# Derivation for Newton's Cooling Law

## Main Question or Discussion Point

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.

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