Question about Newton's Law of Cooling

[gokuls]

Newton's law of cooking
T(t)= Ta+(To-Ta ) e^(-kt)
or search it up online for a cleaner formula.

Anyways, what does the cooling constant k represent. What do larger or smaller values of k mean?

Thanks

 

[CWatters]

What do you mean by a "cleaner" formula? Are you working on a specific problem? Perhaps it doesn't need Newtons law of cooking to solve it?

Anyway scroll down..

http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html

k is a constant. Newton says the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature. "Proportional to" implies a constant...

dT/dt = -k(T-Ta)k depends on the physical properties of the system... How well insulated it is, the heat capacity of the object etc