A simulation of a cooling cup of coffee with the following parameters used:

Plotted with Python.

My previous graph had a sign error in the code generating it, and I therefore deleted it. I also think people missed the point with the graph, so I'll add it here. Suppose you want your coffee after, say, 10 minutes. What will make it the coolest: adding the milk directly or wait until the end? The answer is to wait until the very end; that way it will be the coolest.

The reverse is true as well, pour the milk into the coffee at the very beginning if you want the coffee to be as warm as possible.

The answer is kind of obvious when you realize that the cup of coffee dissipates more heat the larger the temperature difference is, but the point of the graph is to illustrate this fact.

So what does this tell me about when to add ??

Seems to indicate that it doesn't matter when you add

So just proves how it always felt

Don't put it too late if you still want to drink something hot enough, that's what I can conclude 😀

Depends if you want the cup of coffee a couple of degrees hotter or cooler. If you like it hot, add the milk asap. If you like it to be a couple of degrees cooler, then wait.

If you drink coffe to late, it's cold - wow

Why does this sound like an Ig Nobel award winning study?

The xkcd style is nice. Also since here mostly the qualitative result matters, it's not a problem that it isn't that precise.

If there was only a t test to verify thid

> Seems to indicate that it doesn't matter when you add

In this simulation: the temperature after 10 minutes was 55.4 °C if milk was added at the end, compared to 56.5 °C if milk was added in the beginning. So adding the milk at the end made it about 1 °C cooler.

So I would say it probably will not make a huge difference, at maximum some degree give or take.

Uh what? To reach any given temp you're going to have to add or wait or wait then add. Or add differing amounts or change the the starting temp... I don't see any argument for any specific timing given that you can reach whatever temp you want by changing your method.

> Also since here mostly the qualitative result matters, it's not a problem that it isn't that precise.

Yeah, I agree with this. The graph is there to make an illustrative point. The exact numbers will depend on the volume of the coffee, the size, shape and material of the mug, the material of the table the mug stands on and various other factors.

The goal of putting milk in hot coffee is to drink hot coffee with milk in it. So the time to put the milk in is immediately, and then you drink it. Otherwise you're just staring at a cup of coffee while it gets colder.

Its a shit graph is what that is.

I just drink my coffee black

I have no idea what this means

That there is zero difference in temperature whenever you add the milk. So this is BS

I always put the milk in the mug before the coffee because I think the milk is better dispersed this way.

Simulation? You didn't do it irl?

Fun stuff! I think having the green entry begin at the 8 minute mark might make this graph make a little more sense. Other than that, I will make sure I throw in my milk asap to get that nice hot goodness.

> Simulation? You didn't do it irl?

This is a simulation based off Newton's Law of cooling, yes.

Interesting idea. But it's somehow less interesting this way

Have any of you ever tried rotating your hamburger 30 degrees before eating it?

What temperature is the milk? How much milk did you add? It’s a simulation? This post is hot trash.

Hard to say the data is beautiful when's there's not actually any data.

This is just a graph of a mathematical equation.

Thats what confused me

[deleted]

Nice graph! It answers the age-old question. Redditors are a bunch of cynical jerks lol.

Who the hell is determining when to add milk based on minutes or temperature? Isn't it just a question of if you want milk? Drop an icecube in if you want it cooler.

This almost seems like something a robot pretending to be human would focus on.

Generally yes. But I also have a few glass mugs and I simply will not forego watching the calming, billowy milk clouds.

Data, in this case, is also worthless.

Heat the milk up first, noob

taps head

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

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

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

You should add milk only when you are trying to mask the flavor of a bad cup of coffee.

Milk goes in first, always.

The style of graph is nice for informal report (copy of xkcd), but if the difference of the experiments at the end are 1º C, it is the worst style to use because you can't know if the difference at the end is because the data or the drawing style of lines.

Milk and sugar would be already in the bottom cup -- as coffee will be poured into it and it'll mix successfully -- then cup would be emptied in my mouth a second after.

I mean, it is a simulation after all. Not a study or an experiment.

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.

> 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

https://gyazo.com/74f60d63c5d038c50923779a3a06edc8

I derived this equation

x = time milk is added
y = temperature below which not adding milk at all would be quicker than adding milk at time (x) I.E if you want it to cool down to 30 degrees and y = 35 degrees then it would be quicker not to add milk
T_r = room temperature
T_c = Temperature of coffee when it is poured
T_m = Temperature of milk
K = Mass of coffee divided by the mass of milk added
a = constant to be found

​

It takes into account

The change in temperature from the addition of milk

The change in the rate of cooling due to the addition of milk

The change in the rate of cooling due to the increased mass of the coffee

The data indicates the longer you wait to add the milk, the colder the coffee will be. You should add the milk first and pour the coffee over the top.

This data sucks though because it's unclear what the temperature of the milk is initially.

Who the fuck is waiting 2 minutes let alone 8! Just pour your coffee, add your milk and slurp it until you can gulp it.

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.

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.

How the duck do you read this graph

I was just thinking this since the without adding milk trendline at first glance seems to start at the end where as it shows tempature over time. Also maybe a different title? Its a cosy graph though, perfect for the autumn season.

You're as confident as you are wrong my friend.