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In my Differential Equations class we are learning about modelling with first order differential equations. We learned that Newton's Law of Cooling breaks down when the temperature of the object is approaching the temperature of the room its in. You eventually get to a point where you have

**0 = e^x**

or some variation of that, where of course there is no solution. This leads me to a few questions.

1.) Are there mathematical models that don't break down, i.e maybe they aren't perfect but they are still a

**good approximation**and

2.) Have we come up with a newer model of cooling that does not break down at the point were the object temperature reaches the ambient temperature?

Thanks for your time,

-Lee