mixing three water quantities at different temperaturesby beer_brewer Tags: mixing, quantities, temperatures, water 

#1
Jun1310, 11:47 AM

P: 3

I am trying to figure out the following in my beer brewing. I have been able to find equations for mixing two quantities of water, but not three. Can anyone help me out here?
So, I have 5 liters at 100 C and I want to add 18 liters (x at 20 C and y at 8 C) to arrive at 23 liters at 24 C. This is because most of the remaining 18 liters is at room temperature (20 C), and I want to find out how much water chilled in the fridge (8 C) will bring me to the desired 23 liters at 24 C? many thanks 



#2
Jun1310, 12:19 PM

P: 459

Solve the two simultaneous equations the answer is in litres. This assumes that all the liquid is water but I guess that the hot liquid is wort which probably has a higher specific heat capacity then pure water in which case the final mixture will be hotter then intended, these should get you fairly close though.
X+Y=19 293X+281Y=4966 



#3
Jun1310, 03:51 PM

P: 3

Thanks Jobrag, but I need some clarification. Why is X + Y = 19 and not 18? And how did you get the second equation. When I put X = 19  Y into the second equation (which I assume you meant this when you said to calculate both equations simultaneously) I ended up with X=50.08.
cheers 



#4
Jun1310, 04:36 PM

P: 822

mixing three water quantities at different temperaturesOnce you get that figured out, you should be able to figure out how to make up the 18 liters. But I will give you a hint, or rather a prediction: you aren't going to be able to do what you want (your cold water isn't cold enough). 



#5
Jun1310, 09:40 PM

P: 3

Ah ha. That explains the 50 liters. Thank you. I was letting my assumptions get in the way of the calculation.



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