5 ms·

Shortly after completing my second class in thermo during undergrad, this topic came up between with a friend. The particular situation was wether to put the c

Shortly after completing my second class in thermo during undergrad, this topic came up between with a friend. The particular situation was wether to put the creamer in the coffee and let it cool or wait until it cooled and then put the creamer in. The wait time being the same, which would produce the hottest coffee. I got a little hyper focused and spent well into the night scrawling equations on a huge whiteboard and I don’t think I ever felt that I proved it one way or the other. I remember being pretty defeated because I thought I had all the knowledge I needed to solve the problem. I guess it wasn’t so simple after all :)

andbberger 4y ago
you did noneq stat mech in undergrad?
vkou 4y ago
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?
- amluto 4y ago
  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…
  - vkou 4y ago
    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.
- rowanG077 4y ago
  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.
  - grog454 4y ago
    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.
    - HALtheWise 4y ago
      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.
      - grog454 4y ago
        > 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...
- eru 4y ago
  Details depend on how the surface to volume ratio changes when you add them together.
- blindmute 4y ago
  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
vaidhy 4y ago
Did you actually do an experiment? This seems simple enough to run a quick experiment and see which one works better. You had all the knowledge needed to solve the problem, you just chose the wrong approach :)
- marlor 4y ago
  That’s precisely the approach taken in studying the Mpemba effect, with wildly differing results. The article goes into the difficulties in analysing out-of-equilibrium systems (both experimentally and theoretically).
  - vaidhy 4y ago
    I did read the article and interestingly, I learnt we do not know a lot about phase transitions. Even more interesting, why would hot and cold water reach 0'c almost at the same time (according to one of the experiments)? If the rate of cooling were same, we would expect hot water to be tepid when cold water is 0'c. Btw, I have seen similar experiments in really cold climates, where a cup of hot water thrown freezes immediately, but cold water does not. Anyways, I am always one for running the experiments :)
    - semi-extrinsic 4y ago
      > Btw, I have seen similar experiments in really cold climates, where a cup of hot water thrown freezes immediately, but cold water does not. IIRC this is because the surface tension of hot water is significantly lower, so the thrown hot water disintegrates into much smaller droplets, which freeze more quickly.
- MobileVet 4y ago
  For sure, lol. I was just trying to convince myself I was a genius because I could model the real world.
  - vaidhy 4y ago
    What did you find? You left that interesting part out :)
LegitShady 4y ago
an experimentalist would have tried both and figured it out in a half hour.
- unlikelymordant 4y ago
  if it were that easy to solve, the question wouldn't be still be uncertain (i'm talking about the original "does hot water or cold cool faster", to which this question seems related.)
  - thrwyoilarticle 4y ago
    If it's not that easy to solve, the answer won't matter.
deleted 4y ago
[deleted]
EamonnMR 4y ago
We actually ran this experiment in high school physics, reasoning that the color change should decrease the rate of energy loss.

andbberger 4y ago

you did noneq stat mech in undergrad?

vkou 4y ago

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?

amluto 4y ago
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…
- vkou 4y ago
  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.
rowanG077 4y ago
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.
- grog454 4y ago
  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.
  - HALtheWise 4y ago
    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.
    - grog454 4y ago
      > 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...
eru 4y ago
Details depend on how the surface to volume ratio changes when you add them together.
blindmute 4y ago
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

vaidhy 4y ago

Did you actually do an experiment? This seems simple enough to run a quick experiment and see which one works better. You had all the knowledge needed to solve the problem, you just chose the wrong approach :)

marlor 4y ago
That’s precisely the approach taken in studying the Mpemba effect, with wildly differing results. The article goes into the difficulties in analysing out-of-equilibrium systems (both experimentally and theoretically).
- vaidhy 4y ago
  I did read the article and interestingly, I learnt we do not know a lot about phase transitions. Even more interesting, why would hot and cold water reach 0'c almost at the same time (according to one of the experiments)? If the rate of cooling were same, we would expect hot water to be tepid when cold water is 0'c. Btw, I have seen similar experiments in really cold climates, where a cup of hot water thrown freezes immediately, but cold water does not. Anyways, I am always one for running the experiments :)
  - semi-extrinsic 4y ago
    > Btw, I have seen similar experiments in really cold climates, where a cup of hot water thrown freezes immediately, but cold water does not. IIRC this is because the surface tension of hot water is significantly lower, so the thrown hot water disintegrates into much smaller droplets, which freeze more quickly.
MobileVet 4y ago
For sure, lol. I was just trying to convince myself I was a genius because I could model the real world.
- vaidhy 4y ago
  What did you find? You left that interesting part out :)

LegitShady 4y ago

an experimentalist would have tried both and figured it out in a half hour.

unlikelymordant 4y ago
if it were that easy to solve, the question wouldn't be still be uncertain (i'm talking about the original "does hot water or cold cool faster", to which this question seems related.)
- thrwyoilarticle 4y ago
  If it's not that easy to solve, the answer won't matter.

deleted 4y ago

[deleted]

EamonnMR 4y ago

We actually ran this experiment in high school physics, reasoning that the color change should decrease the rate of energy loss.