Say I want to make a glass of iced coffee. I have the following at hand:
4 oz. cold coffee
4 oz. hot coffee
16 oz. glass
Plenty of ice
My objective is to combine the hot coffee, the cold coffee, and the ice so I end up with the least-diluted coffee after it sits for a minute or so.
In what order do I add the ingredients for best results? Or doesn’t it matter.
Note: Glass breakage due to heat/cold variance is not an issue.
How much liquid do you want to end up with?
The glass should end up full to the top.
In that case, 4 oz of cold coffee and 12 oz of water frozen into cubes would result in a full glass, with the least amount of ice meltage.
But, that will also result in the least drinkable amount of coffee. And, it would need to be consumed quickly, because if it was allowed to sit, the ice would dilute the coffee 2:1.
Using all 8 oz of coffee (both cold and hot) with 8 oz of water as ice would probably result in the best combination of drinkable liquid (8 oz to start) and least dilution in a real-world scenario (1:1 if it was allowed to sit).
Pour the 4 ounces of cold coffee and the 4 ounces of hot coffee together into the 16 ounce cup. Nest the cup in a large bed of ice until its contents reach nearly freezing with no dilution whatsoever. Drink your ice-cold, full-strength coffee.
If you absolutely have to have ice in your cup, add the ice to fill to 16 ounces, but drink quickly, because from that moment on you’re diluting the otherwise pure chilled coffee.
Assume that I don’t have time to chill down the hot coffee.
This is the real-world scenario: I often want a glass of iced coffee in the afternoon at work. I always forget about my morning coffee before I finish it. If it’s nearly full, I just put it in a glass and dump in enough ice to fill it up. No problem.
If there is a smaller amount left, then I need to make more coffee in order to get a full-ish glass of iced coffee. Our coffee machine has an “over ice” option where it gives you a smaller amount of stronger-than-normal coffee.
In that case, my current “recipe” is:
I was wondering if it would be better to do it in a different order.
Not that it really matters - it ends up tasting the same regardless and I finish it in about a minute. I was mostly just curious.
Oh, and before you tell me to do something sensible like just dumping out the cold morning coffee and making new, or making coffee in the morning and storing it in the fridge until I wanted it later…Using the forgotten morning coffee makes me feel virtuous, and if I can’t even remember to drink my morning coffee, you think I’d remember to make some for later?
You proably want to maximize the time that the hot coffee portion sits out on its own (to cool) prior to mixing. Even if you let both the cold coffee and the hot coffee sit out separately (allowing the cold coffee to warm and the hot coffee to cool), the end result is going to be colder than if you mixed them right away. This is because the hot coffee (~180F) is a lot farther away from room temperature (72 F) than the cold coffee is (~33F), so the hot coffee cools quicker. If you add the two right away, you get (180+33)/2 = 106.5 F coffee. The longer you wait, the closer you get to 72F coffee after mixing.
If you have plenty of ice and the rules permit it, chilling down the glass and then tossing the melted ice is also going to help.
The cold coffee is actually room temperature - sorry for lack of clarity.
There is an effectively unlimited amount of ice. What do you mean by rules, though?
For my purposes, any approach that involves waiting isn’t feasible - I have work to do! Such discussion might be helpful to someone else, though.
Can i…
Pour all coffee in glas, hot and cold.
Embed glass in the ice since there is plenty
stir coffee until chilled and remove glass from ice
Cold coffee, no dilution ?
Have you considered making a lot of it so it’s always ready?
We make it at work. We steep the coffee grounds (in a rubber banded coffee filter) for about 12 hours, at room temperature. Then pull out the coffee grounds* and put it all in a cooler. When someone wants some we pour it into a cup with ice.
It’s always ready and it starts out cold so it’s not melting ice to get cold. It lasts about 2 weeks without any adverse effects.
If you want to make it and drink it now. Your best bet is going to be to make very strong coffee, pour it over ice to chill it and dilute it to the strength you want, then add ice.
*Don’t attempt to ring out or squeeze the water out of the grounds when you pull them out. Just let the excess drip out. Any attempt to rush it or get that last little bit out can (will) result in the filter ripping and dumping all the grounds into the coffee.
No possibility of making coffee ice cubes like I have in my freezer - straight black cold brew in an ice cube tray?
In addition to beowulff’s answer:
I’m assuming we’re using ice cubes … first put your 8 oz. of ice into the glass and pour in the 4 oz. of hot coffee … this is your maximum temperature difference so this will be your quickest temperature drop … so that when you pour the cold coffee in it will be mixing with warm coffee … give it a stir and wait until the resultant achieves the specific temperature desired …
I suggest trial-and-error to determine the exact timing … you’d have results faster than you can type in all the specifics to us for the calculations … maybe use crushed ice for quicker results, or snow …
The dilution will be the same for the same temperature … colder = more dilute … warmer = less dilute … no way around that, to lower the coffee’s temperature 1º requires the melting of a specific amount of ice, whether it lowers quickly or slowly …
Make morning coffee smaller, and make a separate one at the same time for later.
How cold are the ice cubes? If they’re below freezing to start with, then they’ll absorb some heat before they even begin to melt. And the colder they are, the more they’ll absorb.
If the implied requirement is to use all 8 oz of coffee:
Pour the hot coffee into the glass. Wait until the latest possible moment, then add the cold coffee and ice. That way you let the maximum amount of heat transfer from the coffee into the environment, leaving the minimum amount of heat left to melt the ice.
I think the best way is going to be the ice wand technique.
Get bottle you can fill most of the way with water and keep it in the freezer (you see where this is going, right). Make your coffee, pour it into a vessel large enough to hold the coffee plus the additional volume of the frozen water bottle. Toss the frozen water bottle in and it should cool pretty rapidly. Use the water bottle to stir it or put the entire thing in the fridge/freezer to make this happen even faster. I’ll bet one 16oz water bottle will cool down an entire pot of coffee in less than 10 minutes, and without diluting it at all.
Also, if you put the bottle into a bag, it won’t get covered with coffee, so it can be put right back into the freezer. Also, you don’t have to worry about putting a dirty water bottle in your coffee.
As a side note, there’s a few different types of bottles that are meant either for doing exactly this or just keeping things cold. They use exactly this same idea.
If you’re going to that trouble, you could also use “whikey stones.” Though stone isn’t the best material for it. I think stainless steel would be the best compromise between food safety, thermal capacity and thermal conductivity. You could buy balls of steel sold for that purpose, but I’m sure they are just steel ball bearings like these.
Bring a bit of liquid nitrogen into the office … maybe impress the boss … I’d be impressed that’s for sure …
In the simple analysis there is no difference - you are not giving yourself time for the different rates of heat transfer to really matter. You have a set of masses with different temperature - ie energy content, and you end up with a desired total mass and temperature.
However there are things to do to improve it.
Cool the glass first. It is one of the masses you are optimising over. Fill it with ice before you start anything else, and pour out any meltwater right before you add any coffee. Add your coffee, stir, and decant into another glass as soon as it is cold enough. Prechill the second glass. As chronos says, the colder the ice you start with the better. Dewar of LN[sub]2[/sub] for the ice cubes might work. Or just pour in the right amount of LN[sub]2[/sub] and avoid the ice altogether. 
Bah!, ninja’d on the LN[sub]2[/sub]
There are only 7 possible answers given the parameters - less, since 3 and 6 are functionally equivalent.
Fill the glass in the following order with no waiting time between steps:
ETA: more answers snuck in. Thank you, Francis Vaughan. You win one glass of diluted iced coffee!