Applications of Differential Equation of Newton's law of cooling / warming
The temperature of many objects can be modelled using a differential equation. Newton's law of cooling (or heating) states that the temperature of a body changes at a rate proportional to the difference in temperature between the body and its surroundings. It is a reasonably accurate approximation in some circumstances.
More precisely, let denote the temperature of an object and the ambient temperature. If denotes time, then Newton's law states that:
where is a positive constant. Thus, if the object is much hotter than its surroundings, then is large and positive, so is large and negative, so the object cools quickly. If the object is only slightly hotter than its surroundings, then is small positive, and the object cools slowly. So a cup of hot coffee will cool more quickly if you put it in the refrigerator!
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