Thread: Heat of tea

1. Would tea stay hotter if your added the milk to the tea or the tea to the milk?

2.

3. That's not how I remember the problem. And it's physics not chemistry.

Well, to the question as put: neither. :?

4. From a thermodynamic standpoint, if you mixed the two liquids together, they would reach an intermediate temperature that would be a weighted average of the temperature of the two liquids. It wouldn't matter. But in the practical situation, the temperature of the cup makes a difference, too.

So if you took a hot cup of tea and poured some cold milk into it, It would end up hotter than if you took a cold cup, with a little milk in it, and poured hot tea into it. The cold cup would absorb some of the heat that was in the tea.

5. Not wishing to hijack the thread but yeah,
Originally Posted by Harold14370
the cup makes a difference, too
It goes something like this:

You like your tea with milk, and you like it hot. Now, the tea is poured, but you have to leave it for some minutes. Do you add the milk now, or later?

6. Now. See Newton's 5/4 power cooling law.

7. Let's start with a few assumptions. The teacup is approximately cylindrical. The rate of heat loss is approximately proportional to the surface area and the temperature difference between the tea and the ambient temperature. If there is actually a 5/4 exponent in there, I don't think it will affect our final result.

The milk sits at room temperature before it is poured into the tea. Either that or it sits in the fridge. Either way, it is not gaining or losing any heat in the time between pouring the tea and adding the milk.

Initially, when the tea is poured, Q-dot, the rate of heat loss to ambient is kA delta-T where A is the surface area, delta-T is the temperature difference and k is a constant of proportionality.

If we added an amount of milk at room temperature equal to the amount of tea, the temperature would be half way between the initial temperature and the room temperature, thus delta-T is cut in half. A is greater than the original surface area, but not twice as great because the area of the bottom of the cup and top surface of the liquid are not changed. Therefore Q-dot is decreased if the milk is added right away. This means the tea+milk will stay warmer longer if the milk is added right away.

8. There actually is a 5/4 exponent. The heat transfer coefficient in natural convection is proportional to the temperature difference to the power 1/4, and the driving force is the temperature difference to the 1th. power so combining exponents gives you temperature difference to the power 5/4. Newton found this experimentally and it is still used.

I agree it probably doesn't make a difference to the answer to Pong's question. Funny, I remember discussing this many many years ago with college roommates, sitting around the flat watching tea cool, 'cause we didn't have enough money to go out. It must be one of those perennial questions.

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