| MadSci Network: Physics |
Yes, but the effect is quite small.
For background, please read this previous answer, which I found by searching using our search engine and searching on "mechanical equivalent".
In that previous answer you will find that the mechanical equivalent of heat is about 4.2 Joules per calorie. If the cup of coffee has about 175 grams of water (a reasonable size for a cup of coffee), then 1 calorie of "heat" would raise the temperature by only 1/175 degree Celcius (The definition of a "calorie" is "the amount of 'heat' needed to raise one gram of water by one degree Celcius".). How much stirring would it take to do that?
The one calorie is equivalent to 4.2 Joules. A Joule is the amount of work done by a force of one Newton acting for one meter (the force being assumed to be in the same direction as the motion). One Newton is the force needed to keep about 0.102 kilograms of mass suspended against gravity (f = ma, or m = f/a, so m = 1 Newton / g, so m = 1 Newton / 9.8 meters per second per second, so m = 0.102 kilograms), or about 102 grams. So 4.2 Joules of work would be done by lifting the 175 grams of coffee vertically by 2.45 meters (Work = Force times distance, or distance = Work / Force. Distance = 4.2 Joules / [0.175 kg * 9.8 meters per second per second])
It's a little difficult working out how much actual stirring one would have to do to be equivalent to that amount of work. But imagine raising your coffee almost 2.5 meters above the table top, and that amount of work (if it were work actually stirring the coffee) would raise the coffee's temperature only about 0.006 (= 1/175) degrees Celcius.
Let's make some assumptions. It would seem reasonable to me that a moderate stirring of the coffee would require a force of roughly 1/10 Newton (Very rough estimate, admittedly, but I'm trying to relate this to something we can think about!), and we can stir the coffee at a velocity of roughly 1/4 meter per second (Again, a very rough estimate!). Power is equal to force times velocity, so the power we can stir at is roughly 1/10 Newton times 1/4 meter per second, or roughly 1/40 Watt (a Watt is a Newton meter per second). Work is power times time, so let's assume we stir the coffee for 40 seconds. That is then 1/40 Watt times 40 seconds, or Work = 1 Joule. From above, we can see that 1 Joule is only 1/4.2 calorie, which would increase the temperature of the coffee by only 1/4.2 * 1/175 degree Celcius, or about 0.0014 degree Celcius. To raise the temperature of the coffee by only 1 degree Celcius we would have to stir it for about 29400 seconds, or 490 minutes, or 8.17 hours (If our estimates are correct.)!! And that doesn't account for any cooling that would occur during that time!
My estimates can be challenged, but the idea is that it would take a lot of stirring to heat the coffee!
John Link, MadSci Physicist
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