11.8 Intro to the Second Law

Take a look around you. You are surrounded by air molecules. They are all over the place. Isn’t that messy? Suppose there would be water all over the room, wouldn’t you do something about it? Wouldn’t it be much neater to compress all those air atoms together and put them in a glass? (You may want to wear a space suit while doing this.)

The reality, of course, is that if you put all the air atoms in a glass, the high pressure would cause the air to explode out of the glass and it would scatter all over the room again. All your efforts would be for naught. It is like the clothes of a ten-year old. Nature likes messiness. In fact, if messiness is properly defined, and it will be in section 11.10, nature will always increase messiness as much as circumstances and the laws of physics allow. The properly defined messiness is called “entropy.” It is not to be confused with enthalpy, which is a completely different concept altogether.

Entropy provides an unrelenting arrow of time. If you take a movie and run it backwards, it simply does not look right, since you notice messiness getting smaller, rather than larger. The movie of a glass of water slipping out of your hand and breaking on the floor becomes, if run backwards, a spill of water and pieces of glass combining together and jumping into your hand. It does not happen. Messiness always increases. Even if you mop up the water and glue the pieces of broken glass back together, it does not work. While you reduce the messiness of the glass of water, you need to perform effort, and it turns out that this always increases messiness elsewhere more than the messiness of the glass of water is reduced.

It has big consequences. Would it not be nice if your car could run without using gas? After all, there is lots of random kinetic energy in the air molecules surrounding your car. Why not scope up some of that kinetic energy out of the air and use it to run your car? It does not work because it would decrease messiness in the universe, that’s why. It would turn messy random molecular motion into organized motion of the engine of your car, and nature refuses to do it. And there you have it, the second law of thermodynamics, or at least the version of it given by Kelvin and Planck:

You cannot just take random thermal energy out of a substance and turn it into useful work.
You expected a physical law to be a formula, instead of a verbal statement like that? Well, you are out of luck for now.

To be sure, if the air around your car is hotter than the ground below it, then it is possible with some ingenuity to set up a flow of heat from the air to the ground, and you can then divert some of this flow of heat and turn it into useful work. But that is not an unlimited free supply of energy; it stops as soon as the temperatures of air and ground have become equal. The temperature difference is an expendable energy source, much like oil in the ground is; you are not simply scooping up random thermal energy out of a substance. If that sounds like a feeble excuse, consider the following: after the temperature difference is gone, the air molecules still have almost exactly the same thermal energy as before, and the ground molecules have more. But you cannot get any of it out anymore as usable energy. Zero. (Practically speaking, the amount of energy you would get out of the temperature difference is not going to get you to work in time anyway, but that is another matter.)

Would it not be nice if your fridge would run without electricity? It would really save on the electricity bill. But it cannot be done; that is the Clausius statement of the second law:

You cannot move heat the wrong way, from cold to hot, without doing work.
It is the same thing as the Kelvin-Planck statement, of course. If you could really have a fridge that ran for free, you could use it to create a temperature difference, and you could use that temperature difference to run your car. So your car would run for free. Conversely, if your car could run for free, you could use the cigarette lighter socket to run your fridge for free.

As patent offices all over the world can confirm, the second law has been solidly verified by countless masses of clever inventors all over the centuries doing everything possible to get around it. All have failed, however ingenious their tricks trying to fool nature. And don’t forget about the most brilliant scientists of the last few centuries who have also tried wistfully and failed miserably, usually by trying to manipulate nature on the molecular level. The two verbal statements of the second law may not seem to have much mathematical precision, but they do. If you find a kink in either one’s armor, however small, the fabric of current science and technology comes apart. Fabulous riches will be yours, and you will also be the most famous scientist of all time.