# Formula for mixing liquids of different temperatures?

## Main Question or Discussion Point

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

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Redbelly98
Staff Emeritus
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.

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

Redbelly98
Staff Emeritus