Question

This question is about Newton’s law of cooling, which states that the temperature of a hot object decreases proportionally to the difference between its temperature and the temperature of the surroundings. This can be written as dT dt = −k(T − Ts), where T is the temperature, t is time, k is a constant and Ts is the temperature of the surroundings. For this question we will assume that the surroundings are at a constant 20◦ and A that the temperature changes described by Newton’s law of cooling are the only changes to be considered. Consider making a hot drink such as tea or coffee. The drink is initially at 95◦ . You wait 15 minutes before you drink it. At this time the temperature of the drink is 80◦ . (i) Find the value of k. Use this value of k for the rest of the question. You want to add milk to the drink, which will lower its temperature by 5◦ .

(ii) Calculate the temperature of the drink if milk is added immediately after it is made and then you wait 15 minutes.

(iii) Calculate the temperature of the drink if you wait 15 minutes and then add the milk.

(iv) You want the drink to be as hot as possible after 15 minutes, with the milk in it. Do you add the milk at the start or at the end? Give another ‘real-life’ example which does not involve drinks where similar behaviour could be expected.

Answer 1

If you have any doubts feel free to ask.

if you found this helpful, please give a thumbs up.

thank you :)