halle1 (01/07/83)
Everyone is approaching this problem all wrong. The solution is trivial. Assuming that the cream to be added will be the same temperature at either instance (true if it comes straight from the fridge or if it has been out for a while, and close enough otherwise), and assuming that the final temperature will be above room temperature, which is certainly true, the rest is easy. Adding the cream will reduce the temperature of the tea by the same amount whenever it is added. That is, the temperature will drop by x degrees, not by x %. All that remains is to determine which method cools faster independent of the mixing. For virtually all situations, the greater radiation by the hotter liquid will dominate. The change in color will have no noticible effect. Besides, will white or black have the greatest net radiation at a given temperature? It is unclear, given absorption and blackbody effects. I doubt the difference is more than 0.1 degrees, probably much less. More important is the cup shape. In straight sided mugs, the radiation surface is unchanged. In typical teacups, the surface will increase, but only slightly for typical volume changes. In any case, it will not change by as much as the temperature. I.e., delta S / S < delta T / T , where T here is the difference between tea temp and room temp. In fact, in a tulip cup, the surface will decrease. In summary, radiation is greater if the cream is added later. All other effects have no measurable difference. Mixing reduces the temperature by the same amount independent of timing. Thus it stays hotter if the cream is added immediately. I hope this ends the discussion once and for all. Jeff Halle BTL Holmdel houxz!halle1