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Old 04-08-2013, 07:31 PM   #1
Beaudoin
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Default Calculating PSI

Can anyone here tell me what the equation is to calculate the amount of PSI there would be in a bottle that has a CO2/Vol of about 4 at 20 C?

I'd like to be able to calculate this myself, but I don't know the equation.

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Old 04-09-2013, 12:53 PM   #2
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If I read your question correctly, you are asking for the conversion to psi if there are 4 volumes of dissolved CO2 in the beer/bottle? I could get all fancy and write out the ideal gas equation, and calculate a number based on all the constants, but the reality is much more simple. If you have 4 volumes of gas, then you have 4x the number of gas molecules, which means 4x the pressure. So, 4 x 14.7 psi (atmospheric pressure) = 58.8 psi

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Old 04-09-2013, 09:52 PM   #3
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Yes. That is what I'm after. I appreciate your response.

But, If you don't mind, would you be willing to write out the ideal gas equation so that I can understand all of the constants involved? I understand that temperature plays a major role as well. Why is that? How does temperature influence the PSI?

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Old 04-09-2013, 10:08 PM   #4
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Or use an online calculator.

It's 51 PSI by the way . . .

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Old 04-09-2013, 10:22 PM   #5
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I'm attempting to put this equation in a spreadsheet, which is why I need the equation.

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Old 04-10-2013, 12:47 PM   #6
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Download the pdf at http://www.wetnewf.org/pdfs/Brewing_...%20Volumes.pdf. In contains several formulae based on the ASBC table with information on how well they fit the table.

The gas law is P*V = n*R*T

IOW the pressure x volume product depends directly on the temperature. If you put something with a cover on it into the microwave and fire it off as whatever is in the container warms the pressure of the air over it will increase until the cover pops off. If you look at the pressure gauge on your CO2 bottle you will see that it increases as the temperature goes up. In addition to all this as the temperature of beer rises the solubility of CO2 in it at a given pressure goes down. All this is explained in the .pdf.

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Old 04-10-2013, 05:15 PM   #7
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From what I can read in that PDF, these are formulae to create CO2 graphs. I'm not sure this solves my problem, or answers my question. I'm not a Math or a Science major, so I wouldn't be able to fully understand this.

I came up with this. Can any of you verify if this is accurate:

PSI = [CO2/Vol x (Temperature + 12.4) / 4.85] - (Barometric Pressure x 0.145038)

0.145038 : This number converts barometric pressure to PSI.

Assuming the following values:
CO2/Vol = 4
Temperature = 72
Barometric Pressure = 101.7

We would have:

PSI = [4 x (72 + 12.4) / 4.85] - (101.7 x 0.145038)
PSI = 54.85788

If there is a better equation out there, please let me know.

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Old 04-10-2013, 06:34 PM   #8
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Quote:
Originally Posted by Beaudoin View Post
Can anyone here tell me what the equation is to calculate the amount of PSI there would be in a bottle that has a CO2/Vol of about 4 at 20 C?
I took this to mean that you wanted to know how much pressure would need to be applied to a keg containing beer at 20 °C in order to produce a carbonation level of 4 volumes. Reading it more carefully I confess that I have no idea what it is you want to know. "CO2/Vol of about 4" means nothing to me.

If you are talking about a bottle containing CO2 liquid and gas the pressure depends only on the temperature of the liquid and not how much liquid is in the bottle. Once all the liquid in the bottle is all boiled off and it contains just CO2 gas the gas law (as modified) kicks in and the pressure depends on the amount of gas remaining and the temperature.
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Old 04-11-2013, 12:59 PM   #9
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Humm... ok..., well maybe I can clarify:

If I wanted my beer to have 4 volumes of CO2 in my bottle, how much PSI would be in the bottle at 20 C.

I found the answer on my own, so no need to look into this.

This is the equation I was after from the beginning is:

P = F(Temperature, Volume)

Mind you, I have no idea how the equation turned into this:
P = -16.6999 - 0.0101059 T + 0.00116512 T^2 + 0.173354 T V + 4.24267 V - 0.0684226 V^2

See:
http://www.brainlubeonline.com/GasLawsBeer.html
http://brewery.org/brewery/library/CO2charts.html

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Old 04-11-2013, 01:57 PM   #10
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OK. Then the appropriate equation is

Psig = V/ ( 0.01821 + 0.09011 exp(-(T-32)/43.11) ) + 14.695

obtained by solving Equation 2.1 in the .pdf for P. I forget that the US now proudly holds down 27th place (or whatever the number is) in the worldwide rankings of the math skills of our students.

Psig is gauge pressure and V is the number of volumes at STP. T is the temperature in °F. This comes from looking at the ASBC data and finding parameters which result in the best fit to it under the assumption that the Henry coefficient is a function of temperature only (which it isn't but it's a good approximation).

Polynomial approximations, like the one you quote, are also derived from tabular (measured) data but by finding the coefficients that best fit the data on the assumption that the underlying model is that of a, in your case, second order polynomial. This works too but you must know the range over which the original data were taken. It is characteristic of polynomial fits that they explode if you go outside this range. That's why the exponential form is more robust (though it isn't totally immune to this effect either).

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Last edited by ajdelange; 04-11-2013 at 02:45 PM. Reason: Algebra error.
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