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# Re: exponential cooling

Folks, I may miss the point here, but since when has this been felt to be a
"law"? It is a boundary-value-initial-value def eq with unreal-grossly
-over-simplified assumptions about the problem at that -- something Fourier
might have done based on his ideas of fluid flow -- it has little to do with
classical thermo, which makes assumptions of quasi-statics -- not that this
is any more real. (:-) Besides this sort of cooling is only mistakenly
attributed to Newton.

What did I miss?

JMGreen

At 11:18 PM 12/7/96 -0800, you wrote:
Could someone please tell me what the "exponential law of cooling" might be.
--------------------------------------------------------------
I take that to mean Newtonian heat transfer.
dDelT/dt = -kDelT
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The "law" states that an object approaches the temperature of its
surroundings at a rate which is exponential in time. If The initial
temperature of the object is Ti and the temperature of the surroundings
is To, the temperature varies with time according to

T(t) = To + (Ti-To) exp (-t/tau)

where tau is the time constant for the approach to equilibrium. The
"law" is not highly accurate because the conditions under which it
would be appropriate are not approached often; it lacks generality.
Qualitatively the time dependence is reasonable, however.