Penny Arcade Forums› Help / Advice Forum
The new forums will be named Coin Return (based on the most recent vote)! You can check on the status and timeline of the transition to the new forums here.
The Guiding Principles and New Rules document is now in effect.

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

NibbleNibble Registered User regular
edited August 2009 in Help / Advice Forum
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?

sig.php?id=178
Nibble on

Posts

  • WezoinWezoin Registered User regular
    edited August 2009
    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

    Wezoin on
  • NibbleNibble Registered User regular
    edited August 2009
    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.

    Nibble on
    sig.php?id=178
  • Rhan9Rhan9 Registered User regular
    edited August 2009
    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.

    Rhan9 on
  • SeolSeol Registered User regular
    edited August 2009
    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.

    Seol on
  • Rhan9Rhan9 Registered User regular
    edited August 2009
    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.

    Rhan9 on
  • SeolSeol Registered User regular
    edited August 2009
    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).

    Seol on
  • TL DRTL DR Not at all confident in his reflexive opinions of thingsRegistered User regular
    edited August 2009
    Why not use ice? Less dilution, more cold.

    TL DR on
Sign In or Register to comment.
Penny Arcade Forums› Help / Advice Forum