Suppose you have just poured a cup of freshly brewed coffee with temperature 95

Question

Suppose you have just poured a cup of freshly brewed coffee with temperature 95 degrees C in a room where the temperature is 20 C.

a) When do you think the coffee cools most quickly? What happens to the rate of cooling as time goes by?

b) Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Write a differential equation that expresses Newton's Law of Cooling for this particular situation.

c) What is the temperature of the coffee after t = 5? After a long time?

Explanation / Answer

PART A

The cofee cools most quicly at the beginning. As time passes, rate of colling decrese.

PART B

dq/dt=-k(B-B1) [k is proposrtionality constant, negative sign shows rae of cooling. B is the temperature of the object, B1 is ambient temperature, dq/dt is the rate of change in temperature.

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