Re: How does kinetic energy changing directly to heat violate 2ndLaw?

Fran,

Good question. Before we get started, let me point you at this MadSci answer that I found from 1996 which gives a clear and accurate summary of the three thermodynamics laws. Now that both our memories have been refreshed, let's take a closer look at the second law...

The second law is all about entropy, which in modern physics is defined as the logarithm of the number of states accessible to a system of particles. What does this mean? Well, here is a simple example. Suppose you have a "system" of, say, 10 coins that can be either heads or tails. The number of different permutations for this system is 2^10, or 1024. Now, let's confine the system so that all the coins must be heads. There is only one possible state in 1024 where this can happen, so the entropy of the system is ln(1), or zero. What about 9 heads and 1 tail? There are ten possible states, giving an entropy of ln(10). 5 heads and 5 tails? The entropy goes up to ln(252).

Therefore, if you looked at a bunch of coins and saw they were all heads, you would find it hard to believe that they were the product of a random toss. You are much more likely to see an even mix of heads and tails, because there are a lot more accessible states with that result. In other words, a system will tend to a state with higher entropy. which is the second law in a nutshell.

So what about your projectile example? Well, the projectile is a single particle, and not a system. That projectile could even collide elastically with another body without increasing entropy, since single elastic collisions can be "run in reverse" without violating any laws. Only when your projectile starts interacting with several other bodies does it become part of a "system" whose entropy can be measured (and increased!).

Here is another way to think about it. A single coin cannot have entropy, since both "heads" and "tails" have only one possible state, giving an entropy of zero. It takes a system of two or more coins to have a definable entropy. In the same way, it takes a system of several interacting particles to have a measureable entropy that increases a la the second law of thermodynamics.

I hope this helps answer your question. If any of this was unclear or confusing, please contact the MadSci Network again. Thanks for submitting such an interesting question!

Sam Silverstein