Thermodynamics - hot coffee and ice

I sometimes enjoy drinking my coffee cold with ice. When I order iced coffee at Starbucks, they always poor cold coffee out of the refrigerator onto the ice and ostensibly, the ice doesn’t all melt right away and the coffee isn’t dilluted.

When I’m in the office, the only coffee I have is in the coffee pot and it’s hot. And of course, when I poor hot coffee over the ice, it melts and dillutes the coffee.

I’ve noticed that I’ve gotten into the habit of filling the cup only partially with coffee and ice and then stirring the mixture to cool it more quickly and not dillute the coffee so fast.

So my question is simple… Am I fooling myself, or does this really make a difference? Does the coffee lose its heat more quickly when I stir it or does the ice still melt at about the same rate?

If you let it happen slowly you will lose heat (cold )to the atmosphere. Thats all I can think of.

I’m not quite sure what you are doing, but if I do indeed understand correctly, yes, your coffee will cool more quickly if you stir it while using a smaller volume, but you may not be doing yourself any favors in the coffee dilution department.

Using a smaller volume has the effect of creating a greater exposed surface area to volume ratio. The top (exposed) surface of your coffee is where most of the heat is lost (due to evaporation). To illustrate this, imagine both extremes (note: in both of these examples, the circumferences of the cups are the same):

  1. You pour a cup of coffee that has 2 millimeters of coffee in it. In this case, you have a huge exposed surface area to volume ratio. In effect, you can think of half of the coffee being exposed surface. If you cool the exposed surface, it doesn’t take long for the different temperatures (cool on top, and hot on bottom) to mix.

  2. You pour a cup of coffee that has 2 meters of coffee in it. In this case, you have a tiny exposed surface area to volume ratio. Very little of this cup of joe is exposed surface area. When the exposed surface is cooled due to evaporation, the cool coffee at the top is so dilute that when it mixes with the hot coffee in the rest of the mug, it has little effect on the overall temperature.

As for the ice, the principle is the same (other than the means of cooling). The greater the ratio of the surface area of the ice to the volume of coffee, the more quickly the coffee will cool.

To answer your question though - I would think that you would have to melt the same amount of ice to cool 8 ounces of coffee regardless of how quickly you cool it. This is ignoring cooling of the coffee due to loss of heat to its surroundings, but this is not reality. The coffee will lose heat to its surroundings, so the slower you cool it, the more heat will be lost to the coffee’s surroundings. This means that the ice has less heat to remove from the coffee. This will translate into you having to melt less ice.

I don’t drink coffee myself, so I have no idea at what temperature it comes out of the pot, but I may have a solution for you if this product can take the heat (pun intended). If you go to a bed and bath or kitchen supply type store, you can find some little plastic balls (about the size of a spinning quarter) that are filled with water. They are meant to be frozen and used as a means of cooling your drink, but they have the advantage of not diluting your drink. The only problem may be that the plastic may not withstand the heat. I think they will though. They look and feel to be low density polyethylene, which I believe can withstand temperatures slightly above 100C. Give it a whirl.

It would help to keep your coffee cup in the refrigerator or freezer, so it’s as cold as possible when you pour the coffee in.

Arjuna34

Steveo said
The coffee will lose heat to its surroundings, so the slower you cool it, the
more heat will be lost to the coffee’s surroundings. This means that the ice has less
heat to remove from the coffee. This will translate into you having to melt less ice.
This is true until you reach room temperature. then you will be loosing the cold until you either drink it or remove the cold source(the Ice) .This is probably,scientificly speaking, also considered heat.

Or better yet put the coffee in the cup before putting the cup in the fridge.

The heat of the hot coffee must go somewhere. When you put ice, the heat goes into melting the ice, because that takes energy. It doesn’t make any difference if you put half now and stir first, or dump it all.

If you want to reduce the melting of the ice, you’ve got to dump the heat elsewhere. Like the air. Pour the coffee in the cup, wait for a minute to cool down then put the ice in.

Reminds me of a common and interesting question; say you pour a cup of coffee now and want to drink it in 5 minutes, and want the coffee to stay as hot as possible. Should you put the (cold) cream in now, or just before drinking?

The surprising answer is that you should put the cream in immediately. Rate of heat loss is proportional to the temperature difference between the coffe and air, so the total amount of heat lost in 5 minutes is smaller if the temperature was lower.

Boy, Arj, that would have to be some heck of a coffee mug. Most/many are just common ceramics. They would most likely crack into bits, if frozen and then exposed to a pour of hot coffee. I say, pour some lukewarm coffee into your OWN ice trays,and then voila- you have an ice cube that won't dilute the coffee at all, AND the freezer will smell like coffee. Always a plus ! :)

Cartooniverse


If you want to kiss the sky, you’d better learn how to kneel.

Good idea, Cartooniverse! Even better, just pour the coffee right into popsicle molds, and dispense with the cup altogether!

Arjuna34

Thanks for the answer guys. Sometimes when you break something down into simpler parts, it’s easier to understand the situation. And now, looking back, it was a stupid question.

The heat energy of the coffee HAS to go somewhere, and since it only has too options (convection off the top or melt the ice), then of course, the ice is going to melt in equal proportions, no matter how I do it. Sure, the I might be able to manipulate the rate of cooling of the coffee, but then I’m just also manipulating the melting of the ice, too. I should have thought about this a little more logically before I made the post. Thanks for the help, anyway.

Johnny:
You could also try those “non-melting ice cubes” (blue ice in small plastic balls) sold by fine purveyors of Americana such as Lilian Vernon.

Cartooniverse:
For years, my dad’s frozen the day’s extra coffee in a ceramic mug, which he’ll microwave the next morning. Sounded neat, till I tried it. The freezer did NOT smell like coffee, but the coffee DID taste like freezer. Baking soda’s got nithing on coffee as far as sucking up odors. Ick.


Sure, I’m all for moderation – as long as it’s not excessive.