Gas Law

[Walter]

What could be a better fit than Charles Law?

Since tanks have constant volumes, Charles' Law doesn't fit at all. It is, however, ideal for hot air ballooning. A law that deals with temperature/pressure relationships is better.

No one has hit it yet.

The physical principle known as Charles' Law states that the volume of a gas equals a constant value multiplied by its temperature as measured on the Kelvin scale. The law's name honors the pioneer balloonist Jacques Charles, who in 1787 did experiments on how the volume of gases depended on temperature. The irony is that Charles never published the work for which he is remembered, nor was he the first or last to make this discovery. In fact, Amontons had done the same sorts of experiments 100 years earlier, and it was Gay-Lussac in 1808 who made definitive measurements and published results showing thatevery gas he tested obeyed this generalization.

Gay-Lussac carefully investigated the ratio of the volume of hydrogen gas that combined with a given volume of oxygen gas to form water. He found the oxygen could combine with exactly twice its own volume of hydrogen. There were similar simple volumetric ratios for other reactions between gases and if the product of the reaction was also a gas, it filled a volume simply related to those of the combining gases.
Gay-Lussac combined research with his passion of hot air balloons. Because nitrogen is lighter than oxygen, Gay-Lussac reasoned there might be proportionately less oxygen in the air at higher elevations. To find out, in 1802 he went up in a balloon to 23,000 feet (a record for 50 years). He found the proportions nearly the same.

What you are looking for is Amontons' Law which actually predates both Charles and Gay-Lussac.

Amontons developed the air thermometer--it relied on increase in volume of a gas with temperature rather than the increase in volume of a liquid. Amontons failed to discover Charles' law for the same reason as Boyle: a temperature scale did not exist. Using the air thermometer, Amontons (1702) devised a method to measure change in temperature in terms of a proportional change in pressure. Although Amontons' law became the most obscure of the gas laws, it was this work that eventually led to the concept of absolute zero in the 19th century.

 

[The Chairman]

Anyone else want to tell me I screwed up???

 

[scubatexastony]

Anyone else want to tell me I screwed up???

The key word was obscure. That law would be Guages law. Put a pressure gauge on the hot tank and then again after cooling.

I was wondering, do you assume the gas in the tank is at the same temperature as the outside temp, and at what point in time does the temp reach equilibrium?

 

[Walter]

Pete,

I'd guess well over 99% of all SCUBA instructors think Charles' Law applies to diving and of those few who know it doesn't, less than half could name Amontons' Law.

 

[vertaqua]

The key word was obscure. That law would be Guages law. Put a pressure gauge on the hot tank and then again after cooling.

I was wondering, do you assume the gas in the tank is at the same temperature as the outside temp, and at what point in time does the temp reach equilibrium?

I don't think Gay-Lussac's Law/ Admonton's Corrolary is all that obscure. Any open water diver should know that as pressure increases so does temperature and vice-versa even if he/ she doesn't know the name of the law. So if you leave your full tanks in the trunk of your car on a hot day its very possible your going to hear your burst disk(s) go off and scare the crap out of everyone around in addition to losing your fill. Is it important that you do a calculation before you go in the water to see how much your tank pressure will drop? Not really, its just good to know.

 

[miketsp]

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

Off the top of my head the difference between Wan de Waal and the ideal gas law at 300Bar is about 12% for N2 and 28% for He.

 

[bradshsi]

I'd guess well over 99% of all SCUBA instructors think Charles' Law applies to diving and of those few who know it doesn't, less than half could name Amontons' Law.

That's because the general consensus is that there is no "Amontons Law".

Amonton discovered that the volume and temperature of a gas were proportional earlier than Charles or Gay-Lussac. However the English speaking world tends to refer to Charles Law and the French speaking world to Gay-Lussac. I can't recall any use of the terminology "Amontons Law" in any of the textbooks I've seen.

In any event he still only described the relationship of volume vs temperature. We are interested in an isochoric process which according to my notes is either called the "pressure law" or somewhat incorrectly the "Gay-Lussac law". It is not attributed to one particular scientist.

Thus even to call it "Amontons Law is no more correct than calling it "Charles Law"

Note that even the pressure law will only tell you the change in pressure as the cylinder cools. It will not tell you what temperature the air in the cylinder will reach during filling. As I posted earlier you need the adiabatic laws for that.

Edit: Just for fun I looked out the oldest texbook I have at my desk ("Applied Heat for Engineers" from 1947 if you must know). In it the "pressure law" is simply derived from Boyles and Charles Laws.

Oh and if you do a google search on Amontons gas law you get 686 results. Searching on Charles gas laws gives you 16.2 million. The reality is that it is not in common accepted usage.

 

[lamont]

just keep it simple: PV=nRT

 

[scubatexastony]

"I can't recall any use of the terminology "Amontons Law" in any of the textbooks I've seen."

All found in the NAUI MD text book,

Dalton's Ptotal= P1+P2+P3+.....Pn

Boyle's P1V1=P2V2

Charles' V1/T1=V2/T2

Anontoms P1/T1=P2/T2
(Guillaume Amontons was a French scientist, experimenting with barometers and thermometers. In 1702, he observed the for an equal elevation of temperature, the increase in pressure of a gas was in the same proportion.)

Avogadro's kinetic theory of gases

Gay-Lussac's proportionality of combining volumes

Goes on to the General gas law, which combines Boyle's, Charles' and Amonton's as

P1V1/T1=P2V2/T2, all being absolute.

 

[spectrum]

So if you leave your full tanks in the trunk of your car on a hot day its very possible your going to hear your burst disk(s) go off and scare the crap out of everyone around in addition to losing your fill.

I seem to recall a thread from this past summer where it was shown that you'd have bigger problems than a venting cylinder if it got hot enough for that to happen. I don't have the thread or the math handy but at the thumb rule of 5 PSI per degree F it would take a wicked hot day to hit burst.

Pete