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Vince_Vice t1_iua4exf wrote

Reply to comment by WorldlinessWitty2177 in [OC] When should you add the milk in a cup of coffee? by Prunestand

No, there is a technical difference. At higher temperature difference (to the surroundings) the general temperature loss is faster than at lower temperature differences.

If I have boiling water in a surrounding at room temperature than it will lose, say 5 degrees Celsius in the first minute.

If I have water at 5 degrees C above its surroundings it will only lose 1 degree C in the same minute.

So when I add the milk instantly to the freshly brewed coffee I never let the coffee have the highest temperature difference at which the heat loss would've been the highest.

While adding it just before drinking it the coffee experieced a higher heat loss rate before I cooled it with the milk.

Instantly adding the milk leads to a warmer coffe, adding the milk later leads to a cooler coffee

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N8Lux t1_iubsk25 wrote

Vince_vice is correct. Heat transfer is proportional to the temperature delta. In other words, the coffee cools fastest when the coffee is hottest. The rate of cooling slows as the coffee and outside approach the same temperature. So yes, it makes a difference when you add the cream.

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Equivalent-Bench5950 t1_iuadkac wrote

Mostly wrong. If you choose either the temperature or the time at which you want to drink, it only matters that you add the milk "in time" - all other parameters are meaningless.

There is neither a theoretical nor a practical difference. I think it is the first law of thermodynamics.

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Vince_Vice t1_iub1rt9 wrote

> Mostly wrong.

Not treading ligthly I see. But you're wrong

> I think it is the first law of thermodynamics.

The first law of thermodynamics is conservation of energy in a closed system.

My thought experiment does not violate it. The closed system is the room in which the hot coffee resides.

There is no difference in the amount of energy but in the process in which thermodynamic equilibrium is reached.

At some point the coffee and the room will reach an equilibrium temperature that is very close to room temperature (bc its heat capacity is much higher than that of the coffee)

The coffee is drunk before equilibrium is reached (who wants cold coffee) so this is not about the energy content of a closed system, but about at which point of the state transition it is drunk.

First lets make a slightly different but simpler argument that proves that you are wrong: Lets assume the milk comes from a fridge, it therefore is colder than room temperature, while the coffee is hotter.

It should be obvious that allowing the hot coffee to give its heat to the room, then pouring the milk will be colder than pouring the colder milk into the still hot coffee resulting in the coffee heating the milk instead of the room, right?

I chose this example with cold milk because it makes it easier to comprehend that the milk has a heat capacity that it adds to the mix. With room tempered milk that is still true, its just not as ELI5.

Therefore both methods will eventually reach equilibrium temperature, but pouring the milk earlier will leave you with a warmer beverage at consumption

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