Chamber pressure question
Hi all. I'm working on a project that involves filling a chamber with CO2. I came across the thread with the formula for calculating chamber pressure, 4200/cv. This is just what I needed, but I would like to know, where does the number 4200 come from? Can anyone help me out? Thanks in advance.
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boilingleadbath
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The number 4200 comes from the ideal gas equation (PV = nRT). It is the evaluation of nRT for the amount of CO2 in a 12g CO2 container.
To walk you through the calculations...
(12g/44g per mole)*(.0821 atmosphere-liters per mole-k)*(300K)
Gives us 6.7 liters of gas at 1 atmosphere.
We then convert that into units we like (not that there's anything wrong with atmosphere-liters) by multiplying by 68 (to convert liters into cubic inches) and by 14.7 (to covert atmospheres to PSI).
This... acctualy gives us 6700 psi-in^3
Apparently, whomever did the calculation assumed that the CO2 gas that is created is darn cold (about -84*C) and/or non-ideal.
...or that 12g cartridges don't contain 12g of CO2.
Either way, it's worth noting that (at reasonable temperatures) the CO2 cartridges don't contain anywhere near 4200 psi, but rather liquified CO2 at about 1000 PSI. This means that you can't connect a CO2 cartridges to a 2 cubic inch chamber and fill it to 2000 PSI; the pressure would only be about 1000 PSI, with a bit of left over liquid CO2.
This pressure would continue until the combined volume of the CO2 bottle and chamber was 4.2 cubic inches. (or 6.7, depends which calculation is right)
To walk you through the calculations...
(12g/44g per mole)*(.0821 atmosphere-liters per mole-k)*(300K)
Gives us 6.7 liters of gas at 1 atmosphere.
We then convert that into units we like (not that there's anything wrong with atmosphere-liters) by multiplying by 68 (to convert liters into cubic inches) and by 14.7 (to covert atmospheres to PSI).
This... acctualy gives us 6700 psi-in^3
Apparently, whomever did the calculation assumed that the CO2 gas that is created is darn cold (about -84*C) and/or non-ideal.
...or that 12g cartridges don't contain 12g of CO2.
Either way, it's worth noting that (at reasonable temperatures) the CO2 cartridges don't contain anywhere near 4200 psi, but rather liquified CO2 at about 1000 PSI. This means that you can't connect a CO2 cartridges to a 2 cubic inch chamber and fill it to 2000 PSI; the pressure would only be about 1000 PSI, with a bit of left over liquid CO2.
This pressure would continue until the combined volume of the CO2 bottle and chamber was 4.2 cubic inches. (or 6.7, depends which calculation is right)
