[thedoc (OP)]

STEPHEN LAWRENCE  asked the Naked Scientists:
   
If I make a cup of tea and dont intend to drink it for 15 minutes, am I better to not put the milk in until I drink it or add the milk when I make it?

Simply, is there any difference in therate at which it cools down.

Regards
Steve

What do you think?

[CliffordK]

It would be a fun experiment.
Get two identical cups.
Pour tea into both.
Add a measured amount of cold milk to one (mix?)
Wait 15 minutes.
Add the same measured amount of milk to the other (mix?)
Check the temperatures.

My gut feeling is that they will be similar, but the one that got the early milk will be slightly warmer.

The thought is that, say after the first step, one cup is at 80°C, the other is at 100°C.
Both cups will approach room temperature, but the hotter one will cool down faster.  Later when you add the cold milk, the hot one will already have lost more heat than the cool one, to be cooled down further by the cool milk.

[imatfaal]

I believe loss of heat would be dependent on the difference between the cup of tea and its surroundings.  The difference in temperature is greater without the milk and it will lose more heat to the environment whilst still undiluted with milk - you then add the milk which has a simple mixing effect which will same cooling effect as it would have had if you had done it first. 

[distimpson]

very small effect at least in this approximate model:

Assuming 236 gram tea solution at 100^oC plus 20 gram of milk at 4^oC mixing will result in a final temperature of about 92.5^oC, if this cools for 15 minutes (ambient temp of 20^oC) the final temperature is about 64.86^oC.

If the 236 gram of tea solution at 100^oC cools for 15 minutes (ambient temp of 20^oC) the temperature is 69.5^oC, adding 20 gram of milk at 4^oC will give a final temperature of 64.38^oC.

Assumptions: milk and tea have the same thermal properties as water. Cooling during the 15 minute step follows Newton's law, a thermal constant of 0.032 per minute was used (this was a pure guess roughly based on my experience with cups of tea left on the table).

Web sites: Final temp of after mixing http://www.onlineconversion.com/mixing_water.htm
Newton's Law of Cooling: http://www.endmemo.com/physics/coollaw.php

my usual disclaimer, check my numbers if it is important to you! I'm mostly an Earl Grey drinker, no milk.

[peppercorn]

If the tea is a 'traditional' (British brew) dark brown, almost black colour, this should have an effect on the rate of cooling too.  Since the tea will get much lighter on adding milk, this might exaggerate the difference in cooling effect.

[yor_on]

The cups thickness, material, surface open to the environment, place in the room , like elevation, etc? In fact, I think I better give up even before starting here δ-;) Also, can't I assume a equivalent heat loss at a similar temperature. is it the milk making a difference here?

[Bored chemist]

Don't forget that adding the milk makes the cup fuller so it has more area of "heated cup wall" losing heat and also there's less dead volume above the liquid so evaporation is likely to be faster.

[lightarrow]

Furthermore, adding milk changes the colour of the liquid surphace and so its emissivity
http://en.wikipedia.org/wiki/Emissivity

[Bill S]

Just make the tea 15mins later, Stephen.  With or without milk it would be ruined after 15mins standing about.

[peppercorn]

Ah, so 'emissivity' is the word I should have used

[Bored chemist]

Furthermore, adding milk changes the colour of the liquid surphace and so its emissivity
http://en.wikipedia.org/wiki/Emissivity

True, but it's not obvious in which direction the addition of milk changes the emissivity.
The colour change is obvious, but that only tells you about interaction with visible light.
Tea is not generally served while glowing red hot so you would need to look at what "colour" the tea was in the IR with and without milk.

[chiralSPO]

The rate of heat exchange is greater when there is a greater difference between the hot and cold bodies (in this case the hot tea and the cold air). Assuming that the T(tea)>T(air)>T(milk), the way to get the coldest tea in 15 minutes is to add the milk at the very last second (thereby maximizing the temperature difference between the tea and the air for the longest time).

Unless there is an incredible source of radation acting on the cup (much more than just sunlight) the absorption and emission profiles of the different mixtures is negligible. This difference, however will be different depending on the wavelength of light considered.

[yor_on]

Sound pretty straight forward chiral

[Phractality]

There are four components to the heat loss; radiation, conduction, convection and evaporation.

A sealed container surrounded by vacuum will be affected only by radiation.

A sealed container in thermal contact only with a solid external heat sink will be affected only by conduction.

A sealed container insulated from its surroundings, except for a surrounding fluid, will be affected only by convection of the heated fluid rising against its sides.

If the container is well insulated and the top is open, evaporation is the only cooling factor.

Conduction and radiation obey Newton's law of cooling. I'm not so sure about convection and evaporation.

In particular, I think evaporation increases exponentially as the temperature nears the boiling point. If the container is insulated but open, adding the cream immediately will bypass the critical cooling period when the tea is near boiling. I think adding the cream later will result more rapid cooling.

This needs to be tested experimentally with each type of container. Atmospheric temperature, pressure and humidity should be recorded. Dimensions of the container should also be recorded. For an open top container, the rate of evaporative cooling would be inversely proportional to effective depth of the tea; i.e. volume divided by exposed top surface area. Wind is also important, as it reduces the vapor pressure on the surface by removing the escaping vapor.

[syhprum]

Any decent quality tea should be drunk without milk or sugar !

[Bored chemist]

Any decent quality tea should be drunk without milk or sugar !

Marx would arrest you for that.
"All proper tea is theft."

Also, re"There are four components to the heat loss; radiation, conduction, convection and evaporation. "
Amongst our  weaponry are such diverse elements as surprise, radiation, conduction, convection and evaporation

and advection, if the cup is in a draft.

Evaporative cooling will depend (among other things) on how exposed to any air currents the liquid surface is.
So, adding more milk will raise the liquid level and increase the evaporative loss.
You would, however, need pretty odd circumstances for this to be significant.


"Conduction and radiation obey Newton's law of cooling."
In the very real sense that radiative heat loss is proportional to the 4th power of the temperature and conductive loss is proportional to the first power of the temperature difference.

The OP's tea is now cold, btw.