### How to break the 2nd law and (almost) get away with it

I had been ruminating about writing something along these lines and the post I read this morning about the American thermodynamicist J. W. Gibbs over at the Culture of Chemistry provided the impetus.

Gibbs' name is immortalized as "G", the symbol for "free energy". In P. W. Atkins' words, the free energy of a process, given by the following equation,* is its single most important thermodynamic property*^{1}.

Free energy change = Total energy change - (Temperature x Entropy change)

For any process to be spontaneous, its free energy must decrease. In other words, the change in free energy must be a negative quantity.

If you look at the free energy equation carefully, you will see that there are three combinations that will result in negative changes in free energy^{2}:

1. The entropy increases and the total energy decreases. In other words, both terms on the right hand side of the equation are negative quantities.

2. Both the entropy and the total energy increase, but the absolute value of (temperature x entropy change) is greater than the absolute value of the total energy change, so that the net change in free energy is still negative.

3. Both the entropy and the total energy decrease, but the absolute value of the total energy change is greater than the absolute value of (temperature x entropy change), so that the net change in free energy is still negative.

Here is one way of expressing the famous 2nd law of thermodynamics (again, from Atkins): *Natural processes are accompanied by an increase in the entropy of the universe.*

Now, if you go back and read the possibility #3 that I listed above, you will see that it applies to a process during which the entropy is actually decreasing. So, is the process breaking the 2nd law? It may seem that way, but it is not.

What is happening is that to satisfy the requirement that the change in Gibbs' free energy be negative, the process is releasing heat to its surroundings. The released heat is increasing disorder in the surroundings by making the components of the surroundings move faster, so to speak. And increased disorder means increased entropy. Therefore, the net change in the entropy of the *universe* is still an increase. No law is broken, everyone is happy.

There is, however, a way to *avoid* the 2nd law. But that comes with a heavy price to pay. I will leave that to a future post.

1. My definitions and notations follow Atkins, P.W. 1984. *The 2nd Law*. W.H. Freeman & Co.

2. For simplicity, let's assume that the temperature is always positive.

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