From the blog December 12, 2012 Nathan

The Physics of Coffee & Cream

Every Seattleite has been in this situation: On a cold, rainy December morning, you get your coffee to go from Vivace, Stumptown, or Starbucks, and then watch out the window for your bus. The bus, you know, might be a minute or two late, and you’ll have to wait a few minutes. You want to keep your coffee as hot as possible during your wait so that it’s still piping hot when you step out the door. You grab a lid for your cup, pausing at the cream. Should you add the cream to your coffee now, or will that only cool your drink faster? Maybe you should add your cream at the last minute, before you dash out the door.

The basic physics of heat provides the answer: you should go ahead and add the cream to your coffee now. Coffee with cream cools about 20% slower than black coffee, for three reasons:

  1. Black coffee is darker. Dark colors absorb heat faster than light colors (just think about wearing a black T-shirt versus a white T-shirt on a hot, sunny day). But dark colors also emit heat faster than light colors—absorption and emission are essentially two sides of the same coin. So by lightening the color of your coffee, you slow its rate of heat loss slightly.
  2. Stefan-Boltzmann says so. The Stefan-Boltzmann law says that hotter surfaces radiate heat faster—specifically, the power of emission is proportional to the temperature (in kelvin) raised to the fourth power. So let’s say you have two cups of coffee that start at the same temperature. You pour cream in cup #1 and the coffee drops in temperature immediately. But the rate at which it loses heat also drops. Meanwhile, the hotter black coffee in cup #2 cools so rapidly that within five minutes the two coffees are at about the same temperature. But you still haven’t added the cream to coffee #2! When you do, it cools even more; cup #1 is now the hotter of the two.
  3. Viscosity versus evaporation. This is the clincher. Adding cream thickens the coffee (adds viscosity), so it evaporates slower. You’d be surprised just how much heat evaporation carries away. Slow the rate of evaporation and you avoid a lot of that heat loss. (This is also one big reason that coffee stays warm longer with a lid on the cup.)

So, next time you’re caught in the rain, put the cream in your coffee right away. Your fingers will thank you.

Watch our high-speed video above of cream being poured into coffee at 2,000 frames per second.

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Discussion

  1. Dori Cedillo December 14, 2012 Reply

    I love science.

  2. Tom M. December 14, 2012 Reply

    Nathan Myhrvold entered UCLA at 14, finished his PhD at Princeton in Theoretical Physics… so one should be loath to question any pronouncement of his regarding Physics.

    So in all humbleness, I question the order he ascribes to the heat loss from a (paper) cup of coffee. 1 and 2 as radiant loss. 3 as evaporative.

    Left out completely is conductive (and +convective). Even without doing the simplified (yet complex) calculations, I would bet that the amount of heat loss is almost totally conductive and evaporative, radiative being some orders of magnitude less than the latter two.

    Just saying. If there is interest, we can do some quick “book end” calcs, e.g. assume the cup is a blackbody sphere whose volume is 10 oz. in an ambient 30 degrees F, the coffee at 140F. This gives the absolute maximum of radiative loss.

    Calc the cup’s conductive (and convective) losses assuming some arbitrary (but high) R value assuming a cylinder.

    But all this effort will show that Nathan’s conclusion is still correct and irrefutable… put the cream in first!

    Sorry for being nitpicking.

  3. CJM January 3, 2013 Reply

    Can we assume that something that is darker in visible light is also darker in infrared light where most heat would be transfered? If not, what indicates that an object has infrared absorption/emission ?

  4. Ben February 27, 2013 Reply

    I ask this basic question for mechanical engineering interviews. The answer on that page is mildly correct.

    The first two are basically the same and refer to radiative heat transfer. The effect is virtually nil in this situation. The radiative heat transfer scales fast as the temperature of two bodies changes. But coffee and the surrounding objects are not that far apart in temperature. This effect is massive when you talk about the sun and or outer space (1000′s of degrees and absolute zero).

    The third is reasonably false. Viscosity isn’t a determination of evaporation. That depends on other factors. Adding cream likely changes the evaporation rate slightly. But again, this effect will be negligible.

    The real answer is that heat transfer by conduction (to your hand) and convection (to the air above the coffee or from the coffee cup to the air) is higher the larger the difference in temperature. When you first get your coffee, it is hottest. So it is tranferring heat the fastest.

    The addition of cream is increasing the thermal mass of the coffee with a liquid of a set temperature (energy). The cream doesn’t remove any heat, it only lowers the temp. As such, adding it immediately or later will add the same amount of energy. But adding it immediately will lower the temperature immediately, slowing the rate of heat transfer to the environment.

  5. John Kirk June 8, 2013 Reply

    The black body law states that a black body both absorbs and radiates heat to the fourth power. Adding cream to black coffee preserves heat in coffee by virtue of lightening the color, thus reducing the rate of heat dissipation by the properties of the black body law. Lighter objects both absorb and radiate heat at a much lower rate than darker ones. The cream also places a thin film of fat on the surface of the coffee since fat is insoluble in and less dense than coffee, and this fat layer retards the evaporation of coffee, thus further reducing the rate of heat loss. Since fat is immiscible with the water in coffee, it does not contribute to viscosity. Milk solids in cream contribute very little to viscosity, and it is their light color, not their solute properties, which impact heat dissipation via black body effects.

    Fat not only inhibits evaporation, it is inherently an insulator, further contributing to heat retention by coffee. Keeping a lid on coffee increases the partial pressure of water vapor in the air in the cup, establishing a dynamic equilibrium such that at the equilibrium point, the rates of evaporation and condensation become roughly equal, nearly balancing the exothermic and endothermic reactions of evaporation and condensation, respectively. The surface fat layer added by cream to a very large extent precludes evaporation, thereby retaining the heat which would have been lost by exothermic evaporation.

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