Hot Coffee: Newsletter Challenge (06/13/06)

Gut feel tells one that the hotter an object, the faster it radiates away energy into a colder environment. So putting the (room temperature?) cream in before the 5 min. meeting should leave the creamed coffee slightly more energetic and thus hotter afterwards.

Agreed - 1st year thermodynamics. Personally, not having asbestos internals, I'd leave it 'til after.

Is the cream chilled or at ambient temperature?

It doesn't matter. Either way it's better to add the cream before the break.

What is the primary mechanism of cooling? Is the coffee in a styrofoam cup? a glass cup? a metal cup? If the coffee is in cup that doesn't hold heat so that it reaches ambient temperature in 1 minute - then it doesn't matter which order you put in the cream. Room temperature is room temperature.

It doesn't matter. Either way it's better to add the cream before the break. The coffee never actually reaches room temperature: it aproaches it asymptotically. And the hotter liquid loses energy faster than the cooler.

True, the coffee aproaches it asymptotically and never actually gets there. However, from a practical standpoint the difference between say 20.0001 C and 20.001 C is insignificant. So from an engineering standpoint, if the coffee cools fast enough that the difference between the coffee and room temperature is only a few degrees, we do not care if we add the cream in before or after. The cofeee is still cold.

Visceral recall tells one (that's me) that whenever I cook "cream-of..." soup and "plain-ol' soup (whenever I add milk/cream fat globules to one but not the other), by the time the plain-'ol has cooled off the cream-of is still hot/warm. It reminds one (at least me) of high school physical science where one learns that suspensions (solid-liquid colloidal states) have higher heat capacity than liquids (and liquids more than solids); hence, for example,...stay-cold and stay-hot gel-filled heat packages. So, perhaps (?) milk fat globules added to liquid coffee moves the state towards colloidal suspension and, thus, raises the heat capacity? and accordingly the cooling-off interval? And maybe the increased heat capacity is sufficient such that, even if the cream is initially cooler (before being added to the coffee) the increased heat capacity of the creamed coffee is sufficient both to absorb the initially higher heat content of the coffee, and still leave sufficient heat capacity (in the creamed coffee) so that it stays warm longer (cools down slower) than would be the case if no milk fat had been added to the coffee??....at least up to a point...the point at which continued adding of cooler cream would render the creamed coffee "bereft" of its "surplus" heat capacity...such that too much cream no longer works to keep the coffee...hotter longer??

Oh! Good point! Real cream's heat capacity is probably higher. If true, it would slightly alter the heat decay.

Thanks, even if I'm wrong. But the fact that cream-coffee mixtures do not stratify (Have you ever observed creamed coffee to...precipitate out when at rest?), tends to persuade me that the physical state--the colloidal state--the non-solution state--is the operative criterion for raising the heat capacity. (By contrast, adding sugar in solution has no equivalent effect.) Your reply addresses the suspension issue from a different perspective...it seems to me. That is to say, you could think of adding the cream to the coffee (the suspension to the liquid) as no different, in essence, than adding the coffee to the cream. The coffee most likely lowers the cream's heat capacity, while the cream raises (in effect) the coffee's (the modified coffee's) heat capacity. And since the resultant mixture (within limits) remains in the "neither liquid" and "nor solid" state, the heat-capacity-increasing property of suspension still operates to keep the mixture hotter longer than liquid coffee alone.

Now that is an interesting variant on the idea. They did not say in the problem statement if the coffee cup was covered or not. If it is not covered, the evaporative cooling would be significant. By carefully layering the cream on top of the coffee you could suppress the evaporative cooling effect if the coffee were not covered.

Now this site lists the heat capacity of Cream as being 0.9 BTU/lb/F. The heat capacity of the coffee would presumably be the same as that of water = 1.0 BTU/lb/F http://www.engineeringtoolbox.com/specific-heat-ca pacity-food-d_295.html

Thanks. Your penultimate andecedent posting raises some intriguing points, and I'll come back to it later. Responding to your references to heat capacities--let's assume the figure for cream can be validated--would seem to illustrate the..."paradox" of suspensions. Mix (not "dissolve")a substance of relatively lower heat capacity (it cools quicker) with a substance of relatively higher capacity (it cools slower); get a substance which retains heat longer then either constituent alone--not a substance of intermediate heat capacity.

PS. Friendly hint. If wanting to revise or append to your own comment, respond to the comment above (the one you first clicked beneath to respond to), and not to your own comment. That way your update/supplemental comment appears in line with your first; all the indentures stay lined up as they should and will be easier to follow.

...nor did they need to say....since, all things being equal (an implicit presumption), it makes no difference, thus is immaterial. In like manner, the notion(s), the artifice, of "layering" cream on coffee could be "cut out"....and not only for the reason that it (also) introduces a change to the "experiment." My sense and experience persuades me (until I am set straight?) that, in nature, an attempt to layer cream on coffee in a cup would not succeed (with liquid-state coffee) because they are self-mixing--with the rate (and only the rate) of mixing being dependent on both temperature--in the experiment it was implied to be hot--and the cream-coffee temperature differential...to which the Challenge did not allude. Put the cream (any cream) on the coffee (the "hot coffee"--or any coffee), and they will, at once (more or less rapidly), begin to mix. (In the experiment, the office worker would have given up the layering attempt for fear of missing the meeting; and, whether or not he stirred--and given the coffee's start temperature--he would have returned in five minutes to find the cream and coffee "mixed"--or "sufficently" mixed...in the sense that he would be unable to determine whether or not the creamed coffee had ever been stirred.) "But, why the spoon?" some might ask. To which I would respond--while trying not to be over-tedious or stray too far off topic--consider the original purpose and usage of the "sugar" spoon, and other "cultural" manifestations involved in your recollections of coffee drinking rituals. You might see that the use of the spoon, among other possibilities: (1)...only serves to speed the mixing process; (2)...was, in earlier times before the advent of sweetener (dose) packages, relied on foremost to measure the "number of sugars"; (3)...gives visual and audible, psychological reinforcement that one's coffee is thoroughly mixed; (4) other....whereas, its use for attempted floating of the cream (for making a non-alchoholic "Cup-O Coffee Pousse Cafe," if you will ;-)) might be met with disdainful glances or derisive commentary from bystanders.

"whereas, its use for attempted floating of the cream (for making a non-alchoholic "Cup-O Coffee Pousse Cafe," if you will ;-)) might be met with disdainful glances or derisive commentary from bystanders."

Ah, but we are pocket protector, taped glasses engineers. Disdainful glances and derisive comments have no effect on the likes of us...nes pas?

Now. You imply that the challenge did not need to allude or specify to certain subjects - as ordinary people would assume the standard 12 oz cup of coffee in a paper cup with lid and a small standard room temperature liquid creamer container or two.

But then the question is rather boring as it has been asked and answered a couple of hundred thousands of times before.

It is much more interesting to try to develop a solution where the standard answer is incorrect and the alternative answer (it doesn't matter) or the wrong answer (put the cream in after the meeting) would actually be true.

So using my stainless steel, finned mug and by placing it in a good stiff breeze (Hurricane Katriana scale winds good enough), I can cool my mug of coffee to room temperature in under a minute.

Now to make the wrong answer right, I choose to take the creamer to the meeting with me and hold it in my hand for the entire five minutes - thus warming it up above room temperature.

So now when I add the above room temperature cream to the room temperature coffee, I raise the coffee temperature slightly above room temperature.

So now the wrong answer - put the cream in afterwards - is the correct answer for the hottest cup of coffee.

As for 'why the spoon' - why that is clearly to flick the extra creamer at those people hurling the disdainful remarks...

alternatively, I can design a theoretical perfect insulated coffee mug so that there is no energy loss during the five minute period...(now convection and conduction woudl be easy... hmmm. now how to stop the radiation) then the initial and final coffee temperatures are the same.

If the cream is at room temperature, it then makes no difference when you add it.

If the cream starts of chilled and is allowed to heat to room temperature, then it is better to add it after the meeting.

Add the cream... dont stir.. that way the cream remains suspended at the top, forming those annoying globules that dont go away so easy.. stir when you get back... and yeah - dont gulp the coffee its still hot.

As long as you put it into the microwave when you return!

cause I'm taking the coffee with me, have never been to a 5 minute meeting, ever...

Yeah, I'm with you. If I'm ever called to a meeting first thing in the moring, I take my coffee with me. It's never over in 5 minutes... unless they're giving you your "pink-slip". ;) In which case, who cares about the coffee then.

Okay, I believe in this case it makes sense to wait. My reasoning is based on the following assumptions.

1. Coffee Initial temperature is 50 C

2. Cream is 10 C – assume that it is the same temperature from the refrigerator for both scenarios.

3. The rate of cooling for the cup will be exponential, that is, it looses a % of its heat energy per unit time.

4. The heat capacity of cream and coffee are the same and approximately 1 cal/gram per degree C.

5. The coffee is 250 ml

6. The cream is 25 ml

7. Ambient temperature is 20 C.

Now, basic thermodynamics tells us that when you combine 250 ml of 50 C fluid to 25 ml of 10 C fluid that we should be able to express the final temperature as a function of the heat energy of the coffee with the cream. Since the delta T between the two is 40 C and the coffee is 83% of the total volume (and heat energy) the final temperature after mixing would be 43.3 C.

If you wait five minutes, then the same thing applies, except the coffee temperature is 5 minutes cooler, so the delta T is smaller and the volumes are the same.

Let's assume the coffee cools 10% every one minute. I ran a little Excel sheet to compute this. If the coffee starts at 50 C and cools for 5 minutes it reaches 37.7 degrees. If you add cream at 10 C at that point the delta T between coffee and cream is 27.7 C. At 83% total volume for the coffee the temperature at mixing would be 33.1 C.

If we add cream at the start when the coffee is 50 C, then the mixed temperature is 43.3 C. If the cooling rate of 10% per minute is extrapolated over 5 minutes the temperature at the 5 minute mark is 35.9 C, which is slightly warmer than the post mix scenario.

You can change the cooling rate in the above experiment, but the reason it is better to wait is because the system always cools at the same exponential rate for a fluid with a specific heat capacity. So, when you mix the two ingredients initially, you experience the greatest delta T when mixed at the beginning and the system begins thermal decay at a slightly lower temperature. However, waiting 5 minutes allows the coffee to cool (loose some of its heat energy), so mixing the two (cream and coffee) results in a lower delta T loss for the system. Regardless of the heat loss you choose for the cup or container (if it isn't faster than 5 minutes to reach ambient) the principle will be the same.

Can we now give ourselves a coffee...break?

Adding the cream after the five minute break would work a lot better if you left both the cream and the coffee at foom temperature for the five minute.

Whoops. Your first line conclusion is the opposite of your carefully calculated results.

My results may not be so carefully calculated. I ditched the Excel sheet, so I need to start over to confirm.

On the plus side, this reopens the debate!

I take back my original statement (q.v.) - I've done some Excelling, & now agree.

.. but I'm not sure what I agree with!.
I reckon the pre-add scenario leaves the coffee a little warmer than the post-add.

Im not sure how significant it might be, but shouldnt surface area be taken into consideration? My thinking is that if you add the cream and effectively increase the area of contact with the inside of the cup, thus increasing the effective radiative surface, you will lose more heat faster. As we all know, you can grab a cup of coffee by the top and its not nearly as hot as the sides below the top surface of the coffee. Im thinking the most quick and effective way to keep the coffee hot would be to put a book or something on top of the cup, insulating it.

Or how about putting some cream in the coffee (which will float) adding a "thermal resistive" barrier to the (once open) top of the coffee. Something to think about! ~~Chad~~

Yes, it does, but so will the net volume and the total heat capacity of the system. So, unless the cup is shaped in some abstract form that disportionally increases the surface area the effect should not matter.

Nifty. Don't forget to allow for the cream heating up.

mind your own beeswax...

Now here is an elegant solution...see page 12 (pages 7 to 12 for all the math)

URL:http://www.cheric.org/ippage/p/ipdata/2005/16/ file/p200516-1001.pdf The author suggests that by using 2.5 ounces (0.07kg) of beeswax which melts at 53 C will keep the coffee at the optimum drinkable temperature for 20 minutes...

Try that link again. http://www.cheric.org/ippage/p/ipdata/2005/16/file /p200516-1001.pdf

You should put the cream after the break because the coffee will loose energy (heat transfer) by dissolving the powder cream. The temperature of the system has to stabilize (coffee loose heat, the powder wins it).

Without benefit of math, i wouled guess the fastes heat loss by far will be surface evaporation heat loss, so adding the cream slowly may coat the topy, slow evapaoration, and keep the stuff warmer for later. And who said Powdered cream? cream is cream unless someone says it isn't

Don't add the cream and pour the coffee back into the pot. Whenever the meeting is over - be it 5 mintues or longer - you can get a new cup of coffee which will be hot. C

Everyone seems to be all over the answer. I was asked this question by a business student in engineering school 20 years ago. I felt that if I dealved into a quantitative answer, he would have felt brow beat with gobbledegoop, and given me the yep I understand nod with a blank stare, really not understanding anything. Instead I just explained the following: Between the two temperatures (coffee in the cup and ambient air in the room) there is a difference of temperature that we will call delta t. So, if the coffee is 110 degrees and the air is 70 degrees, the delta t is 40 degrees. If I put in cream, the coffee temperature lowers to 100 degrees and likewise the delta t becomes 30 degrees. Rule: the lower the delta t, the slower the cooling rate. He got it!

Yes, the lower the delta t, the slower the cooling rate, but also the lower the starting temperature. What good is a slower cooling rate if your coffee starts 10 degrees cooler?

Roger, you are correct. I only used the 10 degrees to make a point. It worked for the person I was addressing.

My bad, I missed the context.

That's no fun. How about this site! Laser Interferogram of a Cup of Coffee The image below was taken with a laser interferometer (in infinite fringe mode). Actually, in order to get sufficient interference fringes, it was necessary to precisely line up three coffee cups in a row. This increased the optical path length and "amplified" the phase shift of the light in the test beam. The image shows the thermal boundary layer on the side of the cup and the plume of hot moist air, which rises above the coffee. http://www.ryerson.ca/~dnaylor/Research/Coffee.htm

Has anyone noticed that the questions are repeating? How about some new stuff?

Go on and ask.

I think this means that the discussion has been exhausted. Let's go have a cup of coffee.

yes - this is the third or fourth repeated question.

Perhaps more of us should take a leaf from Jorrie's book...