Question about Newton's Law of Cooling

AI Thread Summary
Newton's Law of Cooling describes how the temperature of an object changes over time, represented by the formula T(t) = Ta + (To - Ta)e^(-kt). The cooling constant k indicates the rate at which the temperature difference decreases; larger values of k signify a faster cooling rate, while smaller values indicate slower cooling. This constant is influenced by the physical properties of the system, such as insulation and heat capacity. Understanding k is essential for accurately applying the law to specific problems. The discussion emphasizes the importance of these factors in determining cooling behavior.
gokuls
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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
 
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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
 

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