Basics of Thermodynamics part 1: Heat is not Temperature!
This is the first of what I hope to be semi-regular science discussions on topics that are of interest for their own sake, and that get frequently abused by various voices in the political media.
Thermodynamics is frequently dragged out by various hacks and pundits to mislead people because it is almost perfectly suited to do so. It is a very old and established theory. Many have heard the word thermodynamics. People know that it is something legitimate that scientists worry about. In fact, it is old enough that it is stated in terms of laws. People who do not understand what the word theory means in a scientific context, and who sew confusion by claiming something is “just” a theory, in the ordinary sense of the word, happily abuse misstated laws. Surely laws have more weight! There is a finality there that can be used to impress a rube. The fact that a scientific law is simply an archaic term for a very well established theory is lost on them, and the propagandists exploit this missunderstanding ruthlessly. Another reason that thermodynamics gets used as such a go to for spreading confusion is that unlike relativity or quantum mechanics, there really are no good books about it written for a general audience. There is a lot less chance of finding someone who is conversant with it at even a basic level. This may be because, thermodynamics contains an elegant mathematical discussion of how everything physical – even the universe itself - eventually dies, runs down, burns out or simply breaks or decays. That simply isn’t sexy.
An old joke about thermodynamics is that the laws of it are:
Life is a poker game that you must play.
You can’t win.
You can’t break even.
You can’t leave the table.
As these lectures move forward, it is one aim to show just how clever, true to the physics and apt that joke really is.
Thermodynamics encompasses or influences almost everything. It is a fundamental topic. Because of that, it can easily be pointed at almost any scientific discussion. Whether or not it is pointed correctly is another matter because thermodynamics is difficult, counter intuitive, abstract and very demanding. Very few people have any clue whatsoever about what it actually says, and further, because it is so abstract, a slam dunk argument, is easily deflected in a debate by a charlatan, because it is all so many big, misunderstood, and misapplied words to both the fraud and his misinformed audience. With that, I hope to start clearing up some of this mess, and giving a basic feel for what this is all about to my readers.
I do hope though that even now, my reader will see quickly that since thermodynamics is something that every physical scientist has to learn and is so central to so many different topics, that the idea of some political hack, preacher, or barnyard “genius” coming up with an obvious proof that some well established theory violates thermodynamics is ludicrous at the outset. It’s rather like claiming that the proof of a well established mathematical theorem failed to notice an error in addition, and none of the mathematicians noticed. Some fool spouting off on a blog or on Fox news claiming that scientists got something wrong thermodynamically assumes that somehow the entire rest of the scientific community missed a very glaring and basic error – yet, it was not hidden to the “scientific prowess” of that journalist, politician or lobbyist (who personally couldn’t tell you the Pythagorean Theorem) and now he is going to show those smart fellers up!
Before even getting into thermodynamics proper, we have to lay some ground work. I wish to discuss heat. Heat is not temperature. We all say it is hot or cold outside, but when we do, we are not talking about heat. Science, in general, does not employ synonyms. If there are two different words, there are almost always two different concepts.
So what is the difference between heat and temperature?
We all have a sense of something being hot or cold. We know by touch, the difference in sensation of holding a glass of iced tea and a cup of hot tea. We know the difference, from our skins, between a blustery winter day and a summer scorcher. In some sense, temperature started as a way to standardize this difference in sensation. The astute reader should already notice that temperature can’t be something fundamental from weather reporting. If the concept of temperature were fundamental, in the sense that it was all there was to say about it, 30 degrees outside would be 30 degrees outside, you would not need to discuss wind chill or being in the shade. For those who are looking ahead, the point is that when we say that there is a wind-chill of 10 degrees, we mean that wind convection and conduction is carrying away a certain amount of heat from you, and in response, it feels colder.
It was discovered that certain metals and compounds expanded or contracted depending on whether or not they were hot or cold. Mercury placed in a glass cylinder expands or contracts depending on the apparent temperature. The thermometer was born and it was a handy way to say in numbers, this or that is hotter or colder, and by how much. But there was a big problem. Say I had a pot of alcohol and another part with an equal volume of water. Say I put them side by side over the same low fire for the same short period of time. They would always be at different temperatures. They would boil at different temperatures too, but the key observation is that it would take “more fire” specifically, more time for the fire to transfer energy, to heat up the water to the same temperature than it did the alcohol. More investigations showed that pretty much every different material would get warmer or cooler at different rates and with different amounts of work done to heat them up. Work in this case being how long you kept the thing on a burner but, for certain, that is just one example.
So you might conclude the temperature is meaningless. But it isn’t. If you have a room at a certain temperature, pretty much everything in it, will come to that temperature, no matter what it is made of, if you give it enough time to equilibrate. We have a conundrum. On the one hand, the amount of work I need to do to change the temperature of different things is different for every different substance. So you might think, that what we really need to worry about is the work needed to heat something up, because what temperature “means” in terms of how much energy you put into heating it, to one thing, is not what it “means” to another. On the other hand though, if you give a collection of things, which are in thermal contact with each other, enough time – even though they are all at different temperatures and made of different stuff, they all come to the same temperature. So temperature seems to be pretty important after all! What is going on?
I have already hinted at part of the answer here.
Heat is a measure of the amount of energy that went into raising something to a certain temperature. Heat is energy. Temperature is a manifestation of that energy that is different for different substances. Different items in thermal contact with each other exchange heat, until they come to the same temperature. Mathematically, a change in heat Q, is related to a change in temperature T, by the heat capacity of a substance. In the simplest case, dQ = CdT, where C is a constant called the heat capacity. Later on, we will take into account things like pressure, molarity and temperature. We will then talk about the specific heat at constant pressure for example. Specific heat is heat capacity per unit mass.
As always, it is good to attach these concepts to every day experience. Anyone who has ever made tea, or noodles, knows that it takes a long time to boil water, and that hot water stays hot for a long time. We say that water has a very high specific heat. This means, that it takes a lot of energy to raise its temperature, and that once raised, it has to lose a lot of energy before it can cool. That is what a large value of C means.
So let’s refine this a little bit. To help us do so, It is helpful to remember that all matter (that we encounter on a regular basis, at least) is made of atoms and molecules. Neutron stars, and other exotic things like dark matter, obey thermodynamics also, but let’s not go far astray.
Atoms and molecules are not static things. Let’s imagine the simplest case. In a tank of monatomic gas, like say a tank of neon, the atoms of the gas can be thought of as little hard spheres. This takes away potential complications due to chemical interactions, or any funny business with quantum mechanics. Noble gasses, (neon is one of them) have nice filled shells. We don’t need to worry about them pairing up and taking energy to make molecules. When they bounce off of each other, to a very good approximation, it is like billiards (all of those things can be taken into account, but basics first). Even so, those atoms are not staying still. They are all moving at very high speeds and constantly colliding with each other and the walls of the tank. In fact, pressure is a measure of how much and how hard they are hitting the tank.
Microscopically, this will give an insight into what is going on. First off, you might ask, how fast are the Neon atoms moving? It would make sense that the faster they were moving, the harder, they would hit the walls of the tank, just from simple conservation of momentum. This is entirely true. It turns out, that in this case, the temperature of a gas, (and hence the heat contained by a gas) is nothing more than a measure of how fast on average the gas atoms or molecules are moving. Heat is energy. In this case, it is nothing more than the average kinetic energy of the gas. If this is true, you would expect that if I heated a tank of gas, the pressure would go up, because then the individual gas atoms would be moving faster, have more kinetic energy and then smack the walls of the tank harder. Of course, this is exactly what happens. If that heating were caused by a rapid chemical reaction that also converted a solid into a gas, this is the idea behind a gun! We see already, that temperature, pressure and heat are all related to each other, even in the simplest case of a tank of non-chemically interacting gas.
If this picture is correct, you would expect, that since energy is conserved, that if I allowed gas to escape my tank, it would carry heat away and that since temperature is related to heat, the temperature would go down. Anyone who has ever used an aerosol spray can has noticed that it gets cold when you use it. Don’t believe me? Try it with a can of shaving cream, or air freshener or whatever you have handy that won’t make too much of a mess. Spray it a bit, and it will get colder. Energy is always conserved! The tank gave up internal heat to the world outside the tank.
In general, though, internal heat is more complex than just atoms moving in a tank of gas. Consider molecules. Molecules are not the static things that you might imagine from chemical diagrams. Depending on the structure of the bonds and the molecules themselves, they may vibrate, flap, or even have little bits that rotate like propellers (like the case of a methyl group attached to a larger molecule). Further, different bonds can be exited into different energy states and give off light. All of those motions take energy to start. All of those motions together are what make for heat. Since different substances have different configurations on the microscopic scale, there are many different ways for a given substance to take on energy and hence heat. This is ultimately why different substances can sit on a flame for the same period of time and yet have different temperatures. There are simply more or less ways for a given molecule to take in energy than some other molecule and it may take more or less energy to excite a certain motion in a molecule or excited state from one substance to the next.
This brings me to how heat gets transferred. There are three mechanisms. They are conduction, convection and radiation.
Conduction occurs when you have direct physical contact between substances at different temperatures. For example, a piece of metal is put into a flame. The atoms of the flame (gas so hot it gives off light, and that is radiation!) literally have more kinetic energy in overall movement as well as whatever modes of vibration. Those hot atoms bounce into the cold ones of the metal and start them wiggling (as in having whatever exited modes of vibration). Those metal atoms are bound to their neighbors and start them wiggling and so on down the line.
Convection happens when there is a mass of hot material carried by an overall flow. For example hot water can be carried downstream.
Radiation, in this case, is giving off light. This happens because the substance is hot enough to excite bonds into higher energy levels which then radiate out that energy as photons. Think red hot metal, or picking up a person with an IR scanner.
Quick note, from this, we can already debunk one bit of pseudo-scientific nonsense. The Earth can only, as a whole, cool by radiation. Why? Because space is a vacuum, and you can’t have conduction or convection in a vaccum. Conduction and convection both require a medium to exchange heat.
We are now ready to state the first law of thermodynamics! Are you ready for it?
It is no more or no less, than energy is conserved. In other words, you can’t win. You can never get more energy out of a process than was put in.
Specifically, dU = dQ – dW.
In other words, the change in total energy of a system is the change in heat of the system minus the change in work done by that system on something else.
Our next lecture will go into some examples of this and build up to the second law.