Gas Law

[spectrum]

Sometime last summer a thread ran about pressure drop after a hot fill. there was an obscure gas law menioned that was a better fit than Charles Law.

I can't find it in a search, could someone repeat what it is please.

Thanks,
Pete

 

[huskychemist]

I think it might be the Guy-Lussac Law (although my spelling might be wrong).

P1/T1 = P2/T2


In general, if the temperature goes down, the pressure will go down. This assumes "ideal conditions" though. In other words, it breaks down some at high pressures, in terms of the accuracy. But the general relationship holds, that in a fixed volume (scuba cylinder), as the temperature goes down, the pressure will go down also.

 

[The Chairman]

What could be a better fit than Charles Law? However, you might be refering to treating this as a "non-ideal" gas because of the increased pressure. Most people just don't realize that they have to use Kelvin or Rankine when they do the math. The entire concept is based on absolute temperatures as well as absolute pressures.

 

[Cacia]

I thought it was Kelvin's law from physics. When you are on a boat in the hot sun and you jump in and your tank pressure drops a couple hundered right off the bat....No?

 

[lamont]

Sometime last summer a thread ran about pressure drop after a hot fill. there was an obscure gas law menioned that was a better fit than Charles Law.

I can't find it in a search, could someone repeat what it is please.

Thanks,
Pete

If its a "better fit" law, then you're probably referring to non-ideal gas laws. That probably means either van der waals, beattie-bridgeman or benedict-webb-rubin.

It really doesn't matter, though, the deviations from ideal gas are probably swamped by uncertainty over the actual temperature and uncertainty in the actual water volume of the tank and other issues.

 

[huskychemist]

Not Charles' Law...as that relates volume and temperature. A scuba tank has a fixed volume...

And yes, the temperature needs to be in Kelvin.


Example:

A tank is filled to 3200 psi, and ends up being 35 degrees celcius. It cools down to 10 degrees when the person gets in the water...


3200 psi/308 K = ? psi/283 K

= 2940 psi


So the temperature drop did lower the psi.

 

[The Chairman]

Yeah, but is 300 bar really considered high pressure enough to consider non-ideal variations?

 

[spectrum]

I think it might be the Guy-Lussac Law (although my spelling might be wrong).

That rings a bell!
http://misterguch.brinkster.net/gaslaws.html

Is it not a better fit than Charles?

Thanks,
Pete

 

[cornfed]

What could be a better fit than Charles Law?

Since there is no volume change Charles's law does not apply here. Guy-Lussac is what you want.

 

[bradshsi]

It depends what your assumptions are regarding the gas fill.

If you want to be pessemistic you can assume adiabatic compression of the gas (no heat in or out of the system). Solving for this would give you the final temperature of the gas in the cylinder(at the end of the fill). You can then use Gay-Lussac's law to determine the final pressure after cool down to equilibrium.

If the fill is quite fast then the assumption of adiabatic compression would not be far away IMO.

For an adiabatic process (T2/T1) = (P2/P1)^[(g-1)/g]

where g (usually written as the greek gamma symbol) is the ratio of Cp/Cv

(Cp = the heat capacity at constant pressure, Cv = the heat capacity at constant volume).

For the purposes of our calculation we can assume g = 1.4, thus our equation becomes:

T2 = T1 x (P2/P1)^0.286