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How do we derive Newtons Cooling Law by considering just the molecules and their interactions?
- Kim (age 17)
National Junior College, Singapore
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
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.
(published on 10/22/2007)
Follow-up on this answer.