources in it and a puddle of water on the floor, which I imagine might be what some parts of a mine might be like.
There seems to be a .pdf copy of Mr. McPherson’s psychrometrics chapter out there in the public domain if you want to take a look. In addition to providing an approachable explanation of adiabatic saturation, it is also an approachable explanation of psychrometrics in general so you might find downloading a copy to be useful.
My Concept of Adiabatic Saturation
For the purposes of this post, I made a little diagram to illustrate the adiabatic saturation concept as I understand it.
You start out with an insulated chamber so that the air and water in it will not experience any heat transfer from external sources which is what makes the process adiabatic.
The chamber also needs to be very, very long, some say infinitely long (which I guess is why you seldom see one sitting around out there in the field since they would get in the way a lot). But the length is necessary so that by the time the air parcel exits the chamber, it has come into equilibrium with the liquid water in the pool inside the chamber and is saturated, meaning the relative humidity is 100% .
In other words, the air is going to exit the process at a point on saturation curve on the psychrometric chart.
Since water will be evaporated from the pool inside the chamber into the air stream, there needs to be a water make-up connection. But to ensure that energy is not transferred from the water to the air stream by radiation or convection, the temperature of the water must be controlled to match the saturated leaving air temperature so that by the end of the process, the water temperature has no influence on the energy content of the air.
Bear in mind that the pressure of the parcel of air entering the process is created by the combined action of the constituent air elements as well as the action of the water vapor molecules, each contributing to the total pressure. The pressure contributed by a constituent element is called its partial pressure. If you want a more detailed explanation of this, or at least my take on it, you may want to take a look at the blog post titled Build Your Own Psych Chart – A Few Fundamental Principles.
Since the air coming into the process is not saturated, the partial pressure of the water vapor it contains is lower than the vapor pressure of the water in the pool inside the chamber. Thus, there is a driving potential causing water to evaporate from the pool and become water vapor in the air parcel.
Conceptually, this is very similar to sensible heat being transferred from a warm object to a cold object. The temperature difference is what causes the heat transfer to take place and the bigger the temperature difference, the higher the heat transfer rate will be.
In the case of water vapor, it is the difference in vapor pressure that causes the water vapor to move around. It will be inclined to travel from an area with a high vapor pressure – for instance the immediate vicinity of a liquid water surface – to an area of lower vapor pressure – for instance, the dry parcel of air entering and moving through the adiabatic saturator.
Because we have insulated the adiabatic saturation chamber and we are maintaining the make up water temperature at a fixed value that is identical to the leaving air temperature, the only source of energy available to cause the water to evaporate is the sensible energy in the air parcel. As a result, the air parcel is cooled while its moisture content is increased until it becomes saturated. At that point, the driving potential (the difference between the partial pressure of the water vapor in the air and the vapor pressure of the water in the pool) is zero and no additional water is evaporated.
Since all of the energy required to saturate the air came from the sensible energy in the air when it entered the device, the latent energy added is exactly equal to the sensible energy lost. The resulting temperature is called the adiabatic saturation temperature or thermodynamic wet bulb temperature, the technical definition of which is:
The temperature a volume of air would have if cooled adiabatically to saturation by evaporation of water into it, all latent heat being supplied by the volume of air.
It is the difference between this parameter and the dry bulb temperature of the air entering the process that sets how much cooling will occur for a given air parcel.
This is a very important thing in the context of evaporative cooling. For a dry air parcel from, say, the Grand Canyon area in the summer, the difference will be large compared to that of a moist air parcel from say, central Pennsylvania after a summertime thunderstorm. As a result, more evaporative cooling can be produced by the Grand Canyon air parcel than the central Pennsylvania air parcel.
For a saturated air parcel, there is no difference between the dry bulb and adiabatic saturation temperature and thus, no evaporation (and no cooling) will occur.
Exploring the Process from a Conservation of Mass and Energy Perspective
Conservation of Mass
From a conservation of mass standpoint, the adiabatic saturation process looks something like this for a parcel of air that enters the process totally devoid of any mosture.
Note that there is a net increase in mass through the process because of the water vapor that is added to the air parcel. This is important and it is why the enthalpy (total energy content) of the air parcel increases through the process.
Conservation of Energy
From a conservation of energy standpoint, the adiabatic saturation process looks like this for that same parcel of air.
Essentially, the equation says that there is an increase in energy (enthalpy) through the process due to the addition of the water that is evaporated into the air parcel.
But to fully appreciate what is going on, I am going to expand the terms in the relationship above a bit. And in doing that, I am going to focus on a special case because (I think) it will allow me to make the point I am trying to make in a bit less confusing manner. Specifically, I am going to focus on the case where the air entering the process is totally dry (0% RH).
Sensible Energy Lost = Latent Energy Gain
The expanded form of the equation includes terms for the sensible energy that is lost from the air parcel (the green term) and the latent energy that is gained by the air parcel (the purple term) as it moves through the adiabatic saturation process. Since the latent energy increase is exactly equal to the sensible energy decrease (by the definition of the process), then the combination of the two terms ends up being zero.
That means that the only reason that there is an energy gain in an evaporative cooling process is due to the energy that comes in with the mass of the water that is evaporated.
In some way’s it’s kind of hard to get your head around the energy represented by the purple and green terms in the equation. It’s there, but it’s not there, kind of like Wile E. Coyote’s ACME Corporation portable hole. But the reality is that, this is very useful thing to recognize for those of us using psychrometrics to assess HVAC systems.
Stated mathematically, the words the latent energy increase is exactly equal to the sensible energy decrease (i.e. the purple term in the expanded equation is exactly equal to the green term) look like this on a per pound of air basis using psychrometric parameters for our special case (check out the Weed Patch for the more general case where the air coming into the process has some water vapor in it).
In other words, we could figure out how much water the totally dry air could hold if we saturated it by measuring the temperature change through the process and multiplying it by the specific heat of air (the 0.24 value).
The temperature change through the process is the difference between the entering dry bulb temperature and the leaving dry bulb temperature. The leaving dry bulb temperature is equal to the adiabatic saturation temperature, by the definition of the process.
If we could come up with those three numbers, then we could figure out how much water a totally dry parcel of air at a specific dry bulb temperature would hold if we saturated it using an adiabatic saturator. Heck, if we could do it, that would let us draw the saturation curve for a psych chart . This could be cutting edge!
We can easily measure the dry bulb temperature of the entering air parcel. And the specific heat of air is also a measurable quantity and well documented (check out the weed patch for more on that).
Gosh, if only there was a real world way to measure the mythical adiabatic saturation temperature of the entering air parcel, we would be able to quantify how much evaporative cooling a given parcel of air could produce.
Wet Bulb Temperature; a Very Close Cousin of the Adiabatic Saturation Temperature
By virtue of a happy thermodynamic coefficient coincidence, a thermometer that has its bulb covered by a wet wick will nearly (but not exactly, more on that later) measure the adiabatic saturation temperature of air at the conditions commonly encountered in an HVAC system.
In fact, the value it indicates is close enough to the adiabatic saturation temperature that we can assume that the the adiabatic saturation temperature is identical to the temperature measured by a thermometer with a bulb that is wet.
In fact, when we plot constant adiabatic saturation temperature lines on a psych chart, we are actually plotting constant thermodynamic wet bulb temperature lines. And, we call them temperature measured by a thermometer with a bulb that is wet lines.
Well, actually, we generally don’t call them that. But my point is that constant wet bulb lines on a psych chart specifically represent a value that goes by two different names (adiabatic saturation temperature and thermodynamic wet bulb temperature) neither of which is what we typically measure out in the field.
The word “thermodynamic” ahead of the term “wet bulb” reminds us that what we measure with a thermometer with a bulb that is wet (which we often call a wet bulb thermometer) is not quite the same thing as the adiabatic saturation temperature, a.k.a thermodynamic wet bulb temperature.
But we sure feel calmer, and thus, continue to breath normally, by calling what we measure the “wet bulb temperature” instead of “the temperature measured by a thermometer with a bulb that is wet” or “the approximate adiabatic saturation temperature”.
So having beaten that into the ground, moving forward, I will refer to the temperature measured by a thermometer with a bulb that is wet as wet bulb temperature.
The Stationary Wet Bulb Thermometer
The stationary wet bulb thermometer was one of the earliest ways that folks used to try to understand the amount of moisture in a sample of air by measuring the temperature of a thermometer bulb that was wet (the images below are courtesy of http://physics.kenyon.edu/EarlyApparatus/Thermodynamics/Hygrodiek/Hygrodeik.html)
Empirical data (data based on observation or experience vs. theory or logic) derived using an instrument similar to the images above was likely the starting point for the psych chart as we know it today.
The stationary wet bulb thermometer evolved to the sling psychrometer, which I will describe and illustrate later in the post.
Incidentally, if you are interested in learning a bit more about the history of psychrometrics in our industry, then you might find the AHSRAE Journal article titled Psychrometric Chart Celebrates 100th Anniversary to be of interest. You can find a copy on the Hands Down Software web site (they are the folks behind the free Pacific Energy Center psych chart that I have written about on the blog).
Returning to our discussion about the perfectly dry air parcel that moves through an adiabatic saturator, recall that we had concluded that we could figure out how much water it would take to saturate the air if we knew the entering dry-bulb temperature (tEntering in the equation below) and the adiabatic saturation temperature (tLeaving in the equation below).
Now we know that we can do it if we measure the dry bulb temperature of the air parcel and also measure the temperature of the air parcel using a wet bulb thermometer. There are two interesting things to recognize as you contemplate all of this.
One is that the only reason there is a change in total energy content/enthalpy through the evaporative cooling process is that the water that was evaporated into the process – i.e. the mass that was added – already had energy associated with it; the enthalpy associated with the saturated liquid for water at the conditions entering the process. But bottom line, the change in total energy/enthalpy through the process is entirely due to the addition of mass and the energy it brings into the process.
The rest of the process is just trading some of the sensible energy in the entering air parcel for latent energy in the leaving air parcel, which is the second point of interest.
If you rearrange my expanded form of the conservation of energy equation to show this mathematically, it looks like this.
In other words, the amount of energy that entered the process as sensible energy in the totally dry air does not change; it stays constant.
The only thing that changed was how much of it is sensible energy and how much of it is latent energy at the end of the process. Willis Carrier recognized this and that is where the term Sigma Heat came from.
In the psych chart below, I started with air at the 0.4% cooling design conditions in a number of climates and calculated Sigma Heat for that air as it moved through an adiabatic saturator to saturation, and also what would happen if that air sample entered the saturator at the same adiabatic saturation temperature but with a lower specific humidity.
Notice how the lines are straight lines that follow the constant wet bulb temperature lines and diverge slightly from the constant enthalpy lines.
Sigma Heat and the Sensible to Latent Energy Trade-off Are Not Exactly the Same Thing
Just to be clear, Sigma Heat and the amount of sensible energy that is converted to latent energy in the adiabatic saturation process are not exactly the same thing. For the temperatures and pressures we deal with in HVAC, the entering air parcel will have a lot more sensible energy available that is required to saturate it by evaporating water into it.
The important point is that the sensible to latent trade-off energy is part of Sigma heat. And the amount of energy traded off is a function of the difference between the entering dry bulb temperature and the entering wet bulb temperature. In other words, Sigma Heat is a pure function of the difference between the entering dry bulb temperature and the entering adiabatic saturation temperature.
Constant Sigma Heat = Constant Adiabatic Saturation Temperature
At this point, I imagine you have realized that the amount of water vapor that exists in a parcel of air is reflected by it’s wet bulb temperature. Relatively dry air will have a lower wet bulb temperature than relatively moist air, all other things being equal.
In addition, the amount of water vapor that a parcel of air can hold will be reflected by the difference between it’s dry bulb temperature and its wet bulb temperature. The difference between the two represents sensible energy available in the air parcel which can be used to pick up moisture via conversion to latent energy. The bigger the difference, the more water vapor that can be evaporated into the air parcel. When the two are identical, the air parcel is saturated and can hold no additional water vapor.
Furthermore, that conversion energy is a component of the Sigma Heat of the air parcel, which remains constant in an adiabatic saturation process. So if you think about it, that implies that for every dry bulb temperature, there is a very specific wet bulb temperature (adiabatic saturation temperature). And:
- Because Sigma Heat is a pure function of the wet bulb temperature (adiabatic saturation temperature), and
- Because Sigma Heat remains constant through the adiabatic saturation process (evaporative cooling process), then
the wet bulb temperature (adiabatic saturation temperature) will remain constant through an adiabatic saturation process (evaporative cooling process). That means that if you wanted to model and evaporative cooling process on a psych chart, you would do it by moving up a constant wet bulb temperature line.
In the psych chart below, I started with air at the 0.4% cooling design conditions in a number of climates and calculated Sigma Heat for that air as it moved through an adiabatic saturator to saturation, and also what would happen if that air sample entered the saturator at the same adiabatic saturation temperature but with a lower specific humidity.
I can imagine that even if you were only mildly excited by the content of this post up to this point, that the revelations of this section have made you ecstatic, perhaps kindling a desire to go get yourself something that can measure wet bulb temperature. So, lets take a look at a couple of the options for doing that next.
Measuring Wet Bulb Temperature the Old Fashioned Way
In the olden days, when I first entered the industry, wet bulb measurement involved using a device called a sling psychrometer (the black gizmo to the right in the picture below), which relied on evaporative cooling to directly generate the wet bulb temperature.
It was an improvement over the stationary wet bulb thermometer for a number of reasons including the variable nature of the velocity of air flow across the stationary device.
Now-days, we use modern electronics and measure relative humidity and dry bulb temperature (the “space age” light gray gizmo on the left in the picture). There are some pros and cons to both approaches, which I will get to in a minute.
In this breath-taking close-up of the sling psychrometer, you can see that it actually has two, identical, factory matched thermometers, one of which has a cloth sleeve (called a wick) around its bulb (the upper one in the photo).
The little cap on the left is actually the cover to a water reservoir that the wick threads into. Once the wick has absorbed some water, it will keep the bulb of the thermometer that it encases wet, thus, the term wet bulb
To take a reading, you use the vertical part that is pointed down and off the picture as a handle and swing the horizontal part as quickly as you can for about 1-2 minutes(while avoiding slamming it into things like walls, ducts, pipes, associates, etc. that are in the vicinity).
As a result of all of this activity, the temperature of the bulb with the wick will drop due to – you guessed it – evaporative cooling. At some point, the temperature of the wick, the bulb, and the water will come into equilibrium with the moisture content in the ambient air and the temperature will stop dropping. That point is what we call the wet bulb temperature.
Slinging the thermometers for 1-2 minutes is harder than it sounds and if you do it a lot, I suspect you get pretty well developed fore-arm muscles on your “psychrometer arm”. But the speed and time are important because you want enough air to flow past the bulb with the wick on it so as to keep the little micro climate in the area of the wick at about the same condition as the ambient environment.
If you don’t keep it moving fast enough, the water evaporating from the wick will influence the local vapor pressure in the immediate vicinity of the thermometer bulb, which affects a number of things. But bottom line, you end up with a high reading.
When I am using a sling psychrometer, after my first 1 –2 minutes of slinging, I stop, take a quick reading, and then sling again for another 30 or so seconds to make sure I have reached the equilibrium state; i.e. if my second reading is the same as the first one, I figure I have.
But if it has dropped some more, I keep on slinging a bit more (aching fore-arm aside) until I get two readings in a row that are about the same. Here is what my psychrometer looked like right after I slung it in my office earlier today; wet bulb above and dry bulb below.
It’s important to take your reading right away because once the airflow stops, the wet bulb will start to rise pretty quickly. In fact the wet bulb reading in the picture is a bit higher than it was when I stopped slinging because of that effect.
Parallax also comes into play in the context of the picture; you need to read the thermometer “dead-on” and some psychrometers even have mirrored scales to facilitate that. The content just below where this link takes you talks about mirrored scales and parallax if you want to know a bit more.
You also want to be careful not to touch or breath on the thermometers since that could also throw your readings off. But bottom line, once you know a dry bulb temperature and a wet bulb temperature (or any other indication of moisture) you can use a psych chart or psychrometrics calculator to come up with other parameters like relative humidity.
Or you can just use the handy slide-rule built into the sling psychrometer.
As you can see from the image above, my little field test said the RH in my office is about 58%.
What I like about that number is that it was generated directly by fundamental principles (evaporative cooling and the expansion of the thermometer liquid from the bulb up a capillary tube) with no batteries or electronics in-between what I was measuring and the result.
But it is very much subject to technique and is also limited by the manufacturing tolerances of the thermometers. If you go to the spec sheet for my little Bacharach tool, you will discover that it is accurate to +/- 1°F dry bulb, which, since two thermometers are involved in generating an RH reading, translates to being accurate to +/- 5% RH.
Thermodynamic Wet Bulb Temperature vs. the Wet Bulb Temperature Measured with a Sling Psychrometer
As discussed earlier in the post, wet bulb temperature lines on a psych chart are more specifically thermodynamic wet bulb temperature or adiabatic saturation temperature lines. The wet bulb temperature we measure out in the field is not exactly the same thing and there are a number of reasons for that.
- As the water in the wick starts to cool off, it starts to pick up energy via convection from the air around it and by conduction from the thermometer itself. As a result, the energy balance is different from what happens in the mythical adiabatic saturator.
- There is likely radiant energy transfer from the sling psychrometer itself as well as the surrounding environment, unlike the process in the adiabatic saturator.
- If the velocity of the air is too low (i.e. you don’t sling fast enough), then the environment in the immediate vicinity of the wet bulb may be at a different state from the free air stream due to the water that is evaporating into it from the wick.
- The temperature of the water to the wick is not controlled to match the thermodynamic wet bulb temperature where-as in the adiabatic saturator, it is.
- If the water is not pure or the wick is dirty, then evaporation will be different from what would occur with clean water and a clean wick.
At a fundamental level, the thermodynamics behind what causes a wet bulb thermometer to register a temperature lower than the dry bulb temperature are fundamentally different from the process occurring in an adiabatic saturator.
But by a happy coincidence of physics. the coefficients associated with the thermodynamics of the real wet bulb process (there is a convective heat transfer coefficient and a mass transfer coefficient involved) are such that the result is very nearly identical to the thermodynamic wet bulb temperature, at least for a mixture of air and water vapor in the range where we apply the device in building science.
If you want to know a bit more about that, there is a YouTube video by a guy named
Mitchell Paulus that will give you a pretty good idea the mathematics behind what I just typed. He also has a couple of videos where he goes through the mathematics of adiabatic saturation, which you probably would want to look at first since that math becomes the foundation for the match in the video about the difference between sling psychrometer wet bulb and thermodynamic wet bulb.
There is also a paper out there titled Calculation of the Natural (Unventilated) Wet Bulb Temperature, Psychrometric Dry Bulb Temperature, and Wet Bulb Globe Temperature from Standard Psychrometric Measurements that explores the topic and includes charts showing the amount of deviation and how it varies with different conditions like wind speed and the radiant temperature of the surroundings.
Measuring Wet Bulb Temperature with New Fangled Technology
As I said previously, in my day, we measured wet bulb temperature by slinging a psychrometer until our arm ached, and we liked it. But people these days want everything to be easy schmeezey so they buy fancy schmancy electronic gizmos to measure wet bulb temperature with the press of a button.
Truth be told, so do us old timers.
Contrast the Bacharach result with what my modern electronic gizmo said was going on at the same time (a Vaisala HM 40 series hand held humidity and temperature meter). At the conditions that existed in my office at the time of the reading, it is accurate to +/- 0.36°F and +/- 1.5% RH.
Pretty different from what my trusty sling psychrometer told me.
But, when I plotted the points on the psych chart along with a box around them to reflect the accuracy of the instrument associated with them and project the Vaisala accuracy window across the Bacharach accuracy window, I concluded that given the stated accuracies, both instruments did their job.
Note how the Bacharach RH window overlaps the projected RH window from the Vaisala HM 40 as does the dry-bulb temperature window. In terms of wet-bulb accuracy, this test result says the Bacharach is probably more like +/- 1.5°F vs. +/- 1°F.
But, as I discussed above, the wet bulb lines on the chart are thermodynamic wet bulb temperature lines, or more specifically, adiabatic saturation temperature lines , and the number they represent is not exactly the same as the temperature I measured with a thermometer bulb that was wet.
The test also says that the sling reading will tend to be higher than the reading derived from the Vaisala instrument. I have used the sling a lot longer than I have used an instrument like the Vaisala; the latter simply was not available for the first part of my career, at least not at an affordable level for me. But in thinking back through my experience taking readings with both instruments, I believe that most of the time, this tended to be true; i.e. the Bacharach relative to something like the Vaisala would tend to be high.
That could be the result of technique, the resolution capabilities of a glass tube with degree marks etched into it, and even the cleanliness of the wick; mine is a bit dirty right now and I should probably replace it. A dirty wick can impact the reading because it can affect the how well the water is absorbed by it and thus, how “wet” the wet bulb really is along with how easily the water can evaporate from the wick.
Some Wet Bulb Temperature Measurement Conclusions
couple of important and interesting things to note about all of this.
Accuracy Comes at a Price
If you wanted to buy a sling psychrometer like my Bacharach tool, it is currently priced at just a bit over $100 on Grainger. In contrast, the Vaisala HM40 starts at $534 for an instrument like the one in the picture and runs up to $1,168 for one with a longer, separate hand-held probe.
For even tighter accuracies, you might be looking at something like a Vaisala HMT330, which is the standard instrument used by the U.S. Climate Reference Network. Those can start at about about $1,900 and go up from there to as high as $3,000 or $4,000 depending on accessories and the specific application targeted for the device. For the added dollars, you get +/- 1% RH accuracy, so a 0.5% improvement over the HM-40 that I have. The temperature accuracy is +/- 0.36°F, which is the same as the HM40.
The Air Inside Came from Outside
If you assume an instrument similar to he HMT330 is being used at the Automated Surface Observation System (ASOS) station at the Portland International Airport (PDX), here is what it thought the humidity was outside when I was taking my readings inside the office.
It can be helpful when you are trying to understand what is going on in a building to remember that the air that is inside came from the outside. That means that the outdoor psychrometric conditions establish the baseline for the conditions inside the building.
Most of the time, unless you have a bunch of open desiccant containers lying around, the dewpoint/specific humidity inside will be no lower than the dewpoint/specific humidity outside. In fact, it will likely be a bit higher because there are things going on in most buildings that add moisture to the air in addition to adding heat.
The ratio of sensible heat or energy added inside the building to the total heat or energy added inside the building (i.e. sensible plus latent energy) is called the Sensible Heat Ratio or SHR. On a psych chart, if you plot that line using the SHR scale, it gives you a “visual” on how much energy is added to a parcel of air as it goes from one state to a different state.
It also helps you determine the leaving air temperature required from a cooling coil given a specific sensible and latent load to be addressed in a zone served by the coil. I discuss that in a bit more detail in the blog post about how to use Ryan’s free psych chart resource if you are interested.
When I plotted the implied SHR line for my office assuming that the air outside my house was about the same as the air at the airport, which is 13 miles East-Northeast of me, it implied that the SHR was about .65 (the orange line in the image above).
Initially, that seemed a bit high; typically, the SHR for a house or office will be in the 0.75 to 0.95 range. But my office has a number of moisture sources in it, some of which are a bit out of the ordinary including:
- A 30 gallon goldfish aquarium that runs with a water temperature of about 75°F (my office runs at about 67-69°F in the winter)
- A candle burning (combustion processes generate water vapor)
- A number of plants
- A hot cup of coffee (not out of the ordinary I suspect)
- An aging engineer who had just been vigorously slinging a psychrometer (probably not very common)
Plus, Kathy was doing some cooking up-stairs and that was generating enough moisture that the windows on the French Doors to the deck from the kitchen had some dew on them. So I am not surprised in hindsight by the higher than normal SHR.
My main point in bringing all of this up is to show how challenging it can be to measure relative humidity and how the humidity indoors is going to be related to the humidity outdoor somehow. For me, these things have been important considerations to keep in mind as I work with existing buildings.
Maintained Accuracy Comes at a Price
Short of breaking a thermometer (what happens if you don’t avoid walls, ducts, pipes, associates, etc. in the vicinity of your slinging), there is nothing much to cause my Bacharach instrument to go out of calibration. My bifocals are probably the biggest issue along with my age because ….
… what was I saying?
Anyway, if you did need to “recalibrate” the sling, then it would involve ordering 2 new thermometers for about $31 each.
In contrast, Vaisala recommends recalibration of their instrument once a year. You can have that done at the factory for $292 per year. If you want an extended warranty that covers parts, no questions asked, for three years plus calibration plus priority service plus shipping and handling, then it costs $380 per year. Alternatively, you could purchase a calibration tool for just under $1,000 and do the calibration on your own.
If you don’t do the calibration, then the industry data out there suggests that at some point, probably sooner rather than later, the Vaisala will have about the same accuracy as the Bacharach. This link (page down a bit after you go there) takes you to a page where there is a report done by the Iowa Energy Center for the National Building Control Information Program (NBCIP) that looked at out of the box accuracy and maintained accuracy for blind purchased humidity transmitters. The results were all over the place as you can see from the images below, which were extracted from the report.
Granted, the report is several years old now. But the technology in the electronic relative humidity instruments we are using currently is the same basic technology that was being used back when the report was developed.
My Sling Psychrometer is Probably as Good or Better than the Average Humidity Sensor Out There in the Field
Given the data in the report, which was specifically targeted at commercial building HVAC sensors, the data I glean from my Bacharach is probably about as good or even better than the average DDC system relative humidity sensor, especially if a high accuracy sensor was not specified and especially if the sensor has not received regular maintenance.
In the experience of FDE as a whole, calibrating a humidity sensor annually would be a minimum requirement. For critical applications, it is probably desirable to calibrate a humidity sensor every three to four months. This conclusion is generally consistent with the NBCIP Humidity Transmitter Product Testing Report Supplement (which looks at the long term accuracy of the sensors covered by the report mentioned previously) all though:
- The amount of drift varied from manufacturer to manufacturer, and
- The point in time when the most drift occurred varied from manufacturer to manufacturer.
For most buildings, where I am just trying to get a general idea of what might be going on, I am pretty comfortable with numbers from my sling if I don’t have anything else with me at the time. But that is contingent on using good technique and not taking the number I get more seriously than warranted given the stated accuracy of the device. If the system I am looking at uses a well maintained, high accuracy sensor, then that is a different situation in terms of what I would do with the data I got from my sling and I would likely want to use my HM40.
The Weed Patch
Just in case you wanted to know …
The Same Symbol can Mean Different Things
With regard to the hf term in the list earlier in the blog post; if you are doing chemistry, it is used to represent the enthalpy of formation, not the enthalpy of a saturated liquid. The way I think of enthalpy of formation is that it is the amount of energy it took to create the substance in the first place.
Enthalpy of formation values are based on molar quantities (the chemistry unit for amount of something usually in terms of number of atoms or molecules or fundamental particles) and are referenced to a specific temperature and pressure condition, typically 1 atmosphere of pressure and 298.15 K as I understand it (about 77°F). In contrast, the enthalpy of a saturated liquid is typically given on a Btu per pound basis for a specific saturation temperature and pressure.
The way I think of it is the saturated liquid enthalpy value includes the enthalpy of formation along with the additional energy associated with the difference between the saturation temperature you are working with and the reference temperature for the enthalpy of formation.
In some ways, the industry is not exactly good about using consistent sets of symbols and terms and you will find different symbols used in different discussions about the same concept by different resources, including some of the ones I will mention. So it is important to make sure you know what a symbol means in the context in-which it is being used. And it’s also important to document your use of a symbol in anything you are working on, just so there is no confusion.
Towards that end, because I am trying to write this so that it is approachable for folks who are wanting to get into working with existing buildings and learn building science, but who don’t necessarily have engineering backgrounds, I am going to use the term “energy” instead of enthalpy most of the time unless I need to explain something very specific in the context of enthalpy. And I will use the symbol “Q” with subscripts like S for “sensible” or L for “latent”. So, for instance, I will use QSAitIn instead of hAirIn to represent the sensible energy content of a parcel of air entering a process.
That’s sort of a judgment call on my part. But in my personal career path, I came into this topic from the perspective of a somewhat math-phobic airplane mechanic. And from that perspective, the term energy was less intimidating than the term enthalpy. From at technical purity perspective, a few objections are probably justified. But in the context of trying to promote a broader understanding, I am taking a few liberties and acknowledging that here (and hope it does make it harder instead of easier to understand).
Enthalpy of Formation is Related to but Not the Same Value as Enthalpy on a Psych Chart
While you probably don’t need to worry about it too much in the real world, day to day, building operations and commissioning environment, out here in the weed patch, it is probably worth noting that:
- The enthalpy of formation of a substance is typically referenced to some baseline condition, which typically is a pressure of 1 standard atmosphere and a temperature of 25°C (77°F).
- The enthalpy of formation is based on forming one mole of a substance, which is the unit of “amount” used in chemistry and related to the mass of a very specific number of fundamental units, like atoms or molecules .
- The enthalpy of formation of a pure substance is considered to be 0.
- The enthalpy of formation for a pure substance is taken for the substance in its most stable state. For instance a carbon atom can exist as graphite, diamond, or a gas with enthalpies of formation of 0, 1.9, and 716.67 kilojoules per mole respectively (kJ/mol). In contrast, the enthalpy of formation for oxygen is zero for diatomic oxygen, which is the form it has in the air around us. A single atom of oxygen has an enthalpy of formation of 249 kJ/mol. For ozone (O3) the enthalpy of formation is 143 kJ/mol.
- The enthalpy of formation can be negative or positive. In other words, sometimes going from the most stable form to a different form involves a release of energy to the surroundings (exothermic, negative enthalpy of formation). But other times, energy will be absorbed from the surroundings (endothermic, positive enthalpy of formation).
- Processes can also be endothermic or exothermic. For instance, ice melting is generally considered to be a process vs. a chemical reaction. But from what I can tell, the difference between a reaction and a process is even more into the weeds than I got here so probably not a huge deal in the context of our discussion in this blog post.
Air is Not a Molecule
It’s important to remember that air is a mixture of elements, primarily Nitrogen and Oxygen but including a number of others.
These elements are not bonded together; they are all just bouncing around together with Boyle’s Law and Dalton’s Law being good models for how we think they are gong about doing it. In other words, there is no such thing as an air molecule in the technical sense, even thought we often talk about air molecules.
That means that the term “enthalpy of formation” is not really appropriate for air, at least that is how I understand it. The enthalpy of a parcel of air is the sum of the enthalpies of the mixture of pure substances it contains, each of which, being a pure substance, has an enthalpy of formation.
That is not totally true in the general case because mixing substances can often release or absorb energy. But for gases, this effect is generally negligible and we can usually just add the enthalpies of the constituent elements.
Enthalpy Values Vary from Source to Source; How Can That Be?
If you go to a chemistry book and add up the enthalpies of the constituents of air, you do not end up with value of 0 Btu/lb at 0°F, which is what most psych charts show for the enthalpy of totally dry air.
Furthering the confusion, if you look at a chart in SI units, you find that the enthalpy is 0 kJ/kg at 0°C. Since 0°F and 0°C are two different temperatures, you might wonder how the enthalpy of air could be 0 at both of them, or at least I did.
The answer to that is that what we typically are concerned about when working with psychrometrics is the change in enthalpy, not the absolute value of it. At some point, for psych charts, the zero values were arbitrarily referenced as indicated above.
We Treat Air as an Ideal Gas Even Thought the Water Vapor it Contains Does Not Behave That Way
For our purposes in HVAC psychrometrics, we generally consider air to be a superheated gas and behave as an ideal gas, meaning it follows the ideal gas relationship.
In words, the ideal gas equation says, among other things, that if the temperature changes, the pressure and volume will change in proportion.
But, if you cool air enough (to about –318 °F), it will become a liquid, which is a phase change, and a phase change is a deviation from ideal gas behavior. When something goes through a phase change the temperature and pressure hold constant while there is a very large change in volume as energy is added to the system.
If you use a steam table to get scientific about this phenomenon for water, like the Keenan and Keyes table below …
… and compare the specific volume of saturated liquid water at atmospheric pressure with the specific volume of saturated water vapor at atmospheric pressure, you would find that they differ by a factor of about 1,600. In other words, one cubic inch of liquid water becomes about 1,600 cubic inches of water vapor when you boil it.
The reason this matters is that unless the you are working with air is absolutely devoid of moisture (RH = 0%), one of the elements bouncing around in the parcel of air with the other molecules listed above are molecules of water in a vapor state.
That means even though the air in our HVAC systems will never become cold enough to change phase (even in place like Minnesota or Siberia or Antarctica), the water vapor in it can and will.
So, confusingly enough, one of the common constituents of air – water vapor – does not behave as an ideal gas some of the time. But since it is such a small constituent, even if the air is saturated, for our purposes, we can assume ideal gas behavior for air.
But we can’t assume that the water will not change phase in our systems or in our environment, and that is important to us for a whole bunch of reasons.
Sensible Energy Lost = Latent Energy Gain for a Moist but not Totally Saturated Parcel of Air
The equation I use for the conversion of sensible energy to latent energy in the body of the blog post is associated with a special case; i.e. the case where the air entering the adiabatic saturator is totally dry. Most of the time, that is not the case; the air entering the process will already have some water vapor in it. And the water vapor brings energy into the process with it, just like the dry air did.
That means that in the more general case (and the more realistic case in terms of what you will actually run into out in the field), the words the latent energy increase is exactly equal to the sensible energy decrease would look more like this on a per pound of air basis using psychrometric parameters.
The darker green term represents the sensible energy content of the water vapor entering the process, and is the difference relative to the special case I used in the body of the blog post.
Specific Heat – A Measurable Quantity
Specific heat (also called heat capacity) is a measurable quantity that is defined as the amount of energy it takes to raise a unit mass of a substance through a unit temperature change. Specific heat values for specific substances can be found in tables in thermodynamic and chemistry text books.
In fact, for water. you could figure it out from your copy of Keenan and Keyes (you all have one of those, right?) …
… or by creating your own steam table using REFPROP.
For instance, in the Keenan and Keyes table above. the saturated liquid enthalpy hg (energy content) of saturated water at 209.56°F is 177.61 Btu/lb. At 212°F, it’s 180.07. Doing the math:
If you were to go through a similar process for the saturated water vapor over the temperature range I show from my REFPROP table, which are temperatures commonly encountered in HVAC systems, you would come up with the .45 Btu/lb/°F value that is shown in the sensible equals latent energy equation above.
There are similar resources out there for air. This graph was generated using valued from a thermodynamic text book.
Hopefully, all of this has given you a sense of the fundamental principles behind an evaporative cooling process. In the next post, I will build on this and take a look at real world evaporative cooling processes. So if you thought this was exciting, wait until you see that.
Senior Engineer – Facility Dynamics Engineering