# Derivation for Newton's Cooling Law

1. Mar 22, 2010

### SpectraCat

I was thinking about Newton's cooling law, which was originally derived empirically, and is often described as an empirical law. Usually when something is defined as a physical law, it means that it is derived from observation of the world around us, and cannot be derived from more fundamental laws or postulates? Is it really true that Newton's cooling "law" is purely observational, and cannot be derived from first principles?

It seems intuitively obvious that Newton's cooling law follows from the 2nd law of thermodynamics. I started trying to prove this, and I think I see how it might be done, although the details look a bit hairy at first glance. Rather than reinvent the wheel, I thought I'd ask if anyone knows of a reference that gives such a proof ... or one that shows such a proof is impossible. I poked around on google for a while, but I couldn't find anything that looked like what I wanted.

2. Mar 22, 2010

### D H

Staff Emeritus
The wikipedia article on heat transfer is a good start -- and also mentions why this is an empirical law. It most certainly is not a physical law.

3. Mar 22, 2010

### SpectraCat

Yes, I have read that .. and the one on conduction as well. They are quite informative, but not really what I am looking for, because they don't appear to even try to make a connection between the empirical phenomena discussed and the 2nd law. What I would really like to see is a derivation of either Netwon's Law or Fourier's Law (probably easier), starting from the second law and working forward. Lacking that a backward-looking rationalization of these laws that shows the connection to the 2nd LAW (we need different words there for empirical vs. physical laws!) would be my second choice.