|MadSci Network: Physics|
Coffee is a beverage loved by many, but only if it is hot. Your question is very interesting and as far as I can tell, no one has provided any data on the effects of holding a cup of coffee. There has been a lot of discussion about whether coffee stays hotter if the cream and sugar are added when the coffee is served or if one delays adding it until just before it is consumed. It turns out that the work of Cornell University students Darwin Novak and Robert Seidel in 1958 clearly established that your coffee stays hotter if the cream and sugar are added immediately, rather than waiting (see http://www.eweek.org/site/News/Features/coffee.shtml). Most people who analyze the problem of when to add cream simply look at the problem as one of conduction and ignore the convective heat losses from the surface of the coffee. Put simply, heat is lost by evaporation much more quickly from a hot liquid surface than from a cooler surface. So, in considering how to answer your question, there are a whole bunch of variables, and calculating a result based upon those assumptions seems unsatisfying. So, instead, I decided to run a couple of experiments and actually measure the results. You can argue over opinions for days; it is hard to argue with data. For my experiment, I used a genuine McDonald’s Styrofoam coffee cup with the included lid as the container. For our test, I used water instead of coffee, since coffee is mostly water. The weight of the empty cup was 7.008 grams; without the lid, the cup weighed 4.406 grams. I filled the cup with deionized water and weighed the cup. I then heated the cup for 3 minutes in a microwave oven. The water was boiling at the time I removed it from the oven. I quickly weighed the cup (having tared out the weight of the cup), and then placed two small Type K thermocouples in the water in the cup. The temperature decrease over time was measured using a PC and data acquisition system. Room temperature was monitored with two other thermocouples and remained between 18 and 20C throughout the experiment. Typical brewing temperatures according to Novak and Seidel for coffee is 85C (185F) and drinking temperature is 62C(143F). I ran three experiments. In the first experiments, the coffee cup containing the water sat on top of a book in a room with stagnant air flow with the lid on. In the second experiment, the cup sat in the same room, on the same book, but with the lid off of the cup. In the third experiment, I held the coffee cup in my hands for the first 40 minutes, alternating the cup from one hand to the other occasionally, again with a lid on the cup. In the first experiment the initial water weight after heating was 285.6g after cooling the weight was 283.857 grams. In the second experiment without the lid, the initial weight was 295.08 grams. When it was cooled, the weight was 277.26 grams. In the third experiment where I held on to the coffee cup, the initial weight of water was 285.72 grams. Final weight after cooling was 283.899. The results of my experiment are shown in the following Figure: . The first thing that is obvious is that there is a huge difference in cooling rate depending upon whether there is a lid on your coffee cup or not. The time for the water to decrease in temperature from 85C to 62C is 15 minutes if the lid is off the coffee. When the lid is on the coffee, it took 39.5 minutes to cool from brewing to drinking temperature if I wasn't holding the cup, and 38 minutes if I was holding the cup. Although it appears that holding the cup increases the rate that the cup loses temperature, I wanted to take a closer look at the data. This second Figure: shows the number of degrees temperature loss from each cup in ten minutes. If you carefully compare the curves where I am holding the cup versus allowing the cup to stand in still air, you can see that for the first 30 minutes or so, the rate of heat loss from holding the cup is slightly greater than the standing cup. You can also see from this Figure some bobbles in the graph when I changed from one hand to the other, and when I got bored of holding the cup and sat it down on the book (about 30-35 minutes into the experiment). So, you might ask, why didn't I hold the cup while the lid was off? As you can see from the data, the heat loss by evaporation of the open cup is huge. Over a period of about 80 minutes, we lost 17.82 grams of water by evaporation, whereas the closed cups lost about 1.8 grams to evaporation and whatever quantity of water stuck to the underside of the lid. At 540 calories per gram of water evaporated, that is a loss of 9623 calories! If I am holding the cup, my breath over the top of the cup could easily increase the rate of evaporation and temperature loss, completely masking the effects of holding the cup. If you want your coffee or hot chocolate to stay hot, keep a lid on the liquid. If we ran the same experiment with a glass cup, it is likely that holding the cup in your hands would again increase the rate of heat loss, however, a cup filled with 85C water would likely burn your hand at the same time (because of the higher rate of heat transfer of glass compared with styrofoam). So, in summary, a cup of water with a lid on sitting on a book lost an average of 36.07C in one hour, compared to a loss of 36.54C when the cup was held in my hand. Without the lid, the cup lost 53.35C in an hour. (These numbers were obtained by averaging the two thermocouple readings). So, it appears that holding a coffee cup increases the rate of heat loss, but not by much. It is a small price to pay for the pleasure of having warmer hands on a cold fall or winter morning, plus you are utilizing heat that would otherwise be lost to the environment. And never let it be said that we Mad Scientists don't occasionally put a lot of time and effort into answering your questions. Thanks for asking.
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