The gold of poets and thinkers,“ said Goethe about coffee, „but generations of coffee drinkers have already been hitting their heads when it came to the question of when the milk comes into the coffee in order to keep the coffee hot for as long as possible. Right after you put the coffee in the cup or let it cool down a little. If you ask the uninterested nice, friendly students in the university cafeteria, most of them know the answer right away, but can hardly explain why. On the other hand, there were students who were firmly convinced that their wrong opinion was absolutely correct because they had tested it themselves. Since it seems that I always need to penetrate my fellow students with everyday questions, I now owe them a decent answer.
Isaac Newton investigated the cooling behaviour of different liquids and solids and was able to write a formula for cooling after some successful experiments and measurements. After a few adjustments and integrations, you can shape your cooling law to give us a solution to our problem.
This formula describes the cooling of our coffee very precisely. A is the temperature of the room in which our coffee is located and T0 is the temperature of the coffee at the time of pouring. t is the time and k is the so-called cooling coefficient, which describes the strength of the cooling liquid-specifically. It can be seen that coffee never becomes colder than room temperature a.
Case 1: We add the milk directly to the coffee. The coffee cools down a little at the beginning. However, its temperature drops evenly and slowly approaches room temperature.
Case 2: Let the coffee cool down for 5 minutes and then add the same amount of milk to the coffee at the same temperature. The coffee has already cooled down for 5 minutes and when the milk is added the temperature drops more than in case 1.
If we put the temperature on against time we get a diagram describing this process. It can be seen that the coffee from case 1 stays warm longer. The coffee from case 2 is only warmer until the milk is added. Then the curve is below that of the first case.
In summary, we can say that it is better to add the milk directly to the coffee and not after a few minutes of waiting.
For all those who are interested in the detailed calculation, I am always available by eMail.