# Hot Tea and an Unexpected Visitor

You're enjoying a Saturday morning, making a cup of tea to start the day. Just as you've finished pouring the boiling water into your teacup, you hear a knock at the door. If you like your tea with milk and as hot as possible. Should you:

1. add the milk now or
2. add the milk after you return from answering the door?

In either case the teacup will sit on the counter and the milk jug will sit in the fridge. Which will result in the hottest cup of tea?

Extra info:

• The amount of milk added is the same in both cases.
• The amount of water that escapes as steam is negligible.
• The temperature of the water is greater than the room temperature.
• The temperature of the room is greater than the fridge temperature.
• @Daedric Not quite. The question you link is adding the milk before or after the water. This is whether adding the milk before answering the door or after will lead to warmer tea. Similar, but not quite duplicate. – tfitzger Jan 25 '16 at 18:32
• @tfitzger The answer to the linked question has the water in the mug at time $t=0$ in both cases. As such, the answer is valid for this question. The answer is not valid for the other question, as no water is added at any time after the beginning of the experiment. Apparently nobody noticed that error. linked question – Logophobic Jan 25 '16 at 18:57
• Could you link the question? – Slepz Jan 25 '16 at 18:59
• @Slepz I noticed the previous comment had been deleted, and added the link to my comment. – Logophobic Jan 25 '16 at 19:00
• Every seasoned tea drinker knows that the milk goes into the cup before the tea, so it won't get scalded... – Oliphaunt Jan 26 '16 at 13:00

as Daedric pointed out, this is kind of a duplicate. But here's a non-math answer.

To get the hottest tea,

add the milk before answering the door

because:

when two liquids are mixed, they will reach a median temperature based on the volumes and temperatures of each (and other factors, but these are more important). So if you have milk that is always the same temperature no matter when you add it, the tea that has had a chance to cool will be cooled more by the milk than the tea that is hotter.

• Here's a 1000! :) – Beastly Gerbil Jan 25 '16 at 18:58
• "The tea that has had a chance to cool will be cooled more by the milk than the tea that is hotter." This is not true. The point is that hotter tea loses heat to the surrounding air faster than cooler tea, so you want to add the cool milk as soon as possible. – Julian Rosen Jan 31 '16 at 0:12