I doubt that the ancient Greek philosophers spent much time on this (especially since they didn’t have coffee), but it’s a challenging question, if not an earthshaking one.
You could settle it with an accurate thermometer, but you’d have to measure out exactly the same amounts of coffee and cream into exactly the same type of cup, all at precisely the same initial temperature. But doing a carefully controlled scientific experiment in a kitchen has its problems, so let’s just think it out.
All other things being equal, you’d think that both methods would lead to the same temperature of the final mixture, because you’re combining x calories of heat in the coffee with y calories of heat in the cream, for a total of x + y calories in the mixture either way. (Regarding the use of the word calorie, see the box on p.
Unfortunately, according to Wolke’s Law of Pervasive Perversity, all other things are never equal. Whether it’s black coffee or creamed coffee, it must sit around until you’re ready to drink it. Meanwhile, it has been cooling off, because the air is cooler than the liquid in the cup and heat is therefore flowing from the liquid into the air. Heat will always flow from a substance at a higher temperature to an adjoining substance that is at a lower temperature.
But there are two important differences between the creamed coffee and the black coffee: (1) the cup of creamed coffee contains slightly more liquid because of the added volume of the cream, and (2) the creamed coffee is cooler than the black coffee.
Difference number 1 means that the creamed coffee with its larger volume will take more time to cool off. That is, more heat must be removed to lower its temperature by any given number of degrees. (A bathtub of water takes more time to cool than a bucket of bathwater of the same temperature.)
Difference number 2 has the same result: the slightly cooler creamed coffee will cool off more slowly than the slightly hotter black coffee, because the smaller the temperature difference between a hot object and its surroundings, the slower will be its rate of cooling. So immediate creaming wins again.
My advice is to add the cream as soon as possible. The coffee will be hotter by as much as a degree or two at drinking time, and I’m sure your life will be much the better for it.
I’ m pleased to report that this problem was the subject of a careful scientific experiment led by the college student Jonathan Afilalo and published in the spring issue of the Dawson Research Journal of Experimental Science. This is a most impressive journal that publishes papers on original, professional-quality research by undergraduate students at Dawson College in Montreal, Quebec.
The students’ experiment came to the same conclusion as I did, as shown by their measured cooling curves plotted in the graph above. In curve 1 the cream was added two minutes after the coffee had been poured, whereas in curve 2 it wasn’t added until ten minutes after pouring. Note that thereafter the temperature in curve i remained about a degree and a half higher than in curve Early addition of cream does keep the coffee hotter.
The higher the temperature of an object, the faster it will lose its heat by radiation. That’s the Stefan-Boltzmann Law. Also, the bigger the temperature difference between two objects in contact with each other (such as coffee and air, for example), the faster the hot one will lose its heat to the cooler one by conduction.
That’s Newton’s Law of Cooling. There are precise mathematical formulas for both of these laws.