# Find ratio of water of different temperatures to attain a specific temperature

Curiosity Science Physics Find ratio of water of different temperatures to attain a specific temperature

• What equation can I use to allow me to mix water of different temperatures together to get a certain temperature as a result?
I.e. I have ‘X litres’ at 5 degrees C and I have ‘Y litres’ water at 10 degrees C. How can I find out the ratio in which to mix them to get a specific temperature?
e.g. 5 litres at 5 degrees C + 5 litres at 10 degrees C = 10 litres at 7.5 degrees C.
What if I want 6.5 degrees C? Or 8 degrees C?

– Mark, via the ask a science question page.

• Hi Mark,

When you have water at two different temperatures and mix them the heat would flow from higher temperature (hot water) to the lower temperature. So the basic equation here is, heat lost by hot water = heat gained by cold water as both reach a thermal equilibrium.

Heat transfer Q = mcΔT.

Where m is the mass of the water, c is the specific heat (4.1855 J/g°C) and ΔT is the change in temperature.

For your case, X litres at 5 degrees C and Y litres at 10 degrees C,

Cold 5——x——10 Hot

(X 103)(4.186)(10 – x) = (Y 103)(4.186)(x – 5)

Solving this, we get

X/Y = x – 5 / 10 – x

Now for your other cases, where you need to find the ratio of hot and cold water to mix and attain a specific temperature (x), all you need to do is substitute the equilibrium temperature value for x. X/Y is the ratio of the water you need to mix.

• I’m sure this is a homework question! 😂

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