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Comment by vkou | Hacker News Reader

A simple application of newton's law of cooling will tell me that for most normal ratios of coffee and creamer, you want to mix them first. Because the bigger the temperature delta between the coffee and the environment is, the more heat the coffee will lose per second. Mixing first will lower the coffee's temperature, and will cause it to lose less heat per second.

Is there something I'm missing?

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I disagree. But I'm no physicist. My reasoning goes like this, with the assumption that the coffee milk has room temperature:

The coffee cools faster if it's hot. So putting in the creamer immediately steals the most efficient cooling period for the coffee. There are some caveats that I don't consider that could make a difference like that the surface area of the combined liquid is larger so it transfers heat more efficiently.

This was actually a controversy some twenty years+ ago on a science show in the Netherlands ('nationale wetenschaps kwis'). The wanted answer was that putting creamer in first was better as the resulting fluid had lower temperature and thus cooled slower. But a given answer was that the creamer made a top layer that made the coffee evaporate slower, hence keeping more of the warmth as well. During the show this answer was counted wrong. But (theoretically, I don't think an actual experiment was made) this is a factor working towards the same answer (first creamer keeps the resulting fluid warmer compared to adding the creamer later) that may actually have a larger contribution. So afterwards the consensus was that this may actually have been a better answer.

> So putting in the creamer immediately steals the most efficient cooling period for the coffee.

Correct, and we're trying to optimize for hot coffee after 30 minutes. We want cooling to be less efficient.

Why would you not consider that caveat? The cooling rate should be generally proportional to both the surface area and the current temperature delta between the liquid and whatever it contacts. Taken to the extreme, if you added the creamer and then poured the coffee out onto the floor, the creamer's mass and temperature would have relatively little impact compared to the surface area change.

For a non-sealed cup of hot liquid, the significant majority of cooling happens at the exposed surface with the air, through a mixture of convection and evaporation. Modeling the cooling as being proportional to total surface area would be pretty inaccurate, although there is definitely still some conduction through the cup/mug worth considering as well.

> For a non-sealed cup of hot liquid, the significant majority of cooling happens at the exposed surface with the air, through a mixture of convection and evaporation.

I don't know enough to argue with any confidence but this is very surprising to me. Ignoring for a moment the thermal conductivity of different mug materials, it seems like a large amount of energy would go toward heating the mug up to near liquid temperature rather quickly. Then you'd have at least as much heat loss between the mug and air (compared to exposed liquid and air).

The mug I imagine we're talking about is a ceramic mug, which I believe to have high thermal conductivity just based on what processor covers are made of. It also has plenty of mass.

If you're talking about an insulated mug obviously this changes. But just the fact that insulated mugs exist proves my point that a large amount of heat is lost through the mug...

… my work here is done.

I think it's just beginning...

Assume for simplicity that we mix half coffee and half creamer. This halves delta t. However the area will not double, since the top and bottom areas are the same. Furthermore, as another commenter pointed out, the top area is where most of the action happen.

However, if we really want to overcomplicate things we could consider the possibility of an insulating air pocket in a half-empty cup, leading to less convective losses. Consider a vacuum flask half full of hot coffee outside in a strong wind. If you fill it to the brim with creamer it might cool faster. Evaporation might become important too.

If you don't fill the thermos to the top, we can also add the small temperature impact of Helmholtz resonance from the wind blowing across the lip to make this more complicated. (Now I wonder how loud a sound needs to be to boil water...)

Details depend on how the surface to volume ratio changes when you add them together.

Please elaborate. Newton’s law of cooling would seem to suggest that the cooling rate is higher if the liquid is hotter. Of course, depending on the exact scenario, the creamer might also be warming up at the same time…

I expect the rate of heating for the creamer to be lower than the rate of cooling for the coffee, unless your coffee is 90% creamer.

My reasoning is that the coffee will cool in a curve having high rate of temperature change at first, and slower later in a long tail until it reaches room temp. Adding the cream will "remove" a fixed amount of "heat units". The heat of the cup can be graphed as heat/time and it will look like exponential decay.

If you remove those units at the start, you've reduced the starting temp a bit, but you haven't much changed the long tail of the cooling. You essentially just started the coffee at a slightly cooler temperature, but this doesn't affect the curve much. Or to think of it another way, the change in temperature at the start corresponds to a small amount of X axis (time) on the curve.

If you add the cream later, the temperature reduction corresponds to a larger amount of time on the curve. This means the temperature will be lower than the above.

So to my intuition, cream first should yield hotter coffee

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