The milk adds heat capacity to the beverage.

Think about it this way: say the milk is out of the fridge, its cooler than room temp, the coffee is hotter than room temp.

If you add the milk to the hot coffee immediately much of the coffees heat warms the milk. If you add the milk later instead it dissipates into the room and when you add the milk your beverage is cooler.

The same is still true for room tempered milk, just not as obviously. It still adds heat capacity. But adding it after much of the heat is gone is like adding SSDs to your server after your company already lost 80% of the customer data, its just not gonna fly.

So yeah, adding milk early gives you a warmer beverage. Adding milk later produces a cooler one.

> 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

Adding milk sooner will get you slightly warmer coffee vs adding it later

Lol, I do this. I started adding milk first bc I like warmer coffee.

So, how do I make sure I am not a robot?

Will also lead to a coffee that is a little bot warmer than if you add it later

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