Potential Energy in a Gas Cylinder

[FirNaTine]

I am trying to estimate the amount of energy stored in a firefighting breathing air cylinder, so I can give my students a grasp and respect of the danger of mishandling their cylinders.

I have looked around for some basics, and found a few threads referncing NIST data Post 5 on physics forum, but I can't seem to find the source.

695D Cylinder on second page is what we use.

It is a 6.75 liter cylinder pressurized to 310 bar (4500 psi) to provide around 45 minutes working time.

In the physics forum thread, they reference a 490cc cylinder at 200 bar having 19,237 J energy using NIST data.

If I scale that linearly and divide the 6750cc volume of the cylinder I use versus the 490cc example I get 13.776 times as much volume and 310bar/200bar 1.55 times as much pressure.

(6750cc/490cc)(310bar/200bar)(19237J)=410,749 J

Does this seem right?

Continuing on NIST TNT Energy Equivalent is 4184J/g

(410,749J)/(4184J/g)=98.17g

So somewhere around the same energy as 98g of TNT?

Am I doing it right?

Edit: I realize that this may be ignoring whether or not it is an adiabatic release....

 

[DominionSeraph]

Converting to grams of TNT isn't going to be useful. Your students aren't going to have experience with it, and considering the starting volume of the tank is much bigger, even if the tank were to evaporate you wouldn't get the same shock wave.
The failure point is going to be the valve and the danger is going to be the SCBA tank becoming a projectile, so it's more akin to a sledgehammer.
I'd pass around a SCBA tank, telling them to get a good feel for the heft. Then show them this: http://www.youtube.com/watch?v=tyINNUaXa8Q

 

[HibyPrime1]

Here's a weird way of looking at that energy. The Tesla roadster has a 185kW engine (248hp). It doesn't produce 185kW throughout the RPM range, it rises with RPM, but lets assume it produces an average of 100kW throughout the range. This isn't accurate but it's close enough for some napkin math. It also takes the tesla 3.9 seconds to get from 0-60mph.

410kJ is enough energy to provide 100kW for 4.1 seconds, long enough to get the 2700lb car up over 60mph.

Theoretically if that calculation is right that there is 410kJ in that cylinder, you could accelerate a Tesla Roadster fast enough to kill yourself in an accident. I'd say that'll work for an explanation of why you should be careful with it lol.

Some references:
http://www.brosen.com/files/torque.png I just roughly guessed that the average on that curve is 100kW. I'm pretty sure it's higher than that, but I'm lazy.

Wikipedia for 0-60 times and weight.

1 joule per second = 1 watt. The math is pretty simple once you know that.

 

[FirNaTine]

DominionSeraph point taken about density comparison and lack of experience with TNT. I love the video as well, but we can experience catastrophic cylinder failures, though they are thankfully rare and usually contained.

The issue is the newer carbon fiber wrapped cylinders are much lighter, but they are susceptible to abrasion and nicks from use. We train in concrete buildings lined with basically furnace tile and that is rough on cylinders over many uses.

The second part is they are also exposed to very high heat that could also lead to failure, both as pressure can been increased by it and the resin coating the fiber wrap is potentially weakened . They actually have rupture discs built in that should dissipate that pressure first. They fail around 5500psi, and the cylinders are designed for a minimum burst somewhere around 8000. But that is before use.

I have never personally witnessed a failure of that type, but it has occurred. We inspect then regularly, before and after use, but we refill our own cylinders also. Part of the procedure is a visual inspection for damage. I want to reinforce the need for a careful inspection, as part of a student firefighters training is learning to fill their own cylinder and I won't be there to watch once they graduate. We use a fragmentation chamber when filling also.

HibyPrime1- honestly the similarity in energy level shouldn't surprise me. It takes a four stage compressor powered by three phase 208 volt service drawing I think 40 amps per phase a long time to fill the cascade station we use to fill the cylinders. I know most of that is waste heat during compression though. I hadn't thought of looking to compare it that way.

Thanks to both of you for taking time to respond!

 

[Ben90]

Tell them the energy in the canister is 2559019000000000000000000 electron volts.