Question

2. You take on cream out of the freezer, kepot - 180. stride it is 32°C After one si
dhe ice cream bus warmed to what is the temperature of the icecream ofter five minud in equetion​

Answer 1

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 T denote the temperature of an object and T0 the ambient temperature. If t denotes time, then Newton's law states that

dTdt=−k(T−T0),

where k is a positive constant. Thus, if the object is much hotter than its surroundings, then T−T0 is large and positive, so dTdt is large and negative, so the object cools quickly. If the object is only slightly hotter than its surroundings, then T−T0 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!

This differential equation is of the same type as ones seen previously in this module.