# Why Doesn’t Heat Flow Backwards?

## Ruminations on the Second Law of Thermodynamics

Why can’t you put a cup of cold coffee on the table, wait a moment, and then enjoy a nice cup of hot coffee? We do the opposite all the time, but what makes the direction of hot-to-cold so special? If you’ve studied physics or taken a class in building science, you’ve heard that the answer is the Second Law of Thermodynamics. But what does that really mean?

Ah, the meaning of the Second Law of Thermodynamics! I might as well ask, What is the meaning of life? It’s a fascinating question and one that we can approach from a lot of different angles. Since we’re talking about building science and not physics or philosophy, I won’t go too far down that rabbit hole. But let’s at least put a little life into this dry concept that seems to be the end of the discussion in so many home energy rater and building analyst classes.

### The Laws of Thermodynamics

First, let’s do a quick review of the Laws of Thermodynamics. At Building Science Summer Camp this year, one of the speakers gave a great summary of them:

• You can never win.
• You can’t break even.
• You can only lose.

The Second Law came after the First Law, of course. (So did the Zeroth Law!) The First Law says that scientists, in all the many ways they’ve studied the flow and conversion of energy, have never found that any closed system ends up with more energy than it started with or less energy than it started with. You may know this law as the Law of Conservation of Energy: Energy can be neither created nor destroyed. (That is, you can never win.)

In the process of studying the flow and conversion of energy, scientists had to confront the fact that heat pretty much always flowed one way: from hot to cold. Yes, you can move heat from cold to hot with a heat pump, but you have to do work to make it happen. Even in that case, however, the process of picking up heat from cold outside air and then dumping it into warmer inside air involves the flow of heat from warmer to cooler bodies.

The Laws of Thermodynamics aren’t as easy to state as Newton’s Laws of Motion because the Second Law can take several different forms, but below is a brief statement of each. If you want to go deeper, the Wikipedia does a good job of explaining all three Laws of Thermodynamics.

• Zeroth: Two systems in thermal equilibrium with a third system are also in thermal equilibrium with each other.
• First: A closed, isolated system doesn’t gain or lose energy. Heat and work are related, and when all forms of energy are accounted for, energy is conserved.
• Second: The disorder (entropy) of systems generally increases, which means that heat flows from hot to cold and getting 100% efficiency from heat engines is impossible.
• Third: Disorder goes to zero in perfect crystals at a temperature of absolute zero. Another form is that it’s impossible to take any material to a temperature of absolute zero in a finite number of steps.

### The power of numbers

A lot of discussions of the Second Law explain it by using the concept of entropy. I think an easier way to grasp it is with statistical mechanics. Naturally, we need to heed the warning from David Goodstein’s book, States of Matter, which was my introduction to the subject:

Ludwig Boltzmann, who spent much of his life studying Statistical Mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study Statistical Mechanics. Perhaps it will be wise to approach the subject cautiously.

Well, OK, we’re not going to go nearly as deep as they did, so fear not, intrepid readers.

Think about the air in the room you’re sitting in right now. Are the molecules spread evenly throughout the room? Or are they clumped? Unless you’re in an extremely odd room, they’re spread evenly throughout. All those nitrogen, oxygen, and other gas molecules are bouncing around randomly and filling all the space in the room.

One of the things that statistical mechanics attempts to understand is the likelihood that a system, say the air in your room, can be in any particular state. One state might be that all the air is clustered up in one corner of the room, leaving you gasping for air. That state, it turns out, is so unlikely that we can say with a high degree of confidence that it will never happen.

Did you buy a ticket for that big lottery jackpot? Your odds of winning that were maybe one in 200,000,000. I didn’t because I don’t like throwing away money. Those odds just don’t appeal to me.

When we’re talking about molecules rather than lottery tickets, the odds are way, way worse for that ‘jackpot’ that has all the air molecules in one corner of the room. First, think of the number of particles involved. We’re talking Avogadro’s number here, or something on the order of 10 to the 23rd power. For the record, Avogadro’s number is:

602,000,000,000,000,000,000,000

When we start talking about all the possible states those molecules could be in, the numbers get crazy big. And the main result is that the odds for unusual states like all the molecules in one corner are minuscule. No, they’re smaller than minuscule. Take your odds of winning that lottery jackpot and divide by a million. Then do it again and again and again and…

In other words, it ain’t gonna happen.

### Heat flow and the arrow of time

Now, back to heat flowing from hot to cold, the same thing applies. Yes, heat from the room could flow into your cold coffee. It won’t, though, because the odds for states of matter like that are tiny, tiny, tiny. It’s pretty much the same as all the air molecules piling up in one corner of the room.

Another expression used in discussing this phenomenon is the “arrow of time.” If we run films backwards, a lot of what we see is funny because we know things can’t work that way. For example, the smoke in that photo at the top is diffusing throughout the air and becoming invisible. The state of those smoke molecules coming back together is so unlikely that we know if we see that happening, the film must be running backwards against the arrow of time. Likewise, a broken egg can’t spontaneously become unbroken or a cold cup of coffee suddenly warm.

Oscar Wilde clearly understood the arrow of time when he said about Niagara Falls, “It would be more impressive if it flowed the other way.”

Let’s also remember Homer Simpson’s admonishment of Lisa when she brought him a perpetual motion machine that just kept going faster and faster: “In this house, we obey the Laws of Thermodynamics.”

Allison Bailes of Decatur, Georgia, is a RESNET-accredited energy consultant, trainer, and the author of the Energy Vanguard blog. You can follow him on Twitter at EnergyVanguard

1. GBA Editor
| | #1

The three laws
Allison,
Many scientists have summarized the three laws; one version I'm familiar with is “you can’t win,” “you can’t break even,” and “you can’t get out of the game."

Concerning the third law (which relates to the impossibility of reaching absolute zero), I like Henry Gifford's explanation: A material cannot reach absolute zero because "you have to have something colder to absorb the last bit of heat."

Finally, the last word belongs to Homer Simpson, whose response to Lisa (tinkering with a perpetual motion machine) was the memorable line: "In this house, we obey the laws of thermodynamics!"

[Later edit: I see that in response to my suggestion, Allison has added the Homer Simpson quote to the end of his blog. Thanks, Allison. After all, building science bloggers don't often have a chance to quote Homer Simpson -- so we wouldn't want to let the opportunity escape.]

2. GBA Editor
| | #2

Of course!
Martin,

Yes, I've added Homer's famous quote to the end of the article now. I've used it many other times but somehow left it out of this article...initially. Thanks for the reminder.

Regarding the Third Law, Henry's right in a very simplistic way, but physicists have achieved very low temperatures by methods other than transferring heat from one object to something colder. That works down to about 4 K, the temperature of liquid helium, and then you have to start using other processes to extract energy, mainly magnetic, as I recall. The University of Florida, where I did my graduate work, has a facility called the MicroKelvin Lab that has set record low temperatures.

3. | | #3

Water Molecules
Allison,
If the absolute humidity in the room is high....
Isn't it likely that there would be a concentration of Water Molecules near the ceiling or peak?

4. | | #4

Stratification
Isn't it also very likely that most of the air molecules in the room will stratify ....
and there will be a Concentration of Molecules near the floor?

5. GBA Editor
| | #5

Response to John Brooks
Good question, John. First of all, any nonuniformities that you might find in a room due to buoyancy or other forces are tiny compared to the kind of clumping I referred to in the article. The kind of macrostates you're referring to are quite probable and depend on the conditions.

I don't think that there would be much stratification in a sample of uniformly-distributed air and water vapor because it would have to happen as a result of diffusion. Also, it's good to remember what Bill Rose wrote in his wonderful book, Water in Buildings:

"The quantity of water in the air is almost purely a function of the temperature and wetness of the bounding surfaces than it is of any characteristics of the air itself."

When you have a mass of dry air and a mass of humid air, like the air that meteorologists study, it's...

Wait a minute! Are you leading me down the path of discussing the stack effect again?! ;~)

6. | | #6

If--
I read this eagerly, hoping to learn something. And I believe I learned a little. But -- if I were writing an article on the Second Law of Thermodynamics, I would at least state somewhere exactly what that Law is. Yes, I gather that it has to do with heated air moving toward cold. But nowhere do you state the essence of it in black and white. Instead of a straightforward list of the Three Laws, you give us this in-joke about "You can't win" etc. What good is an in-joke if we don't possess the knowledge that lies behind the in-joke? You do give us the First Law, but not the Third, and you move off into exposition of the logic behind the Second Law without giving us a solid basis for understanding it. Your whole point of view seems to be that, Hey, everybody here knows what the Second Law is, so I'll just riff on it for a while. No. I do not know what it is. I would like to learn. Would you teach me, please? (Or am I supposed to go to Wikipedia before reading?)

I value Allison Bailie's comments very much, by the way, both at GBA and Energy Vanguard. I'm just frustrated in this case. If I were an editor, I'd send it back to rewrite.

7. | | #7

Good ...it's not only me
Allison, concerning Image 1
Can you explain how Smoke rising and Dispersing demonstrates the 2nd Law of Thermodynamics?

As you may know "Smoke" (like hot air) does not ALWAYS rise.

8. | | #8

Take a ride over to wikipedia
Take a ride over to wikipedia boys.... There's so much over there on thermodynamics that both of your entropys will most certainly change but I'm not sure which way as you both are life forms and autopoetically in certain spaces and time reverse it.

Here's the question. Does entropy and the coursing toward disorder drive the engine of exponential fractal roughness, to life form, to order, to a repeated rebirth of the entire universe, instead of heat death?

The battle is.

9. GBA Editor
| | #9

Because Allison is busy...
Gordon Taylor,
I'll make a stab at stating the three laws of thermodynamics. Eventually I'm sure that Allison Bailes will respond to your comment.

1. The First Law is usually referred to as the Law of Conservation of Energy. It can be stated many ways. For example:
Although energy can be transferred from one system to another, it can neither be created nor destroyed, absent a nuclear reaction.
The total amount of energy available in the universe is constant.

2. The Second Law is often referred to as the Law of Entropy. It can be stated a variety of ways:
The quality of energy (or matter) deteriorates over time.
Though energy can be changed from one form to another, something is always lost in the process.
Heat can never pass spontaneously from a colder to a hotter body.
Both energy and matter in the universe are becoming less useful as time goes on.
The spontaneous flow of heat from hot to cold bodies is reversible only with the expenditure of mechanical or other nonthermal energy.
It is impossible to move heat, by a cyclical process, from something at lower temperature to something at higher temperature unless work is added to the system.

3. The Third Law governs absolute zero (0° K). It states:
Although it is possible to achieve a temperature that is very close to absolute zero, it is impossible to reach it.
At absolute zero, all the thermal motion of molecules (kinetic energy) would cease, and all bodies would have the same entropy. But because entropy cannot be reduced to zero by finite means (according to the Second Law), no system can reach absolute zero.

10. | | #10

By the Way
The smoke image Allison posted is very fascinating/ illuminating.

The Smoke and Lighting reveal a sort-of Neutral Pressure Surface or membrane

11. GBA Editor
| | #11

Response to Gordon Taylor
Gordon, you're absolutely right. I wrote the article thinking of how many times I've heard and read about the Second Law in building science discussions, and there it's always just thrown out as justification for claiming that heat moves from higher temperatures to lower temperatures. I've added another section stating the 3 laws briefly, but as I mentioned there, these laws aren't as easy to state as Newton's Laws of Motion. There are many forms of them, and the whole concept of entropy takes a while to understand. Martin's explanations are also good summaries of the laws.

Gotta run out on a site visit now and check out a ducted mini-split heat pump install. I'll check back later to get to your questions, John Brooks.

12. | | #12

All cool here...
I look forward to learning more.

13. | | #13

Thermodynamics
One of the problems we all face with regard to the laws of thermodynamics is that they are mathematical expressions, not semantic expressions.

"Thou shalt not steal" is fairly clear to most of us.

Entropy and absolute zero and anything involving the word quantum takes more than a few sentences (and/or beers).

I think anyone trying to explain the laws of thermodynamics with words only should be given great lattitude with the understanding that the words are only an approximation and always have some short comings.

Having said that, I think its also important to remember that our mathematics is also just our best attempt at explaining things and its more important to remember and work with the facts as they are: balls roll down hill, heat goes from hot to cold, etc. Unfortunately, water vapor really throws a monkey wrench into the system since a number of variables are involved - temperature, pressure, chemical potential, etc.

Thank you Allison and Martin, the understanding of difficult subjects benefits from discussion.

14. GBA Editor
| | #14

On smoke & the 2nd Law - response to John Brooks
John, the smoke in that photo spreading out happens through the process of diffusion, molecules dispersing by the random kinetic action of collisions. In the basic building science you get in classes like the HERS rater training, you learn that heat goes from hot to cold, water goes from wet to dry, and air goes from high pressure to low pressure.

In the article above I wrote about how unlikely it would be for all the air molecules in a room to suddenly find themselves in one little corner of the room because that would be like heat going from cold to hot. It's the same thing with smoke. It spreads out to go from more concentrated to less concentrated, and once it does so, the chances of it coming back together are pretty much zero. That's the Second Law in action.

15. | | #15

Reusing heat
All buildings (unless you consider a building with no walls) will be resistant to heat flow to some extent. If you add insulation you increase the R value or the resistance to heat flow. But no matter how much insulation you use heat will flow. It is possible to capture the heat and move it back to the side of the structure wall that is most desirable. Energy will be consumed in moving the heat. It will be less economical to cool the structure than to heat it. But if you need to keep as much heat in a structure the energy used to move the heat can also be used to heat the structure. Therefore keeping the heat in will cost less than keeping the heat out! Using the walls and roof of the structure like a structure sized HRV.

• ## Understanding Pressure Differences

Suction cups demonstrate the second law of thermodynamics, which dictates much of building science

• ## How Does a Heat Pump Get Heat From Cold Air?

The physics of heat pumps isn’t really that difficult to understand

• ## The Four Laws of Thermodynamics

We often talk of the second law, but what are the other three?

• ## The Fundamentals of Series and Parallel Heat Flow

The R-value of a building assembly depends on how heat can flow through it

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