What's the pressure in a CO₂ cartridge?

Simple question today... What is the pressure inside the CO₂ cartridges used by cyclists to inflate their tubes when they get a puncture?
Huge thanks to the REFPROP team at NIST! The software I use to plot all charts you see in the video is FREE for download here: trc.nist.gov/refprop/MINIREF/...
00:00 What is this cartridge?
01:08 The pressure is not constant
02:19 Is that PV=nRT!?
05:03 The pressure-enthalpy chart
05:50 Constant density
08:56 The contents are liquid
10:01 What happens when we heat it?
10:53 Heating to the limit
12:00 Homework for next time.
Process with Pat is the place to come for perspective and to ask stupid questions. I want you to leave more knowledgeable, confident, motivated, and most importantly, curious. I also want to invigorate a field that seems tired and uninspiring, at least if you get your perspective from internet forums. These are not lectures. This is a place for you to leave thinking “Oh! That’s why...”
This channel is not only for chemical engineers - anyone who works with processes should be able to find something of value here.
#ProcessEngineering
#ChemicalEngineering
#CO2Cartridge

[@MartinHealy]

Hi Pat, Thank you for making a hugely complex subject a little more understandable. I use 12g CO2 cylinders in pistols. As gas is released from the cylinder it causes a temperature drop and the consequently the pressure drops and this effects the following shots. What I am unsure of is if the full cylinder has a pressure of 58 BAR at 20C and I empty 6g of the CO2 then allow the temperature of the cylinder and contents to stabilise again at 20C then what would be the pressure in the cylinder? Thank you in advance for your time. All the best, Martin

[@ProcesswithPat]

Hey Martin, thanks for the interesting question! To help me answer it I have prepared compiled a diagram which you can find here: imgur.com/gallery/8LTZU1p First and foremost, this is all under the assumption that the cartridge is 21 mL in volume. I would guess they don't change in size depending on their charge, but who knows. Nor do I know how accurate this volume measurement of mine was. As you consume more and more gas, the mass drops but the volume stays fixed (rigid container). That means that density drops the more CO2 we let out. In the video I calculated a density of 760 kg/m³ with 16g. If the cartridge volume is the same for 12g, then the density is 570 kg/m³ (three quarters of the start density). By the time we drop to 6g, the density is 285 kg/m³. I have shown these constant density lines on the diagram. Despressurising the cartridge moves us to a progressively lower-lying yellow line. Every time the cartridge warms back up to 20 °C the pressure is wherever the yellow constant density line (called an isochore) intersects with the red constant temperature line (called an isotherm). You can see from 16g all the way down to 4.1g it always intersects the horizontal portion of the isotherm. It's horizontal because it is at a constant pressure of around 58 bar. This means as along as you have more than 4.1g of CO2 you will always have 58 bar. Remember, you have liquid in there. Any time you fire a shot and depressurise the cylinder, liquid boils off until the pressure is 58 bar again. As long as there is liquid, the pressure will be maintained. This is exactly what happens in your deodorant can or your lighter. You start with liquid, and whenever you release some of the contents then a portion of the liquid boils, so you maintain a nice steady pressure as you consume the contents. Back to our CO2 cartridge... Below 4.1g there is no liquid left, and only then does the pressure start to drop. Dropping down from 4.1g to 0.3 g drops the pressure from 58 bar to 8 bar (which I wouldn't have guess considering you have less that half a gram, but intuition can be pretty rubbish at times). Does that makes sense? Remember that all pressures are absolute pressures, not gauge pressures.

[@MartinHealy]

@@ProcesswithPat Hi Pat, Many, many thanks for putting in so much time to produce your comprehensive response. I have several KZbin channels so I do appreciate the time it takes to answer viewers questions. You have answered many of the questions that I have been grappling with from a CO2 pistol shooting perspective. My real world observations of the affect of temperature on the cylinder pressure (as judged by the point of impact (POI) of the pellet on the target) have been born out. In the low ambient temperatures of winter the POI is lower than in the summer months. So I carry replacement cylinders in my trouser pockets to get the contents to body temperature. When I shoot a single shot pistol slowly and methodically the POI is more consistent. When shooting semi-auto pistols in rapid fire the POI drops significantly with successive shots due to the cylinder temperature drop. As the cylinder becomes exhausted the POI falls off a cliff and this is exactly what your Enthalpy chart predicts as the 'knee' is reached at 195kg/m3. I have now carried out some measurements on the 12g cylinders used in pistols. My accurate jewellers scales unfortunately have a max weighing capacity of 10g so I have had to use digital kitchen scales which may not be entirely accurate or repeatable. To help on the accuracy I collected up 5 x empty cylinders = 150g = 30g each. 10 full cylinders = 417g = 41.7g each Average contents therefore = 11.7g of CO2 (branded Umarex cylinders) I used a medical 5ml syringe to fill an empty cylinder with water by injecting via a hypodermic needle through the piercing hole of the cylinder. I measured exactly 15ml to fill the entire cylinder so that a tiny bead of water appeared above the piercing hole. To double check this volume measurement I put tape over the piercing hole and weighed the water filled cylinder at 45g = contents of 15g of water. This data provides a calculation of 11.7g/15ml = 780kg/m3 So your assumption that these CO2 cylinders varieties would be similarly filled appears to be correct. I would be grateful if you could use this data to produce another chart for 12g cylinders and predict the 'knee' point where the pressure drops from the isotherm line. This information will be of interest to many shooters around the world so I will make a video to explain all these findings. I will of course credit you with all the science. At the end of your video you set a homework question. I am struggling a little to read the enthalpy charts on my screen but my answer is that if you depressurise the cylinder from around 60BAR to 1BAR rapidly the cylinder temperature will drop from 20C to -35C. Thanks again for all your help. All the best, Martin

[@ProcesswithPat]

Super interesting, and fantastic to hear that you were so methodical in measuring cartridge volumes. Makes me feel like an arse for hacksawing one in the kitchen! Cool to hear we get to similar densities. Also, great observation about the single round vs. semi-auto. How many shots do you get out of 12g? I guess it depends on how generous you are feeling in qualifying the last few as shots... There is actually no need to plot another chart. The plot in the link is THE plot. The density lines do not move because density is what we usually refer to as an "intensive property" - it is not a function of the amount of material you have. Water has a density of 1 g/mL regardless of whether I have a teaspoon or a bucket. Same thing with CO2, or any other substance. The only thing that changes moving from my 16 g/ 21mL cylinder to your 11.7 g/15 mL cartridge is the mass of CO2 remaining at the "knee" as you put it. The point is called the saturation pressure of CO2 at 20 °C, and this always has the same value. If you have pure CO2 in a container, and it contains liquid, then if it is at 20 °C it will always exert 58 bar. I have a nasty engineering habit of rounding off a bit too frequently - the actual value is 57.3 bar (www.ddbst.com/en/EED/PCP/VAP_C1050.php). Regardless what cartridge you use, the saturation point at 20 °C (the knee) will always have a density of 195 kg/m³. I have looked in another source (Perry's Chemical Engineers' Handbook) and interpolation gets me 203 kg/m³. Close enough. That means your 12g cartridge will run out of liquid when there is 2.9g remaining (0.195 g/ml x 15 mL). This is also true regardless of whether that cartridge was filled with 12.5 g, 12 g, 11.7 g, or even 8 g to begin with. You could try figuring out the mass consumption rate per round (which will undoubtedly be firearm related) and if it remains constant figure out how many shots you need to fire to get down to 2.9g. See whether this corresponds to the drop off that you see. PS Regarding the homework - depressurising to 1 bar absolute actually gets you below -70°C. Go see the follow up video if you have time: kzbin.info/www/bejne/q5-Zd5qLa8mZhqc. You start forming dry ice at any pressure below 5 bar. That is why there is the big blank region at the bottom of the pressure-enthalpy chart. That is a region of solid-vapour equilibrium - there is no liquid phase.

[@MartinHealy]

@@ProcesswithPat Hi Pat, Thank you so much for another fulsome response. I have learned a great deal from you and the mystery surrounding the science behind the humble CO2 cylinders is now largely dispelled. The CO2 pistols are pretty crude really. They don't have regulators in between the cylinder and the transfer port into the breech behind the pellet. A simple spring driven hammer is released by the trigger and strikes the valve releasing cylinder pressure CO2 behind the pellet sending it down the barrel. So the number of shots per cylinder is generally around 50/60 but will depend on many factors: - how hard the hammer is driven onto the valve and hence how long the valve is held open; - whether the hammer bounces on the valve and so opens it several times wasting gas; -ambient temperature affects the starting temp and pressure of the cylinder and how quickly the pressure in the cylinder rises after each shot. Hence the problem with semi-autos being fun to shoot rapidly at say 1 shot per second the CO2 temp keeps stepping down and the cylinder pressure steps down and hence the muzzle energy steps down causing the POI to step down. Some pistols such as the SA10 (see my review - kzbin.info/www/bejne/hniuqneKq72Babc ) have a drop out magazine that holds the cylinder and valve. I have recommended buying a spare magazine so that after firing 8 shots the magazine can be ejected and put into a trouser pocket to warm up and the spare magazine put into the gun for the next 8 shots. This would improve POI consistency. Am I right in thinking that although 12g CO2 cylinders are universally zinc plated they would perform better in pistols if they were painted matt black to absorb heat better? If I get some time I will try to make a video testing the cylinder temp and muzzle energy during rapid firing. I will send you a link. Many thanks again for all your help. All the best, Martin

[@MartinHealy]

@@ProcesswithPat Hi Pat, Sorry I forgot to say thanks for sharing the CO2 vapour pressure tables. At first it made no sense until I twigged and did the Kelvin to Celcius and kPA to BAR conversion and hey presto go the confirmation of 57.5BAR at 20C. Cheers, Martin

[@rubensluz9627]

Friend, your video is very good! Quite detailed. Just an observation, it would be interesting to check the theoretical pressure values again at a temperature of 50°C. The pressure should increase to just 65-66bar or kgf/cm³. In the table, in 11:15, the unit of measurement is "kg/m³". I believe it was interpreted as "kgf/cm²". The first unit is about density, the second about pressure. For reference, I personally heated a 12g CO2 cylinder to a temperature of 100°C with cartridge in good shape. Thank you for excellent material!

[@ayushsaxena7770]

This is genius. I'm process engineer trainee at worley and I learn so much from your videos. First time I saw the application of thermodynamics charts. I suggest you to make such videos.

[@ProcesswithPat]

Awesome! Hope they’ve put you on some interesting projects! Go kick arse!

[@rasmussverdrup7479]

Constant density lines is a weird concept that I never thought about before. Great video.

[@ChemEngWeekly]

Amazing concept for this video pat! A practical application of gas laws if I’ve ever seen them, so kudos to you for that 👍 👍

[@ProcesswithPat]

Glad you enjoyed it!

[@ozguryusufkavukcu3449]

perfect video for all about co2 thanks

[@xse345]

Very Interesting video 👍👍

[@beyondwhatisknown]

Those cartridges fail by blowing through the sidewall and opening up completely, if the pressure inside is high enough. However, I did my experiments with the top already pierced. The way to raise the pressure quickly enough so that the leakage through the open hole becomes insignificant is by using a powder that generates a lot of gas volume quickly, and then further increases the pressure of that gas because it also generates a lot of heat. To do this, fill the empty CO2 container with black powder, and use a long fuse that is narrow enough to fit through the piercing. These experiments are best performed at an age lower than eighteen, just in case a government representative discovers your fine workmanship and then refuses to view the experiment as the fun that it really is.

[@ProcesswithPat]

Thank you for your service to science! (If not to HSE) I’m pretty impressed that you found the cartridge afterwards… how far did it fly? Not sure your experiment can be read off of my chart.

[@beyondwhatisknown]

@@ProcesswithPat I used the green CO2 cartridges from a soda siphon. They travelled about 150 feet. If contained, the surrounding shrapnel would travel further and faster than expected. The zip-thwack-boom sound indicated supersonic velocity of small pieces. I never got in trouble for my experiments, but I was twice asked by professionals to apply for a job at CSIS. Later, CSIS refused my written freedom of information request. Two of my smart friends complained about their phone lines being tapped. Things are not quite what they seem and one can never really know.

[@pegasz]

Hey Pat! Having some thermodynamics in high school right now, and as a mountain biker I became interested in the phenomenon of the cartridge becoming cold after usage. I discussed it with my teacher but got nowhere so far. I THINK it relates to 1. decompression and therefore it getting cold and 2. the conversion from liquid to gas which needs energy (takes it from the air, which then becomes cold) Could you bring some light into this?

[@Fredengle]

HI PAT have a question for you may be you can answer I just bought a fire extinguisher it's powered by a 33 gram co2 cartridge technical this product is supposed to be tested but in theory would this not almost be a giant seltzer bottle if it a metal fire extinguisher provided by 33 grams of co2 as previously stated this unit is supposed to be tested but I would assume if the metal cylinder is in good condition it's probably fine ? I mean in a seltzer bottle directions it does not say anything about hydro testing I would guess the answer is as long as it's in good condition I would bet it's fine but I am sure this is the part where you would say you would think it should be finner but wish to disclaim liability in case of a surprise failure sound right? Thoughts please thank you

[@shoeoffhead3692]

Amazing video! Is there a way to get this chart without the logarithmic values or some way to get the numeric pressure values for certain temperatures? I can only guess since the chart is logarithmic. Thanks!

[@ProcesswithPat]

Yeah absolutely. The logarithmic axes are necessary because the values on these types of charts span pretty wide temperature ranges, so you need them so they don't become unwieldly! Your best bet is to use Antoine's equation for CO2 (here is a link to NIST: webbook.nist.gov/cgi/cbook.cgi?ID=C124389&Mask=4&Type=ANTOINE&Plot=on) this will give you the saturation pressure & temperature.

[@argiirizarryrealtor]

Que te mejores pronto amigo

[@JetSnake128]

Can they be refilled with compressed air?

[@elchochos8948]

Hi Pat, I’m currently working on a project that involves using one of these things as propulsion for a small car, I came across your video and I'm wondering if there's a practical way to measure the force exerted through the discharge of CO2 when you pierce them. Any advice would be greatly appreciated.

[@0LMG]

Do not pierce them.

[@Fredengle]

HI PAT in case it some how got deleted it have a metal cylinder fie extinguisher powered by a 33 gram co2 cylinder this unit is supposed to be hydrotested but it seems it almost a large seltzer bottle I would imagine your answer would be theoretically it should be fine if the cylinder is in good condition but you also say you would like to disclaim liability in case of a suprise failure? Sound right ? Thoughts please thank you

[@Fredengle]

In case I was unclear I think as expecting to use this as an untested cylinder like previously stated I would bet nothing terrible would happen but I would guess she you answer is its probably fine but you would also like to disclaim liability in case of a surprise failure sound right thoughts please thank you

[@pavithraa2915]

Hi Pat.Are you in linked in?kindly share the id

[@ProcesswithPat]

You can click the link in the channel banner (bottom right corner).

[@earthenscience]

These things fail in weird ways. Guy put one in his hot truck, then he puts it in his house for a while. House was under 100 degrees. Then it just randomly explodes in his hands.

[@generalafton8955]

0:26 are you sure about that, my bike holds about 40 psi, my sisters are the same, and my parents is as well, we have different sized rims, and different brands of bikes, 120 psi is a lot, my grandparents 5th wheel used 90 psi on all 4 tires. that then i have never seen a car that uses 30 psi in the tires

[@ProcesswithPat]

Yep. On my road bike with 23c (narrow) rims I pump up my tyres to 8 bar. Check it out online if you doubt it!

[@ARCHSTANTON61]

120 PSI IN A BIKE TIRE ? ARE YOU CRAZY..

[@ProcesswithPat]

www.bicycling.com/repair/a20004232/how-to-achieve-the-perfect-bike-tire-pressure/#:~:text=Pump%20it%20up.,tires%2C%2040%20to%2070%20psi.

[@brianstranyak1049]

Road bike tires are inflated to ≈90-160 psi.

[@Rizeon1]

you made lots of mistakes brah

[@ProcesswithPat]

Point them out and if they are mistakes I’d be more than happy to correct them. Brah.

[@unclenemononame]

Hi, Somewhere in the comments. I noticed they were using 12g cartridges for their airgun. A lot of detail. The question was where to find some type of chart for determining the max amount of fill to the point where the pressure drops off. Here is a chart for CO2 pressure/temp scale www.warpig.com/paintball/technical/gasses/co2pv.gif