Tea kettle question - part two

[Rum]

Suppose you have a hot cup of coffee (or tea!) an you want it to cool down to make it drinkable. Is it quicker to leave it standing and then add room temperature milk when the liquid has cooled a bit or add the milk straight away? Which gets it to a drinkable (i.e. cooler) state quicker, if either?

[Gawdzilla Sama]

Conduction vs. convection. Direct contact with the cooler milk will transfer heat faster than having it sit there cooling by air contact. If you really wanted to cool it down quickly, put it in a bowl and pour cold water around it.

[PsychoSerenity]

If adding the milk doesn't cool it down enough by itself, I think it would take the same time for the whole mixture to reach the desired temperature, whether the milk is added at the beginning, or at precisely the time that the milk will cool it down to the desired temperature. Though I'd have to do some calculations to check, and there might be other discrepancies that my model wouldn't account for. - perhaps milky tea doesn't evaporate as efficiently? I don't know.

But adding the milk to begin with does allow you to test it as you wish, whereas if you wait to add the milk you may end up over shooting the mark - so when you do add it, it gets too cold.

[Gawdzilla Sama]

If adding the milk doesn't cool it down enough by itself, I think it would take the same time for the whole mixture to reach the desired temperature, whether the milk is added at the beginning, or at precisely the time that the milk will cool it down to the desired temperature. Though I'd have to do some calculations to check, and there might be other discrepancies that my model wouldn't account for. - perhaps milky tea doesn't evaporate as efficiently? I don't know.

But adding the milk to begin with does allow you to test it as you wish, whereas if you wait to add the milk you may end up over shooting the mark - so when you do add it, it gets too cold.

That's what microwaves are for.

[MiM]

If adding the milk doesn't cool it down enough by itself, I think it would take the same time for the whole mixture to reach the desired temperature, whether the milk is added at the beginning, or at precisely the time that the milk will cool it down to the desired temperature.

Nope. Adding the milk last is faster. The heat transfer from the liquid to the surrounding materials is more efficient the higher the temperature difference.

[Gawdzilla Sama]

If adding the milk doesn't cool it down enough by itself, I think it would take the same time for the whole mixture to reach the desired temperature, whether the milk is added at the beginning, or at precisely the time that the milk will cool it down to the desired temperature.

Nope. Adding the milk last is faster. The heat transfer from the liquid to the surrounding materials is more efficient the higher the temperature difference.

The Transit Slope.

[PsychoSerenity]

If adding the milk doesn't cool it down enough by itself, I think it would take the same time for the whole mixture to reach the desired temperature, whether the milk is added at the beginning, or at precisely the time that the milk will cool it down to the desired temperature.

Nope. Adding the milk last is faster. The heat transfer from the liquid to the surrounding materials is more efficient the higher the temperature difference.

I thought I was already taking that into account. Doesn't the temperature drop, caused by adding the milk, also depend on the difference between the milk and the tea? So as it gets cooler, adding the milk won't cool it down so much, so you have to wait longer anyway, and it balances out?

I've tried to work it out with numbers, but I seem to have forgotten how they work.

[Gawdzilla Sama]

The Transit slope height is determined by the difference in temperatures. The angle of the slope is determined by the interface between the two bodies. If you put a hot object on one side and a cold on the other with 8 inches of styrofoam in between the angle will be very small and the heat exchange will be slow. When you combine two liquids the angle is nearly vertical, resulting in a quick exchange even when the liquids near equilibrium.

[MiM]

If adding the milk doesn't cool it down enough by itself, I think it would take the same time for the whole mixture to reach the desired temperature, whether the milk is added at the beginning, or at precisely the time that the milk will cool it down to the desired temperature.

Nope. Adding the milk last is faster. The heat transfer from the liquid to the surrounding materials is more efficient the higher the temperature difference.

I thought I was already taking that into account. Doesn't the temperature drop, caused by adding the milk, also depend on the difference between the milk and the tea? So as it gets cooler, adding the milk won't cool it down so much, so you have to wait longer anyway, and it balances out?

I've tried to work it out with numbers, but I seem to have forgotten how they work.

No.

You can try to think at it like this. Your original combination of tea and milk has a certain amount of excess heat energy. This total energy does not change when you mix the liquids. So your task is to make the transfer of heat to the surroundings as efficient as possible.

Of course you could make an interesting case out of it if you took the milk out of the fridge at the same time as you draw your teacup. Then it would all depend on weather the milk heats faster or slower than the tea cools off. That could become a nice calculation for Jim's students

[JacksSmirkingRevenge]

Adding milk immediately would increase the surface area of the tea up the side of the cup too, thereby (maybe only slightly) increasing the rate of convection of heat to the surrounding air?

I think this is a question for someone from the Department of Big Sums.

[Gawdzilla Sama]

Adding milk immediately would increase the surface area of the tea up the side of the cup too, thereby (maybe only slightly) increasing the rate of convection of heat to the surrounding air?

I think this is a question for someone from the Department of Big Sums.

Cool. I'll be at Big Sur if you need me.

[Rum]

Adding milk immediately would increase the surface area of the tea up the side of the cup too, thereby (maybe only slightly) increasing the rate of convection of heat to the surrounding air?

I think this is a question for someone from the Department of Big Sums.

Jim'll fix it!

[Gawdzilla Sama]

Adding milk immediately would increase the surface area of the tea up the side of the cup too, thereby (maybe only slightly) increasing the rate of convection of heat to the surrounding air?

I think this is a question for someone from the Department of Big Sums.

Jim'll fix it!

He's dead, Jim'll.

[Warren Dew]

Suppose you have a hot cup of coffee (or tea!) an you want it to cool down to make it drinkable. Is it quicker to leave it standing and then add room temperature milk when the liquid has cooled a bit or add the milk straight away? Which gets it to a drinkable (i.e. cooler) state quicker, if either?

Considering tea becomes undrinkable once you add milk, you should wait as long as possible to add the milk.

Coffee, of course, is undrinkable to start with, so with coffee it doesn't matter.

[Tero]

You theoretical guys are useless. Do the experiment. First, define the temperature. Where in the cup?