Water Temp Formula - Home Brew Forums

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02-03-2010, 04:30 PM   #1
JayInJersey

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May 2009
New Jersey
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What's the formula to determine how much water at a certain temp to add to x amounts of water at another temp to reach a final temp?

No grains...just water and water

Thanks!

02-03-2010, 04:51 PM   #2
rocketman768

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Feb 2008
Evanston, IL
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If you assume that the two masses of water only transfer heat energy to each other and not to their surroundings, then you assume that the heat energy lost by the hotter water is the same as the heat energy gained by the cooler water.

Q = m*c*(T1-T2)
Is the amount of heat energy required to raise an object with mass "m" and specific heat "c" from temperature "T2" to temperature "T1."

m1*c1*(T_hot - T_f) = m2*c2*(T_f - T_cold)

Where T_hot is the temperature of the hotter object, m1 is the mass of the hotter object, c1 is the specific heat of the hotter object, (T_cold,m2,c2 for the colder object), and T_f is the final equilibrium temperature of both objects.

In your case, c1=c2 since both the objects are water. Reducing the above equation, the final temperature is

T_f = (m1*T_hot + m2*T_cold)/(m1+m2)

02-03-2010, 05:13 PM   #3
JayInJersey

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May 2009
New Jersey
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I swear...my brain hurts reading over all the Electrical stuff, but this just makes sense to me.

But just to make sure I'm not making a too long away from Algebra error...

If I have 4 Gallons of 180* water and want to get the water to 155* adding ~1Gallon of 60* water should do it right?

02-03-2010, 08:52 PM   #4
rocketman768

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Feb 2008
Evanston, IL
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Quote:
 Originally Posted by JayInJersey If I have 4 Gallons of 180* water and want to get the water to 155* adding ~1Gallon of 60* water should do it right?
Looks right.