[Math!] Adding cold water to boiling to get a desired temp

Nibble

If I have 100mL of water boiling at 100C, and I add 100mL of water at 50C, then I should get 200mL of water at 75C, right? What if I have room-temp water at 25C and I want to reduce 100mL of boiling water to 80C or 90C? How much room-temp water should I add? I'm thinking the formula should be like this:

(T1 x V1 + T2 x V2) / (V1 + V2)

Where T is temperature and V is volume. That would mean that I should add about 15mL of room-temp water to make 90C water, or add 36mL to get 80C... right?

Wezoin

Yeah, just use weighted averages to figure it out (assuming you aren't incorporating other variables such as wind or general air temperature or rate of natural cooling) then it should be accurate. I guess what I'm saying is if this is for a homework question, then yes weighted averages would be the best way to figure it out, if you're trying it in real life ymmv

Nibble

Well, I just want to make green tea and French-press coffee without having to wait 5 minutes for the water to cool on its own :P As long as I can get the temperature somewhere in that range, I'm happy.

Rhan9

If I'm going for ~80C, I usually go by the rule of 3 parts of boiling water for each part of water at room temp.(around 25C).
Seems to work pretty well, although I've noticed that most green teas I brew tend to taste better in the neighbourhood of 70C. For this, the ratio to use would be 1.5 parts boiling water, 1 part room temp.

80C tends to bring out more bitter flavors in a lot of green tea, as far as I've noticed.

Seol

Wezoin wrote: »

Yeah, just use weighted averages to figure it out (assuming you aren't incorporating other variables such as wind or general air temperature or rate of natural cooling) then it should be accurate. I guess what I'm saying is if this is for a homework question, then yes weighted averages would be the best way to figure it out, if you're trying it in real life ymmv

Don't forget latent heat of vaporisation, though. That might mean that 100ml of boiling water plus 100ml of water at 50 degrees will result in 200ml at 80 degrees, or something.

It would work if it wasn't in the middle of a state change, though.

Rhan9

Seol wrote: »

Wezoin wrote: »

Yeah, just use weighted averages to figure it out (assuming you aren't incorporating other variables such as wind or general air temperature or rate of natural cooling) then it should be accurate. I guess what I'm saying is if this is for a homework question, then yes weighted averages would be the best way to figure it out, if you're trying it in real life ymmv

Don't forget latent heat of vaporisation, though. That might mean that 100ml of boiling water plus 100ml of water at 50 degrees will result in 200ml at 80 degrees, or something.

It would work if it wasn't in the middle of a state change, though.

This is all easily circumvented by taking the water off the heat the moment it starts to boil.
Besides, he's making tea. Approximate values tend to work just fine, unless you're really anal about getting the temperature and time correct to the second/celsius.

Seol

Rhan9 wrote: »

Seol wrote: »

Wezoin wrote: »

Yeah, just use weighted averages to figure it out (assuming you aren't incorporating other variables such as wind or general air temperature or rate of natural cooling) then it should be accurate. I guess what I'm saying is if this is for a homework question, then yes weighted averages would be the best way to figure it out, if you're trying it in real life ymmv

Don't forget latent heat of vaporisation, though. That might mean that 100ml of boiling water plus 100ml of water at 50 degrees will result in 200ml at 80 degrees, or something.

It would work if it wasn't in the middle of a state change, though.

This is all easily circumvented by taking the water off the heat the moment it starts to boil.
Besides, he's making tea. Approximate values tend to work just fine, unless you're really anal about getting the temperature and time correct to the second/celsius.

Yeah, it's overkill for the situation. Depends on whether he wants the right answer or the good-enough answer (the only time he should really care about the right answer is if it's for a homework, though, and then the question would probably be sufficiently leading to make it obvious that latent heat is an issue).

TL DR

Why not use ice? Less dilution, more cold.