Formula for mixing liquids of different temperatures?

In summary, the conversation discusses filling a container with 3500 litres of water and reaching a temperature of 40 degrees Celsius. The equation used to calculate the amount of boiling water needed assumes that the temperatures can simply be added together, but this may not be accurate. The solution is to use a weighted-average method, which should be precise enough for most applications. A small scale test can also be done to confirm the accuracy of the calculations.
  • #1
kenewbie
239
0
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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  • #2
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.
 
  • #3
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
 
  • #4
You could also do a test by making 3.5 liters first, using 1.17 L of boiling water.
 
  • #5
Yeah, I'll do a small scale test first, to make sure.

Thanks again.

k
 

What is the formula for mixing liquids of different temperatures?

The formula for mixing liquids of different temperatures is known as the "heat transfer equation." It is expressed as Q=mCΔT, where Q is the amount of heat required, m is the mass of the liquid, C is the specific heat capacity, and ΔT is the difference in temperature between the two liquids.

How do I calculate the specific heat capacity of a liquid?

The specific heat capacity of a liquid can be calculated by dividing the heat required to raise the temperature of the liquid by its mass and the change in temperature. This value is typically given in units of J/g·°C or J/kg·K.

Can I mix liquids of any temperature?

Yes, you can mix liquids of any temperature. However, the resulting temperature will depend on the specific heat capacity and mass of each liquid, as well as the amount of heat transferred during the mixing process.

What is the best way to mix liquids of different temperatures?

The best way to mix liquids of different temperatures is to slowly pour one liquid into the other while continuously stirring. This will help to evenly distribute the heat and prevent any sudden temperature changes or separation of the liquids.

Can the formula for mixing liquids of different temperatures be applied to gases?

No, the formula for mixing liquids of different temperatures is specific to liquids. Gases have different properties and require different equations to calculate heat transfer and temperature changes.

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