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View Full Version : Wort-cooling problem [beer] for the physics geeks



Quikfeet509
27th July 09, 11:24 AM
For an overview, one of the most important steps in brewing beer is when the wort is cooled from boiling (212*F / 100*C) to a proper temperature to pitch the yeast (70*F/21*C). The reason why a rapid cooling is important is because it precipitates out proteins and other gunk that you don't want in your beer plus is shortens the time that your beer can get infected by something other than the yeast you are using.

Typically homebrew shops try to sell a wort-cooler as a vital piece of equipment in order to get a rapid cooling (30 minutes) but I would rather spend $80 on beer ingredients...plus I know with proper timing of using an ice bath and refrigerated purified water, it can be done much faster.

I need help making creating a formula to determine the optimum timing necessary to bring the wort down as quickly as possible without overshooting (which I did last night) which causes a slow start to fermentation (which is also bad).


Here's the data:

- 3 gallons of wort at 100*C
- wort is in a 5 gallon stainless-steel pot that is fairly thin (maybe 0.5 cm?)
- ice is placed in the sink and the sink is deep enough to hit all the sides of the pot up to about 3/4's the height of the pot
- 2 gallons of 5*C water is ready to add - end volume is 5 gallons
- thermometer can be used to stir the wort in the pot to redistribute the heat of the wort
- ambient temperature of the room is 24*C


Now it is obviously easier to cool 3 gallons of hot wort (specific gravity around 1.050) at 100*C then it is to cool 5 gallons at 70*C (which I found out the hard way). On the other hand, using only the ice bath is rapid initially until the temperature of the wort gets closer to room temperature (?).

Last night I used the ice bath to get the wort down to 48*C (took 15 minutes) then added the 2 gallons of cold water. The final temperature actually overshot at went to 18*C.


So what I want to know is what is the optimum temperature to add the 2 gallons of water to to bring the total wort temperature to right about 21*C? Is it easier to just forget about the first part (ice bath) and just focus on what temperature to add the cold water to (making it the initial temperature) so that the end temperature is 21*C?

WarPhalange
27th July 09, 11:55 AM
Trial and error would be your best bet. There is too much shit to account for to do it theoretically and accurately. If your water is at 21C, then that's as low as you can possibly get your "wort" (wtf?). But theoretically it will take forever to get there.

Only thing I would recommend is getting something with a lot of surface area to hold your shit in, to help with cooling. Shoving it all in a pot = bad. You'd be better off stuffing it all into a bunch of smaller pots, separated from each other or really shallow pots with a lot of area. But it looks like you've got that taken care of.

Having a fan blowing at the whole thing will help cool it faster, too.

I think your idea with the ice bath + cold water is fine. You said you overshot by 3C, right? Then put the cold water in sooner, or less of it.

Quikfeet509
27th July 09, 01:05 PM
Oh Poops, we are going way beyond that. I'm talking about a formula for the second stage [I think the first part would indeed have too many variables], which is basically at what temperature should 3 gallons of wort be when you add 2 gallons of 40*F water to make the final volume 70*F.

I'm going to have my "Physics of Anesthesia" teacher help me set it up next Monday if we don't solve it before then.

Zendetta
27th July 09, 01:07 PM
Just get the wort cooler. Seriously.

Scrapper
27th July 09, 01:10 PM
Oh god.

U*A Delta T to determine heat transfer, but the medium will be changing temperature as transference occurs. This is a bit of ugly calculus I have no desire to participate in.

DO what PL said.

Cullion
27th July 09, 04:40 PM
or use ready made malt or make cider instead

WarPhalange
27th July 09, 04:59 PM
Oh Poops, we are going way beyond that. I'm talking about a formula for the second stage [I think the first part would indeed have too many variables], which is basically at what temperature should 3 gallons of wort be when you add 2 gallons of 40*F water to make the final volume 70*F.

That's even more complicated as you need to know the heat capacity of water (which you can easily look up) and the heat capacity of your "wort", which I suspect isn't so easy to find. If it is mostly water anyway, you can make a decent estimate, though.

What you want is 3*x + 2 * 40 = 5 * 70.

=> 0.6*x + 2*8 = 70 => 0.6*x = 54 => x = 90F

To make sure I'm not talking out of my ass, convert 40F and 70F to Celsius, do the math again, then convert back to Fahrenheit and make sure you have something close.

If wort is not mostly water, then you can't really use that formula. It will more complicated. Water has a huge heat capacity, so it's a safe bet that anything else in the wort has a lower heat capacity, meaning it's easier to cool and heat up.

Basically it would be something like:

(% of wort that is water)*3*T*(heat capacity of water) + (% of wort that is not water)*3*T*(heat capacity of other shit) + 2*40*(heat capacity of water) = (% of whole thing that is water)*5*70*(heat capacity of water) + (% of whole thing that is not water)*5*70*(heat capacity of other shit)

Cullion
27th July 09, 05:13 PM
buy the wort cooler. jesus.

Ajamil
27th July 09, 09:37 PM
Did I mention the book I'm reading about superpowers from home brew? Just making sure.

Quikfeet509
28th July 09, 01:24 PM
Poop - I can get the specific gravity of the wort with the hydrometer so if specific heat can be calculated from that, they we are set.



Everyone else - why buy a wort chiller if you can use cold water, ice, and physics and get the right temperature in 1/2 the time?

Zendetta
28th July 09, 02:01 PM
Everyone else - why buy a wort chiller if you can use cold water, ice, and physics and get the right temperature in 1/2 the time?

Laziness and/or consistency.

All the beer I have had that was made without one had bitter undertones.

WarPhalange
28th July 09, 03:24 PM
Poop - I can get the specific gravity of the wort with the hydrometer so if specific heat can be calculated from that

No.

Quikfeet509
28th July 09, 04:21 PM
Actually the rationale for a wort chiller was explained to me on a different site - if you do a full 5 gallon boil (like for an all-grain recipe, for example) then you can't use 2 gallons of cold water to rapidly cool the wort.

Quikfeet509
28th July 09, 04:23 PM
No.


Suck. Guess I'll just use distilled water as an approximation and see how accurate it is.

WarPhalange
29th July 09, 12:36 AM
It's pretty reasonable to assume that the wort would have a lower heat capacity than water.

http://en.wikipedia.org/wiki/Specific_heat_capacity#Table_of_specific_heat_capa cities