Is My Logic Correct Here?

[mark.f]

Simple chemistry problem, but for some strange reason I cannot, for the life of me, "double check" to make sure my logic is correct before continuing.

You have two tanks at two different pressures and two different volumes, with a ball valve between the two, then, you open the ball valve and allow the pressures to equalize.

To solve for this pressure, this is the method I use:

I realize that P*V is equal a constant for a sample of gas. Therefore, I assume that P₁*V₁ + P₂*V₂ = P_f*V₍₁₊₂₎ and then solve for P_f.

Is this logic correct and accurate? I have no earthly clue why, but for some reason I cannot verify this on either the internet or in my AP Chem study book thingo I bought last year.

Here's some sample problems.

I have a 60mL tank at 3 atm and a 1200 mL tank at 5 atm. Final equalized pressure would be ~4.9 atm?

I have a 1000 mL tank at 4 atm and another 1000 mL tank at 4 atm. Final equalized pressure is 4 atm (both logically and calculated).

EDIT: if this logic is correct then I may have a simple solution to hybrid fueling woes.

[jrrdw]

"Logic" as I understand it, tells me the 2 tanks have no other physical characteristic but being equal if a hose/connection allowing contents/pressure to transfer freely between the 2. It can only be equal if free transfer is introduced in the described situation.

[mark.f]

jrrdw, the only physical characteristics of the two tanks I'm working with are the pressures because they're connected and, yes, free transfer is allowed. The important part of this situation is knowing the final pressure in the entire system if the tanks are connected (ball valve opened), with the tanks having different initial pressures.

[jrrdw]

Ok, I see the difference now. You do have gauges on the tanks? They should be accurate enough to check your math, a good comparison. Unless your worried about one tank being pushed over the pressure rating limit, baring that open the valve and watch what happens.

[D_Hall]

Assuming ideal gases and all that jazz, yes, your logic is correct.

[Velocity]

I don't see anything wrong with your prediction...it certainly makes sense intuitively. Granted, I have not taken AP Chemistry.

[mark.f]

Actually, this is for a set of hybrid fueling formulas I'm working on. The above equation in my post is part of a two-equation system which is used to derive meter pipe and chamber pressures to achieve a good, clean, stoichiometric burn.

There's gonna be a gauge on the chamber and one on the meter. So far I've set up a BASIC program to do all the calculations for me, and rounding the answers to the nearest whole percentage only yields around a 0.1% error in fueling, typically.

BUT, of course, ALL of this methodology hangs on the assumption that my logic outlined in the first post of this thread holds true.

[dongfang]

Hi,

Yes your formula is correct, although the notation is a little strange:

P1*V₁ + P₂*V₂ = Pf*V₍₁₊₂₎

which is:

P1*V₁ + P₂*V₂ = Pf*V₃

Surely you mean:

P1*V₁ + P₂*V₂ = Pf*(V₁ + V₂)

BTW, I am working on the same program, just in JavaScript. When done, I will have it hosted somewhere (here, hopefully), and u can all use it.

Regards
Soren

[SpudUke5]

I am working with programs as well but its java rather than javascript (I take java class at my school). I have created a couple of GUI programs but still need to improve. Once i can learn how to make the programs applets, then i will put then on the internet.

Sorry to hijack by the way.

I am learning about this kindof stuff in chemistry now, and im pretty sure your correct, sounds logical.

[mark.f]

Thank you dongfang. The notation is a little strange, I'll admit, but the equation is equivalent to yours.

This is a good thing. I'm now off to another thread to do a write up on the formulas I derived using this logic.

Thanks again.