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Apr 28, 2016 at 10:49 comment added Jonathan Hartley "that degree of detail" - only pathalogical pedants are remotely interested in questions like this in the first place. Not that I'm saying that's a bad thing - I count myself among their number.
Apr 25, 2016 at 20:14 comment added David @DanHulme It's an approximation when the tea/milk is mixed quickly. Water has a high specific heat capacity, so it's reasonable to assume that the small energy lost in the time it takes to mix the tea results in only a small error in the temperature. The long term cooling of the tea has nothing to do with the order things are mixed anyways.
Apr 25, 2016 at 8:35 comment added Dan Hulme If conservation of energy applied in the way you say, the tea would never get cold.
Apr 25, 2016 at 0:52 comment added David @JonathanHartley I don't disagree, but if you consider the problem in that degree of detail, it becomes unsolvable. What if there's a lot of sugar and milk, and adding the milk first results in the sugar taking a long time to dissolve, cooling the tea even more? You need to draw your approximations and assumptions somewhere, and I applied the approximation that the milk/sugar are mixed relatively quickly, and the energy lost is insignificant.
Apr 24, 2016 at 22:37 comment added Jonathan Hartley Tea does have a memory, because it has a state: its temperature. Let's use period 'B' (for 'between') to denote the period when milk has been added but sugar has not (or vice versa.) During period 'B', the tea will be cooling down. As always, the rate it cools is dependent on the current temperature. If milk, say, cools the tea more than sugar, than the amount the tea cools during period B will be less if milk is added first. So adding milk first results in tea that is warmer at the end of the process.
Apr 24, 2016 at 21:17 comment added David @MartinUeding If you dislike my answer, then think of it as a supplement to Ilja's answer as to why the order doesn't matter when the processes are instantaneous.
Apr 24, 2016 at 20:45 comment added Martin Ueding Energy is only conserved in closed systems. The cup and dissipation of steam are not part of the system.
Apr 24, 2016 at 20:25 comment added Henry The order of tea and milk does make a noticeable difference and led to developments in the design of experiments and the Fisher's Exact Test: en.wikipedia.org/wiki/Lady_tasting_tea
Apr 24, 2016 at 12:47 comment added jpa Though how much you mix it does matter, as it adds energy.
Apr 24, 2016 at 10:13 history answered David CC BY-SA 3.0