# Darthrambelt: (principal has wide applictaion)

### #51

Posted 31 December 2011 - 08:58 PM

You can't really know the final volume, because the barrel adds volume because the dart has already started moving.

PV=nRT is used in stuff that isn't going to change. It assumes that you have 3 of the 4 things that aren't R, and that you are measuring a gass in only one state.

I THINK you might be looking for the Combined Gas Law, or P1V1/T1 = P2V2/T2, In which you can edit out P, V, or T, and get 3 different equations, Charles's, Boyle's, and Gay-Lussac's.

So, let's say you have a plunger at room temp (70=21.1=294.1), is at atmospheric pressure (1 ATM), and has, oh, 1 liter (1000 mL) of gas in it.

Then it ends up at, say, just for a pluggable number, .01 liters (10 mL). Not bad in terms of deadspace.

So, 1000 ATM * 1mL / 294.1 K = ?ATM * 10mL / ?K. Just make up a number for either temperature of pressure, and then you would se the relationship.

Do you know what a fire piston is? It's an old device used to start fires. You would put the kindling in the plungertube, then you'd put the plungerhead+rod in, and push. The volume would decrease, the pressure would increase, and the temperature would increase and ignite the kindling.

Some of what Doom is saying is slghtly more indepth than what I learned in my high school chemistry class last year.

### #52

Posted 31 December 2011 - 09:44 PM

Yeah, I just didn't know how to determine how much of a change in each would occur when neither was held constant.

You would use another relationship that corresponds with the situation you are using. As this situation has negligible heat transfer to the outside, adiabatic relationships determine how much the pressure (or volume) changes for a change in volume (or pressure).

Basically, substitute the adiabatic relationship P * V ^ gamma = constant where you might use P * V = constant for isothermal processes.

So for this you'd use:

Gamma= 1.4

V= Liters

P= ATM

M= kg

T= Kelvin

?

Sure, all that would work aside from M, which is in g/mol. Just make sure the units work out by using conversions as appropriate.

Thanks a ton for taking the time to explain this btw.

Sure. I'm happy to help.

You can't really know the final volume, because the barrel adds volume because the dart has already started moving.

Final refers to when the dart leaves the barrel. The corresponding volume is known for a hypothetical case or can be measured for real cases.

PV=nRT is used in stuff that isn't going to change. It assumes that you have 3 of the 4 things that aren't R, and that you are measuring a gass in only one state.

I THINK you might be looking for the Combined Gas Law, or P1V1/T1 = P2V2/T2, In which you can edit out P, V, or T, and get 3 different equations, Charles's, Boyle's, and Gay-Lussac's.

The "combined gas law" or whatever they teach in high school chemistry is derived from the ideal gas law. As I said, assuming that the amount of gas is constant between states (so either m or n is constant) you can derive other relationships.

If n is constant then n * R is constant. So P * V / T = n * R is also constant in the process. So P_1 * V_1 / T_1 = P_2 * V_2 / T_2. (I said this a few posts ago too.)

### #53

Posted 01 January 2012 - 12:55 AM

### #54

Posted 01 January 2012 - 04:32 AM

Sure, all that would work aside from M, which is in g/mol. Just make sure the units work out by using conversions as appropriate.

And molar mass of air would be the molar mass of its components x the components percentage?

### #55

Posted 01 January 2012 - 09:20 AM

Ah. This whole thread is such a mess of equations I didn't see it. And I see what you are saying about the barrel, bit you could still have draw that hasn't plunged, which would be hard to determine.

For a particular gun, the final plunger volume might be hard to determine. But if we're interested in finding ideal barrel length, we expect the plunger volume to be nearly zero when the dart leaves because if it wasn't then the pressure probably would still be above atmospheric. So this assumption is probably okay for my ideal barrel length equation I mentioned before.

The plunger volume when a dart leaves for an arbitrary gun seems to be small but not negligible, so using an estimate for the final plunger volume could be okay, too.

Admittedly, this is all very approximate. To use these relationships you have to assume that the pressure is independent of location, i.e., the pressure in the barrel and plunger is the same. This isn't true in general but it is true for "heavy" projectiles (as I defined them earlier). If you don't make this assumption then the equations have to be solved with computers.

And molar mass of air would be the molar mass of its components x the components percentage?

Yes, you can sum the components like that.

You don't need to do this if you're using the adiabatic process relationships. You can use something like the mentioned combined gas law to find the last variable you want, i.e., if you have initial and final pressure and volume and initial temperature you can find the final temperature with the combined gas law or another adiabatic relationship.

**Edited by Doom, 01 January 2012 - 09:49 AM.**

### #56

Posted 01 January 2012 - 08:11 PM

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