Which scenario would my coffee be warmer?

[xx44]

So this morning I pour my cup of coffee add milk. Before I could get to it I took a call that lasted 10 mins, got to the coffee which at that point was tepid (sucky way to start the day).

Anyway I thought if I added the milk after my call it would be warmer. I actually asked a few people about this and of course got the three different possible answers.

Which scenario would the coffee be warmer?

[PLOlover]

too hard I say do an experiment

[luckyme]

Hottest coffee is having the milk in cup prior to coffee.
Next is adding milk asap.
coolest is adding milk after a while.

luckyme

[Max Raker]

This is actually pretty intresting. My guess would be to keep them seperate. This way the milk at least will get a little warmer while the cofee cools? I am curious to the logic of the other methods as this might be way off.

[SBR]

[ QUOTE ]
Hottest coffee is having the milk in cup prior to coffee.
Next is adding milk asap.
coolest is adding milk after a while.

luckyme

[/ QUOTE ]

You think it makes a difference in the temperature if you pour coffee into milk or milk into coffee? Say I have 2 cups, one with a bit of milk, one with coffee. If I pour the coffee into the milk it will be warmer than if I pour the milk into the coffee? Are you insane?

[godBoy]

[ QUOTE ]
This is actually pretty intresting. My guess would be to keep them seperate. This way the milk at least will get a little warmer while the cofee cools.

[/ QUOTE ]
And the coffee will get a little colder while the the milk warms.

[Victor]

[ QUOTE ]
Hottest coffee is having the milk in cup prior to coffee.
Next is adding milk asap.
coolest is adding milk after a while.

luckyme

[/ QUOTE ]

do u teach physics?

[luckyme]

[ QUOTE ]
[ QUOTE ]
Hottest coffee is having the milk in cup prior to coffee.
Next is adding milk asap.
coolest is adding milk after a while.

luckyme

[/ QUOTE ]

You think it makes a difference in the temperature if you pour coffee into milk or milk into coffee? Say I have 2 cups, one with a bit of milk, one with coffee. If I pour the coffee into the milk it will be warmer than if I pour the milk into the coffee? Are you insane?

[/ QUOTE ]

Perhaps. That doesn't affect results in this case.
Heat loss from the higher temperature while the coffee sits there waiting for the milk is the shortest way I can explain it. Excessively hot things give up more heat per time unit than from the lower combined temperature.

luckyme

[Max Raker]

[ QUOTE ]
[ QUOTE ]
This is actually pretty intresting. My guess would be to keep them seperate. This way the milk at least will get a little warmer while the cofee cools .

[/ QUOTE ]
And the coffee will get a little colder while the the milk warms.

[/ QUOTE ]

Yes thank you. I was thinking that atleast some of the system will gain energy. If you mix first the whole system will loose energy. This still could be way off.

[Silent A]

what about these factors:

coffee is dark and milk is white and the mixture is inbetween --> different radiation absorbtion characteristics (although, I admit it's a minor effect over only 10 minutes)

coffee and milk are in different containers --> different insulation --> different characteristic cooling/warming time scales

related to the last one ... I assume the milk is in a closed container --> much less convection --> stays cool longer

[Metric]

The rate of heat flow out of your coffee will be roughly proportional to the temperature difference between the coffee and the atmosphere (this is basically Newton's law of cooling which is oversimplified but gets to the basic principle here). Thus it's better to add the milk asap if you want to minimize heat loss to the atmosphere over a fixed, 10 minute interval.

If you consider that the milk was also left out during the 10 minutes and so was getting warmer during this time, the basic answer does not change -- the temp. difference between the atmosphere and milk is much less than the difference between the coffee and the atmosphere, and also the heat capacity of a jug of milk is larger than that of your cup of coffee -- all these things mean you can basically pretend the temp. of the milk is a constant and not change the basic conclusions of the problem. Add the milk quickly.

[PLOlover]

[ QUOTE ]
You think it makes a difference in the temperature if you pour coffee into milk or milk into coffee? Say I have 2 cups, one with a bit of milk, one with coffee. If I pour the coffee into the milk it will be warmer than if I pour the milk into the coffee? Are you insane?

[/ QUOTE ]

whatever happened to freshman chem and the water/acid thing don't add one to the other.

anyway, someone do an experiment so we know for sure.

[Victor]

just to be clear, metric and luckyme, pls answer. if i have 2 cups of coffee fresh out at the same temp, and i pour some milk in one cup and leave the other alone, in 10 min the cup with milk will be a higher temp????????????

[vhawk01]

[ QUOTE ]
just to be clear, metric and luckyme, pls answer. if i have 2 cups of coffee fresh out at the same temp, and i pour some milk in one cup and leave the other alone, in 10 min the cup with milk will be a higher temp????????????

[/ QUOTE ]

No.

[luckyme]

[ QUOTE ]
just to be clear, metric and luckyme, pls answer. if i have 2 cups of coffee fresh out at the same temp, and i pour some milk in one cup and leave the other alone, in 10 min the cup with milk will be a higher temp????????????

[/ QUOTE ]

No.
You have 2 cups with hot coffee in at the same temp.
1) you leave 10 min then add milk.
2) you pour milk in immediately then wait 10 min.

take temp - 2 will warmer.

Warmest of all is to pour milk in cup first and the pour in coffee asap.

The rapid heat loss of high temperature difference is the culprit.

luckyme

[Phil153]

This is an old one. luckyme and Metric are right of course. A body at 200 degrees Farenheit will lose heat faster than one at 150 degrees Farenheit, without even counting heat loss through evaporation. So there is greater energy loss when you add milk last.

The milk "warming" is irrelevant because because the combine milk-coffee system never gets colder than room temperature in this scenario.

[Victor]

ok ic.

one other thing, surely you must wait a bit before taking temperature for this to be true?

[PLOlover]

[ QUOTE ]
The milk "warming" is irrelevant because because the combine milk-coffee system never gets colder than room temperature in this scenario.

[/ QUOTE ]

There could be spoiler scenarios though if you like a lot of milk/cream in your coffee. extremes would be you live in michigan cold temp scenario versus vegas summer hot scenario.

[SBR]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Hottest coffee is having the milk in cup prior to coffee.
Next is adding milk asap.
coolest is adding milk after a while.

luckyme

[/ QUOTE ]

You think it makes a difference in the temperature if you pour coffee into milk or milk into coffee? Say I have 2 cups, one with a bit of milk, one with coffee. If I pour the coffee into the milk it will be warmer than if I pour the milk into the coffee? Are you insane?

[/ QUOTE ]

Perhaps. That doesn't affect results in this case.
Heat loss from the higher temperature while the coffee sits there waiting for the milk is the shortest way I can explain it. Excessively hot things give up more heat per time unit than from the lower combined temperature.

luckyme

[/ QUOTE ]

Sorry I was making assumptions I shouldn't have been. I was thinking about a scenario in which the coffee and milk were poured into 2 separate cups then either pouring the coffee into the milk or the milk into the coffee (after the same amount of time). It retrospect I'm insane.

[Borodog]

This whole thread is ridiculous. Next time, put a saucer on top of your coffee cup. Your coffee will still be piping hot when you're done with your phone call.

Evaporative cooling FTW.

[m_the0ry]

Basic heat transfer is governed by a differential equation. If K is the ambient temperature and h is the object temperature then,

dh/dt = C(K-h(t))

and the general solution is exponential decay. In other words it exponentially decays (Ae^-at) to the ambient temperature. Adding milk cools off the mixture so it's rate of loss of temperature decreases at that moment.

At the time when the milk is added the coffee drops in temperature to

(pctMilk*Tmilk + pctCoffee*Tcoffee)

assuming they have the same thermal properties because they are both mostly water. note Tmilk is constant because it just came from the fridge whereas Tcoffee is a function of time.

Proving mathematically is a little tedious for my liking but it's pretty easy to see graphically that adding the milk later will always result in colder coffee as long as the milk is below ambient temperature.