From the HBD Archive
From: caeco!jj@cs.utah.edu (Jeff Jennings)
Subject: Homebrew Digest #339 (January 17, 1990)
Date: 1990-01-17 16:11:43 GMT

>can someone familiar with the heat capacities of wort vs water calculate the
>volume of (say) 40F water necessary to bring wort from (say) 190F to 90F?

The formula for the resulting temperature of a solution made by mixing two
liquids together is:

Tf = (T1 * V1 + T2 * V2) / (V1 + V2)

where:
Tf is the temperature of the mixture
T1 is the temperature of the first liquid
V1 is the volume of the first liquid
T2 is the temperature of the second liquid
V2 is the volume of the second liquid

So if one added 2 gallons of hot wort at 200 degrees F to 3 gallons of
cooled water at 40 degrees F in your carboy, the temperature of the mixture
would be:
Tf = (200 * 2 + 40 * 3) / (2 + 3) = 104 degrees F

To solve your question of bringing 5 gallons of wort at 190 degrees F
down to 90 degrees F using 40 degree F water:
90 = (190 * 5 + 40 * V2) / (5 + V2)
and solve for V2 and come up with 10 gallons. Of course in this example
the liquids are not being mixed so we are assuming perfect heat exchange
between them.
- -------------
Jeffrey C. Jennings Silicon Compiler Systems
uunet!iconsys!caeco!jj 7090 South Union Park Ave., Suite 200
caeco!jj@cs.utah.edu Midvale, Utah 84047 USA
(801)255-8880

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