Newton's Law of Cooling Question?

Question

According to Newton&rsquo;s law of cooling, the temperature of an object decreases at a rate proportional to the difference between its temperature and that of the surroundings. Given a constant of proportionality equal to 100 s^&minus;1, estimate the time taken for a freshly brewed cup of coffee to become drinkable.

Would anyone be able to help me with this? I've been trying for a day and I keep getting ridiculous answers of like 0.02 seconds.
Been taking ambient Temperature at 25, Drinkable at 50, and initial as 100 for estimate.
Is it just a ridiculous constant, or am I doing something wrong when I use T(t)=Ta+(T0-Ta)e^(-kt)?

Answer

Newton's law says the rate of heat transfer is proportional to the temperature difference. It is expressed in watts per square meter or equivalent measure. You don't specify any units so there is no way to analyze the problem.

In physics you put the units right into your equation as parts of the fractions so you can verify that they cancel the way they should. If you have no units you have nothing to work with.

Newton's Law of Cooling Question?

Answers (1)