SpudFiles

If you pressurised a tube of air to 100 psi, and then rapidly (ie. a few milliseconds), reduced the volume of the tube to 1/4 of its original size, the air should reach a pressure of 400 psi.

My question is, how hot would this air become, and how would that affect its speed of sound?

It depends on the type of tube, really. If it's copper, you can count on the pipe absorbing a lot of the heat energy produced. PVC however, is a half decent insulator.

Higher temperatures would increase the speed of sound within the gasses.

(sorry, I kind of danced around the "how hot?" question.
I don't know for sure, but if I had to take a guess I'd say about 600F IF the air was compressed from a normal atmosphere to 400 psi very quickly)

Hi,

Try to see

http://en.wikipedia.org/wiki/Adiabatic_process

- If your pressure increases to 400 psi, then it is implied that the temperature did not change.

The computations are not dead simple... but with enough effort, sure they are understandable. The graph on the wikipedia shows work done by the gas - in your case that work is negative.

...

So it would seem that....

- Approximate air to be ideal, diatomic.

Then alpha = 5/2
upsilon = (7/2) / (5/2) = 7/5

V T^alpha = constant.

Before compression: V T^alpha = V * 293K^alpha = 1.47 * 10^6 V K^alpha

After compression = V/4 T'^alpha = 1.47 * 10^6 V K^alpha

T'^alpha = 4 * 1.47 * 10^6 K^alpha

T' = (4 * 1.47 * 10^6 K^alpha) ^(1/alpha)
= 510 K
= 237 C

And

P^(upsilon - 1) * T^(-upsilon) = constant

Before compression:
(1 bar) ^(upsilon - 1) * (293 K)^(-upsilon) =
bar ^ (upsilon - 1) * 3.52 * 10^-4 * K^(-upsilon)

After compression:

P'^(upsilon - 1) * (510K)^(-upsilon) = bar ^ (upsilon - 1) * 3.52 * 10^-4 K^(-upsilon)

P'^(upsilon - 1) = bar ^ (upsilon - 1) * 3.52 * 10^-4 * K^(-upsilon) / (510K)^(-upsilon)

P' = bar * (3.52 * 10^-4 / 510^(-upsilon)) ^(1/upsilon)

= 1.74 bar


That looks funny -- can anyone see if I did something wrong?

OOPS: I remembered the problem wrong - I took it to be V/4, not 400 psi.

Regards
Soren

This is a job for GasEq ...

Air compressed to 100 PSI, how long does it sit there? Compressing to 100 PSI will heat the air, letting it sit will allow it to cool off.

GasEq will tell you the final temperature, pressure and speed of sound.

Assuming the gases are not allowed to cool after the first compression (this is what you would get if a high capacity compressor pressurized the gun chamber directly, without a storage tank) ...

Adiabatic Compression/Expansion calculation for air in GasEq.

For air compressed from 14.7 PSIA to 114.7 PSIA (100 PSIG, 7.8 ATMA);
Temperature goes to 536 K (505F)
Pressure 7.8 ATM
Volume 0.229 of the original
speed of sound 461 m/s (1512 FPS)

Copy previous products/results to reactants

Now compress 4:1;
Temperature goes to 889 K (1140F)
Pressure 51.8 ATM
Volume 0.25 of the previous
speed of sound 586 m/s (1920 FPS)

All of the above is for an adiabatic (no heat lost to the chamber or outside world) system. In the real world the first compression would be done with a compressor. Most of the heat generated would be transfered to the storage tank, which would heat up only a couple degrees since the heat capacity and mass of the air is tiny compared to the heat capacity and mass of the compressor's tank.

When the compressed air from the compressor is used to fill the gun chamber the air will cool off. If it was at ambient temperature in the compressor tank then it will be cold in the gun. As with the compressor, the gun's much higher mass and heat capacity means it'll warm the air up fairly quickly, and the gun will cool by very little.

Download GasEq and fiddle with it to reproduce what you are trying to do.

jimmy i'd have to say that was the most useful, informative, and on topic reply i have ever seen.

Somewhat related: http://www.firepiston.com/

PVC Arsenal 17 wrote:Somewhat related: http://www.firepiston.com/

Has anyone here ever tried making one of those?

I have. It is a very simple concept. Few people realize how quickly and high the temperature rises when you rapidly compress air. The answer to the question is hot enough to ignite flammable materials. If I place my thumb over the end of my high pressure pump and rapidly push the handle there is a noticeable spike in temperature.
That is why oil for pneumatic tools is not a flammable variety.

Check the copper pipes on top of your compressor sometime after a long run, should be too hot to touch from the heat of compression.

This is the grounds for how two-stage light gas guns work, a primary powder charge slams a piston against a compressed cylinder of hydrogen and a burst disc, the compression heats the gas to thousands of degrees making the gas extremely light (hence it moves like a mother). Sends projectiles out at hypersonic velocities.


Has anybody ever considered trying this idea out in a spudgun? A hybrid would be good grounds for something like that...

I'm surprised that no one has mentioned yet that this is the basis for how a diesel engine works. Theoretically, it could work in a hybrid, but depending on your fuel, you would need an INSANE amount of pressure to get there (I think the compression ratio for detonation of gasoline is somewhere around 14:1? Correct me if I'm wrong here). Plus you would need a really fricken strong burst disk to be able to to withstand that until it goes off. But yeah, it could still be done.

My dad and I tried making a traditional firepiston out of wood once, but we couldn't find good enough quality bamboo to make it with. They just split from the pressure all the time.

Dude, that fire-piston thing is sweet. I'll have to make one sometime. What's on the end of the rod that heats up?

Take your avarage pneumatic cannon, use a lightweight, airtight piece of
"ammo" ( a patatoe might even work once)better yet, an O-ringed piston.
Put a reducer on the end of the "barrel" and attach a smaller diameter barrel onto the front ( or elbow it back over)

put some flamable substance in the barrel and load ammo...


it should work...but nobody tried it yet

Brian the brain wrote:Take your avarage pneumatic cannon, use a lightweight, airtight piece of
"ammo" ( a patatoe might even work once)better yet, an O-ringed piston.
Put a reducer on the end of the "barrel" and attach a smaller diameter barrel onto the front ( or elbow it back over)

put some flamable substance in the barrel and load ammo...


it should work...but nobody tried it yet

Or nobody talked about it, because that would be a flaming projectile...

paaiyan wrote:

Brian the brain wrote:Take your avarage pneumatic cannon, use a lightweight, airtight piece of
"ammo" ( a patatoe might even work once)better yet, an O-ringed piston.
Put a reducer on the end of the "barrel" and attach a smaller diameter barrel onto the front ( or elbow it back over)

put some flamable substance in the barrel and load ammo...


it should work...but nobody tried it yet

Or nobody talked about it, because that would be a flaming projectile...

Which would make it unfathomably cool.

PVC Arsenal 17 wrote:

paaiyan wrote:

Brian the brain wrote:Take your avarage pneumatic cannon, use a lightweight, airtight piece of
"ammo" ( a patatoe might even work once)better yet, an O-ringed piston.
Put a reducer on the end of the "barrel" and attach a smaller diameter barrel onto the front ( or elbow it back over)

put some flamable substance in the barrel and load ammo...


it should work...but nobody tried it yet

Or nobody talked about it, because that would be a flaming projectile...

Which would make it unfathomably cool.

Unfathomably cool, yes. But also against forum rules...