Question

luid/Heat Level I: A coffee drinker faces the following dilemma: she wants to wait ten minutes to drink her hot coffee with cream, but wants it to be as hot as possible. IA] Is it better to immediately add the room-temperature cream, stir the coffee, and let it sit for ten minutes, or IB s it better to let the coffee sit for ten minutes and then add and stir in the cream? Start with ewton's Law of Cooling T = T e-kt and draw the temperature vs time graph for [A] and [B] se the graph and reasoning to answer this question

Answer 1

Newton's Law of Cooling states that the rate at which an object cools is proportional to the difference between its own temperature and the temperature of its surroundings. So, a bigger temperature difference gives a faster cooling.

The addition of cold milk to the hot coffee reduces the overall temperature of the mixture, so Cup A is colder than Cup B before the ten minutes wait. But the cup with the greater temperature difference between itself and its surroundings will cool faster, therefore, it should be Cup B which cools quicker as it is at a higher temperature than Cup A during the 10 minutes wait.

The cooling graphs for both cups would look something like this

TI'c Top lB] 15