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Adding a cold water to tea

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This morning i was making a tea. I heated up the water, till it started to boil. Usually instead of filling full cup with very hot water, i fill only half, because the rest i fill with cold water, so the tea is not so hot. At the moment, when hot water was poured into the cup, i decided to go to check my email. And then suddenly curious question popped up into my mind. Curious question: In which case the tea will be hotter? If I add a cold water and go for 5 minutes to check my mail or If I go and check my mail for 5 minutes, and when returned, add a cold water The answer is not obvious. Because in first case difference between hot tea and room air is greater, and thus energy will flow faster away from the cup. And on the other hand, in the second case the surface between tea and air is greater, so again it means that energy flows faster away. I did a few calculations to find the answer. It turns out that it is very important what shape is your cup is in. And also the temperature of co...