# Q & A: Thermal conduction

Q:
How do we derive Newton’s Cooling Law by considering just the molecules and their interactions?
- Kim (age 17)
National Junior College, Singapore
A:
Kim- this is a really good question, even though I only dimly remember "Newton's Law of Cooling". I think what you are referring to is the idea that heat flows from a hotter object to a cooler one, and that the rate of heat flow is more or less proportional to the difference in their temperatures.

The answer to your question is then simple- you cannot derive this law or any similar law by "considering just the molecules and their interactions," unless there are some other interactions basically different from all the ones we know about. The reason is that all the relevant interactions work the same forward and backward in time, in the same way that a planet can obey Newton's laws whether it's orbiting a star one way or the opposite way. In contrast, the heat transfer law would look backwards if you viewed it in reverse- heat would flow from cold to hot!

The laws of heat transfer instead require that you add a new principle to the laws of "just the molecules and their interactions". The new principle, called the second law of thermodynamics, says that more and more microscopic states of the molecules get to be equally likely as time goes forward. It turns out there are many more microscopic states with two nearby objects at the same temperature than there are with them at different temperatures.

Mike W.

(published on 10/22/2007)