KING@KESTREL (12/28/82)
From: Richard M. King <KING at KESTREL> The standard answer is to add the milk BEFORE answering the phone, because the mixture will cool slower than the tea. I am suspicious for the following reasons: 1) if you don't add the milk, it will warm up. If the temperature of the milk is above the dew point, the milk will gain heat much faster than would be implied by the temperature difference between the milk and the air 2) if you add milk the fluid level in the cup increases. This increases the dissipating surface. It can be easily shown that if the dissipation of a container of fluid is proportional to the temperature difference times the volume of fluid, than it doesn't matter when the milk is added when the fact that the milk would have warmed up during the telephone call is taken into account. Dick -------
dkw (12/29/82)
If one assumes ( as is reasonable, given energy conservation ) that the temp. of the milk is close to or above room temperature ( and it certainly is closer to room temperature than the tea is ) then the warming efect Dick talks about is very small, so one should add the milk to the tea as soon as possible.
rtris (12/30/82)
Since physics is an empirical science, perhaps somebody should perform the appropriate experiment with milk and tea, and then attempt to explain the actual results they get! Ralph.
mmt (12/30/82)
This tea-milk problem is often given to first-year physics students
after they hear about Newton's law of cooling. Newton's law only applies
if the interface between hot and cold systems stays the same. If you
put milk into hot tea, there are two kinds of difference:
(i) the total contact areas between (a) milk and room and (b) tea
and room changes. If your milk was all in a small jug and was added
to a larger cup of tea (no milk remaining in the jug), the total
heat-transfer surface is probably reduced.
(ii) Hot tea cools at the surface (and edges), inducing convective effects
which increase the rate of heat transfer as more hot tea is brought
to the surface. Cooling the tea with milk can reduce these effects.
The answer to the question of whether the tea will be warmer when drunk
after early or late milk addition depends on several things, including
the shape of the teacup, the shape of the milk-jug, and maybe other
things like how carefully the milk was added.ss (12/31/82)
In my experience the milk is COLD, having been just taken out of the refrigerator. In that case you might do better if you wait...
rb (01/04/83)
why doesn't somebody just try it, and report the results? -Ronen
lemmon (01/06/83)
Jearl Walker, in his Amateur Scientist column in Scientific American, described a series of experiments in which he measured the freezing times of containers of water at various temperatures. Rather surprisingly, he found a NON-monotonic relationship! Hotter containers apparently convect more vigorously, and the effect lasts after cooling to the temperature of other candidates in the race. Anyway, the situation in the real world is more complicated than one would think. Alan Lemmon (Sorry, I have forgotten when, but I think it was in 1982.)
paul (01/07/83)
"why doesn't somebody just try it, and report the results?" Hey come on, be empirical? How provincial, how utterly 18th century. (Tongue in cheek, natch).
jj (01/07/83)
My parents used to float the cream on top of the tea. There was clearly a phase boundary between the cream and the tea that stayed there for most of the time it took to dring the tea. How might this affect the problem. rabbit!jj
pat (01/09/83)
#R:watmath:-414000:uicsovax:19400004:000:106 uicsovax!pat Jan 8 22:58:00 1983 Adding milk first may not allow the tea to retain heat longer but it sure makes the tea taste better.
freund (01/16/83)
Several million englishmen have done the experiment (of course). When you add the milk to the hot tea you scald it. The necessary equipment is: Bone China tea set Silver teakettle Hot water milk ... and tea, loose tea preferably. applicable references: Adams, "The Restaurant at the End of the Universe" bob freund