Here's a little engineering riddle.
You're standing outside in the cold and you have a cup of coffee that's too hot to drink. You also have a small amount of cold milk that you plan on using in your coffee. If you put it in now, it'll be colder but still be too hot to drink. If you want to drink your coffee as soon as you can should you put the milk in now and let it cool off the rest of the way? If not what should be your strategy?
@professor_stoke Add a small amount of coffee to the milk (instead of adding the milk to the larger amount of coffee) so you get something you can drink right away while the rest of the coffee cools. Then learn how to make coffee that's not too hot by the time you're standing in the cold.
@professor_stoke You could also get extra cooling by pouring the still too hot coffee and milk into the then empty milk cup, which some might find preferable.
@neal lol this is great. I think the riddle is normally phrased about when you should add the milk to the coffee, but since I inadvertently left it more open ended, it leaves room for great answers like these!
@neal like let's analyze these. In the first case where you add coffee to the milk instead, this may or may not be acceptable to the drinker - maybe they don't like black coffee, for instance. this shows the importance of understanding the full bounds of the problem. but let's say the drinker is okay with this. in that case you get a beverage that's at a drinkable temp immediately, and depending on how quickly you drink that, the coffee may be at an acceptable temperature by the time you're done
@neal in the second case, you're utilizing the heat capacity and surface area of both vessels in order to cool down the coffee faster. (This assumes that both vessels have a volume equal to or greater than the sum of the milk and coffee). The very act of pouring is also exposing more surface area directly to the cold air, improving your rate of heat transfer to the atmosphere.
@professor_stoke There's no need to pour all the coffee at once, and indeed you may want to only pour a little at a time to preserve heat in the original cup and maintain a longer enjoyable drinking time.
@neal both excellent points
@professor_stoke Constraints are made to be lifted.
@neal @professor_stoke
An engineering problem?? ☕
Here, old folks have that technique of pouring some into another cup and drinking from that. My mother does that. A lot. The milk in your example is irrelevant in real life. If you wanted milk in your coffee you'd already put it in before you step out to enjoy your coffee. Then maybe you'll decide it's still too hot and pour some (not too much so that it cools better) of it into another cup to drink right away.
@neal @professor_stoke
I suppose the milk is included in your engineering problem because it provides you with the tool to solve the problem -- it comes in a cup. Ergo you've got your solution waiting for you.
Not good for someone who doesn't like milk though. 😋
@evelynyap @neal Yeah definitely not at all relevant for someone who doesn't like milk haha. Like a lot of these kinds of riddles, you'd have to constrain the parameters quite a bit before the problem and its "answer" becomes significant enough be relevant to a person in real life lol. Still love the out of the box thinking I'm seeing though!
@evelynyap @neal I'll give it a few more hours before I post the "canonical" solution to the problem in case anyone wants to respond with anything else
Okay so the "solution" (which you guys have proven is not the only solution for many cases) to this problem is to wait until the point where, when you put the milk in, the coffee drops to the highest allowable temperature. This is because the rate of heat energy transferring to the atmosphere, all else being equal, is dependent on the *difference* in temperature between the two. If you put the milk in first, that difference decreases, and so does the rate of heat transfer.
@professor_stoke @neal
Waaaaait a minute! 🤨
You ask "if you want to drink your coffee as soon as you can" and your solution is "wait until the point..." ??
What is the indication you've reached that point? I'm not waiting to reach any point while standing in the cold with #coffee in one hand and milk in another. Throw out the milk and use that cup for a quick coffee drink! Quiero beber mi café. Ahora!
Only #engineers can appreciate that puzzle. 🙄
@evelynyap @professor_stoke Our answers were better, arguably more correct, and easier to get right by a person without a thermometer and a slide rule.
@neal @evelynyap lol sorry that it disappoints y'all. All the answers including the textbook answer delight me ☺️
@neal @evelynyap This is the kind of thing that you might be asked in a class on heat transfer where the focus is specifically on the mechanisms of how heat moves and what parameters drive them. If it helps and if you're interested I can set up arbitrary constraints that make the textbook answer make more sense "in real life".
@professor_stoke @evelynyap That's okay, I've taught heat transfer classes so this is not something unfamiliar.
@neal @evelynyap cool! thanks for playing along and stay curious :)
@professor_stoke @neal The textbook does not delight me. At all. 😝 The conversation did though.
Okay. Next puzzle! 🤓
Come on, Mr. Engineer.
Bring it on! 🤯
@evelynyap @neal haha glad you liked it. I'll see if I can come up with another one this week ☺️
@neal
lol clever response :) makes me think of beastie boys ""I like my sugar with coffee and cream"