With or without milk
Kuba is preparing a cup of his favorite milk tea. Everything goes normally but the moment he was going to do the last step, add the milk, he heard a door bell. Kuba assumes it may be the postman he was expecting with some tea packages and it can take him several minutes to do the paperwork.
Kuba likes his tea hot so he started to wonder - if I'm going to be back in few minutes and I want my tea to be as hot as possible - should I now add the milk or do it after coming back?
Few assumptions:
- The milk has room temperature.
- The volume of the milk added doesn't depend on the moment Kuba adds it.
- The volume of the tea is small and unimportant comparing to the volume of the tea.
- The milk gets evenly mixed with the tea immediately after being added.
Image by User:MarkBTomlinson - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=25831283
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1 solution
From the Fourier's law the rate of the heat transfer is directly proportional to the temperature difference between the two bodies (actually, it's a bit more complicated but that form satisfies us for purpose of this proof). In this case the tea and the room. Adding the milk will cool the tea so the difference becomes smaller, so the tea will loose less heat during the time Kuba will be away.