(Posted with www.reefscapes.net and Breefcase's permission from works written in reefs.org)
The pressure inside a closed cylinder containing a volatile non-polar liquid like CO2 is determined solely by the characteristic VAPOR PRESSURE of the substance, not by how many pounds of liquid are put into it. Vapor pressure is defined as the pressure of the vapor of a liquid in equilibrium with its liquid state. (Solids have vapor pressure, too, even though that seems odd at first. Just think of dry ice, which is solid CO2 but turns to vapor very quickly due to its high vapor pressure at room temp.)
As long as a CO2 cylinder is at a reasonable, constant temperature, as gas is (slowly) used out of the cylinder liquid CO2 "boils" off as gaseous CO2, at the vapor pressure of CO2 at that temperature. This is about 860 psi at normal room temperature, or about 72 degrees Fahrenheit. This process of evaporation continues until all the liquid CO2 is gone. That is why CO2 tank pressure is constant (at a given temperature) until it's almost empty (i.e., no liquid is left), and then falls off rapidly as the remaining residual gas is quickly used up.
Rapidly releasing gas will lower the tank temperature dramatically (as you observed in your frozen kitchen) due to expansion cooling as the CO2 soaks up its "heat content of evaporation" from the surrounding environment, but we can ignore that tiny effect for normal slow CO2 usage rates. (This is also why aerosol cans sometimes get very cold to the touch if you spray them too quickly for too long.).
So, as strange as it seems, how much liquid CO2 (in pounds) was put into your cylinder had NOTHING to do with its internal tank pressure. Just as long as there was SOME liquid present inside the cylinder, the internal pressure was identically fixed at the vapor pressure of CO2.
There are four basic things that can influence vapor pressure - the "polar" or "non-polar" nature of the molecules of the substance, how much surface area of the liquid is exposed to the gas in the cylinder (i.e., cylinder diameter in this case), the concentration of the vapor molecules above the liquid, and lastly TEMPERATURE. In your case, on the inside of a closed CO2 cylinder at equilibrium everything else is fixed (held constant), so TEMPERATURE is all that controls the CO2 vapor pressure, and thus temperature is also all that controls the pressure inside the tank. As other people in this thread have noted, CO2 tank pressure varies with the temperature, and this is why.
"Polar" substances have di-polar molecules, i.e., they have positive and negative ends to the molecules. The inter-molecular forces acting on polar liquids are much stronger and the liquid molecules are kept in the liquid state easier. Polar substances tend to have lower vapor pressures at a given temperature.
On the other hand, if the molecules of a liquid are non-polar like those of CO2, then there will be weaker intermolecular forces keeping them in the liquid state. Non-polar substances like CO2 have weaker forces between them and therefore their vapor pressures are characteristically higher than those of polar substances. The rate of evaporation for non-polar molecules is generally far greater than polar molecules in comparison. This gives CO2 its comparatively high vapor pressure.
Any increase in the temperature of the CO2 tank increases the average kinetic energy present in the molecules of the liquid CO2. The more energy that the surface liquid molecules absorb (heat), the faster they will be able to overcome the intermolecular forces acting upon them, and the sooner they will become vapor.
Here's the really nasty part that apparently bit you with your CO2 cylinder. Increasing the temperature of a liquid increases it's vapor pressure not linearly, but LOGARITHMICALLY. Doubling absolute temperature increases pressure by a factor of ten times.
This is defined by the Clausius-Clapyron Equation, that you probably remember having seen in science class:
Log P2 / P1 = Delta H vaporization [ 1 / T1 - 1/T2] / 2.303 ( R)
R = universal gas law constant = 8.31 J/mol-K = 8.31 X 10-3 Kj / mol-K
P1 and P2 = vapor pressure at T1 and T2
T1 and T2 = Kelvin Temperature at the initial state and final state
This tells us that at about 40 degrees Fahrenheit, CO2 has a vapor pressure of 600 psi. At 72 degrees F, it's up to about 860. At about 80 degrees F, the CO2 vapor pressure rises to about 970 psi. So, if your pressure gauge before your uncontrolled CO2 discharge was off-the-dial at over 1200 psi, the internal temp must have climbed to 90 degrees F or more due to where the tank was located, or due to being in the car.
Does this seem reasonable to you given conditions in your house/car, Jeff? (Feeling the outside of the metal tank won't tell you much, because the thermal conductivity of metal is so high it will likely feel cool to the touch of your 98.6 degree hand, even if it is relatively hot inside.) If so, the CO2 was well into the highly dangerous and unpredictable so-called "critical zone."
The critical zone is temperatures and resulting pressures above the "critical point," a unique combination of temperature and pressure for a given substance at and above which gas and liquid begin to behave the same, and normal fluid dynamics laws no longer hold. For CO2, this critical point is 88.88 degrees F, at about 1080 psi vapor pressure. It is unclear to science what state of matter the CO2 would be said to be in at and above this point - gas or liquid. At or above these temps, all bets are off as far as guessing the fluid behavior and/or the gas pressure of the CO2 inside the cylinder.
(I'm pretty sure I did the calculation here correctly, but math is not really my thing and I did do these calculations on the fly, so corrections are welcome from you more math-savy reef keepers out there.)
Bottom line - be very careful with heat and bottled CO2. If you leave it in a car, house, or closet with temps above 90 degrees or so, you are asking for big, big trouble. The only reason more people don't blow themselves off the face of the earth messing around with these compressed CO2 cylinders is because industry standard tanks are so tremendously over-engineered, to protect us from ourselves for both safety and liability reasons.
The total pressure acting on the total square inches of the walls of a typical size cylinder at 1000 psi or more is mind-blowing (pun intended). If you really did badly overheat your CO2 cylinder, you were fortunate that a small valve failed before the tank walls ruptured. As mentioned before in this thread, tanks contain rupture disks to prevent this.
So, keep those CO2 tanks cool, people. ALWAYS below 80 degrees, for sure. (Your pressure gauge should never read more than 1000 psi. If it does but your room temp is below 80, suspect that the gauge needs recalibrating.)
Forewarned is forearmed.
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