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Formula for mixing liquids of different temperatures?

  1. I'm going to fill a big container (3500 litres) with water. I'll use water from a hose, and boiled water, and I want to hit 40 degrees celcius.

    Now, I figured that this was straight forward,

    Temperature in hose = 10 C
    Temperature of boiled water = 100 C

    ( 100 * X + (3500 - X) * 10 ) / 3500 = 40

    Which gives 1166 litres of boiling water.

    However, this assumes that 1 litre of 10 C water + 1 litre of 20 C water = 2 litres of 15 C water. In other words, that I can just add the temperatures together and then divide by the total amount of liquid.

    Someone (who unfortunatly was not able to provide a formula) said it is not as straight forward as that.. so, I'm looking for the formula for mixing liquids of different temperatures.

    k
     
  2. jcsd
  3. Redbelly98

    Redbelly98 12,036
    Staff Emeritus
    Science Advisor
    Homework Helper

    How precise do you need to be? I guess you could take thermal expansion into account if you wanted to, but the simple weighted-average method you used should be good enough for most applications.
     
  4. Oh, ok then I am golden. I only need to be accurate enough to avoid boiling anyone that ventures into the pool :)

    Thanks a lot.

    k
     
  5. Redbelly98

    Redbelly98 12,036
    Staff Emeritus
    Science Advisor
    Homework Helper

    You could also do a test by making 3.5 liters first, using 1.17 L of boiling water.
     
  6. Yeah, I'll do a small scale test first, to make sure.

    Thanks again.

    k
     
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