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re: coffee and tea
21 apr 1999
sunfire wrote:
>physics-wise, i know it's better to add milk as soon as possible to the
>coffee or tea, rather than later on just before you're about to drink
>it. some people might think that since the milk is cold (usually) that
>it would lower the temperature of the drink and thus cool it faster. on
>the contrary, the fats in the milk, being less dense than the coffee/tea,
>would rise to the top and act as a buffer. milk evaporates less quickly...
that's true too, but the tea's heat loss is proportional to the difference
between the tea and room temperatures (newton's law of cooling), so higher
temperature tea loses heat faster. hmmm. a covered cup with 0.5 ft^2 of us
r1 surface containing a pound of water has rc = 1ft^2-f-h/btu/0.5ft^2x1btu/f
= 2 hours or 120 minutes, so after 6 minutes in a 70 f room, 212 f tea cools
to 70+(212-70)exp(-6/120) = 205.1 f. when we add 10% 40 f milk, the mixture
acquires the average temperature of (1x205.1+0.1x40)/1.1 = 190.1 f.
adding milk first, the mixture instantly becomes (1x212+0.1x40)/1.1 = 196.4,
but the time constant rises to 132 minutes, so t = 70+(196.4-70)exp(-6/132)
= 190.8 f after 6 minutes.
putting the milk in the cup a half-hour before teatime allows it to rise to
70-(70-40)exp(-30/12) = 67.5 f. when we add 212 f tea, the mixture becomes
(1x212+0.1x67.5)/1.1 = 198.9 f, and it cools to 70+(198.9-70)exp(-6/132)
= 193.1 f after 6 minutes.
steamed milk and teawater at 212 f would cool to 70+(212-70)exp(-6/132)
= 205.7 f after 6 minutes.
it helps to scald the cup first, and put a low-thermal-mass cover on top,
eg one of those plastic cat food can covers, reserved for this use, which
can also serve as a handy place for the used teabag.
hope this helps.
nick
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