Cylinder to Cylinder gas transfer (filling)

[TexasMike]

For some reason, I got to thinking about filling cylinders from other cylinders...and this question popped in to my head...

Cylinder A is a 80cf filled with 3000psi of gas

Cylinder B is a 40cf that is completely empty (ambient pressure...assume 1 atmosphere)

If we were to connect the two with a hose, and then slowly open the valves, we know that eventually the two would equalize pressure.

The questions are A) what volume of gas will be transferred? and B) at what pressure does equalization take place?

Please show math if possible so I can follow along with your answer.

 

[MikeS]

Assumptions
The true capacity of the AL80 at 3000 psi is the equivalent of 80 cubic feet at 14.7 psi (probably more like 77.4 )

The true capacity of the AL40 at 3000 psi is the equivalent of 40 cubic feet at 14.7 psi

The interconnection hose has no volume


Then
The capacity of the AL80 = 0.392 cubic feet (80/3000*14.7)
The capacity of the AL40 = 0.196 cubic feet (40/3000*14.7)

Originally the volume is 0.392 cubic feet at 3000 psi
Expanding the volume to 0.588 cubic feet (0.392 + 0.196) reduces the pressure to 2000 psi (0.392/0.588*3000)

The Al80 now holds the equivalent of 53.3 cubic feet at 14.7psi (2000*0.392/14.7)
and
The Al40 now holds the equivalent of 26.6 cubic feet at 14.7 psi (2000*0.196014.7)

 

[Uncle Pug]

Anyway...
Lets pretend that an 80 holds 80cf and a 40 holds 40cf.
Transfill the full (3000 psi) 80 to the empty (absolute vacuum) 40.
You have now increased the volume by 50% to 120cf
And decreased the pressure by .66666667 (80/120) to 2000psi.
And the 40 now contains .66666667 of 40 or 26.666667 or 27cf
And the 80 now contains .66666667 of 80 or 53.333333 or 53cf
And since 27+53=80 we see that matter was neither created nor destroyed in the process.

 

[TexasMike]

I got the drysuit....

I'll come let you and shane play u/w tour guides any day.

 

[Uncle Pug]

Would you be willing to go ground UPS?

 

[sheck33]

P1 x V1 + P2 x V2 = P3 x V3 at constant temperature

P1, V1 and P2, V2 are the volumes and pressures of the 2 tanks before connecting them, P3, V3 will be pressure and volume of the connected pair. Note: the volumes in this formula are the ACTUAL inside volumes of the tanks used. This by the way would be a reason to designate tanks by their actual volumes instead of by how much air they hold at some workingpressure. To me that makes way more sense.

anyway

 

[Uncle Pug]

what's the internal volume of a 40?

 

[sheck33]

Uncle Pug once bubbled...
what's the internal volume of a 40?

it's .196 cuft, see MikeS's earlier post.
you can calculate this for any tank.

 

[Uncle Pug]

sheck33 once bubbled...
it's .196 cuft, see MikeS's earlier post.
you can calculate this for any tank.

 

[sheck33]

math is fun once you get it