# The Second Law of Thermodynamics

There are several equivalent formulations for the Second Law of Thermodynamics. We will state them here, and in the following sub-units each of these formulations will be explained in more detail.

1. It is not possible to change heat completely into work, with no other change taking place.
2. It is not possible to transfer heat from an object at a lower temperature to another object at higher temperature without other changes taking place as well.
3. It is not possible to construct an engine with greater efficiency than that of a Carnot engine.
4. The total entropy of a closed system going from one equilibrium state to another can never decrease.

By the way, while science crackpots most often try to show that the theory of relativity (more of this in the second semester) is wrong, the equivalent challenge for engineering fools is the second law of thermodynamics:

There is an old dream, that of making a machine that runs forever without using energy, or at least produces more energy than it uses. This machine has a Latin name: perpetuum mobile, perpetual motion. Over the years the U.S. patent office has been absolutely swamped with patent applications for a machine of this kind. One divides these perpetuum mobile attempts into two different classes: perpetuum mobile machines of the first and second kind.

Those of the first kind violate the law of energy conservation and ever since the work of Mayer, von Helmholtz, and Joule during the middle of the last century these first kind perpetuum mobile machines are easily discarded as impossible.

Hopeful inventors of perpetuum mobile machines of the second kind realize that there is all this "free" energy around us, in the form of heat, i.e. random thermal motion of molecules and atoms. Thus they argue that one only has to capture this energy and, voilà, one can run an engine without gasoline. These machines then violate the second law of thermodynamics, as we will see in the following, and thus cannot work. This is much harder to see, because the concepts are rather delicate. However, we will begin to discuss them now. And hopefully what you read will convince you, too, that it is absolutely pointless to attempt to construct a perpetuum mobile machine of the first or second kind.

Unfortunately, the physical impossibility of these energy producing machines does not stop certain individuals (fools, criminals - you decide) to try and sell them to the public. Every so often you see them advertised in newspapers, and the generally uneducated public is scammed out of lots of money.