Boyle's Law question

[oszillodrom]

Coming from a (physical) chemistry background, the only law I use in diving is the ideal gas law, it has (almost) everything:

pV = nRT

where p is pressure; V is volume; n is moles and therefore directly proportional to the mass of gas; R is a constant; and T is temperature.

Edit:
To adress OP's problem, your result of 0.39 cf for the internal volume ('water volume') and 80 cf for the volume of uncompressed air are correct. When guesstimating the size of a tank, you mixed up your units.

Americans often give the capacity of a tank in volume of uncompressed air (which personally I consider very practical for SCUBA) while Europeans etc. will give you the 'water' volume in liters, so an Al80 tank roughly corresponds to an 11L or 12L tank in Europe or Asia.

 

[dumpsterDiver]

Coming from a (physical) chemistry background, the only law I use in diving is the ideal gas law, it has (almost) everything:

pV = nRT

where p is pressure; V is volume; n is moles and therefore directly proportional to the mass of gas; R is a constant; and T is temperature.

Edit:
To adress OP's problem, your result of 0.39 cf for the internal volume ('water volume') and 80 cf for the volume of uncompressed air are correct. When guesstimating the size of a tank, you mixed up your units.

Americans often give the capacity of a tank in volume of uncompressed air (which personally I consider very practical for SCUBA) while Europeans etc. will give you the 'water' volume in liters, so an Al80 tank roughly corresponds to an 11L or 12L tank in Europe or Asia.

0.39ft³ = 11.044L

So he did not mess up his units

 

[mrdre]

You can get to the same numbers many different ways.

Alum Catalina 80 is 11.1 liters. 1 liter is 0.0353 cubic feet, therefore: 11.1 * 0.0353 ~ 0.39183 ~ 0.39 cft

"80" means it will hold 80 cft under 3000 PSI. One atmosphere is ~14.69 PSI, therefore 80/3000 * 14.69 ~ 0.3917 ~ 0.39 cft

 

[oszillodrom]

0.39ft³ = 11.044L

So he did not mess up his units

No, that is correct. I meant when he wrote:

"I don't have an actual tank in front of me but taking some guesstimate measurements, 3.14 x (.33')^2 x 2.5' = 85 cf. Pretty close to the standard 80 so the actual volume of an 80 cf tank should be 80 cf...? Not 0.39 cf."

 

[Agility]

with the metric system a 10l cylinder will hold 10l of water - or 2000l of air at 200bar :blinking:

 

[The Chairman]

Is the actual volume of an 80 cf tank only .39 cf? The 80 is the volume of the air before being compressed?

Good job. Your answer is correct. The tank holds approximately 80cf at it's rated pressure (3,000 psi).

Here's another way to look at it. 3,000psi/14.7 psi/atm= 204 atm. 80 cfm/204 atm = .39 cfm/atm

 

[BradMM]

Thanks to all, I just love learning more about all this! The title of this message was based on the question falling under the Boyle's Law section of the book the question came from.

First of all, I never questioned where the "80 cf" capacity came from for the standard aluminum tank I use. It's the volume of UNCOMPRESSED air, not the volume once compressed... i.e. the "water capacity." That was the heart of the question. Without that conceptual understanding, it doesn't make sense. Now that I get that, the formula makes perfect sense.

I also don't know the inside diameter of a tank, I was approximating the outside diameter which may be useless if the tank wall thickness is significant.

Like I said, I'm really enjoying just learning about the science behind it all.

 

[Lorenzoid]

I guess the term "water capacity" is popular because it emphasizes incompressibility--everyone intuitively knows water is incompressible for all intents and purposes. But it just means the volume of the tank when the pressure of the gas inside is one atmosphere--when the tank is "empty."

 

[NAM001]

p1v1=p2v2 is a formula that states that they are equal in that they give that same amount of compresed cuft in the tank. The transpositions of hte formula's is what is needed to make this work. The pretucular transposition is tied to what you want to know ans what you are starting with. As written p1v1 the statement says that if you take a tank with a water volumn filled with x psi you will have a given amount of compressed gas. When you put the = sign in it then you are comparing 2 tanks with independant caractoristics and making them =.

Whrn comparing 2 al80's the v1 and v2 is the same. So what is said is that teh gas in the tank in the tank is = to the ratio of the tank psi's beiong compaired.
eg.. an al80 with 3000 psi ans an al 80 with 2000 psi in it. with the v's v-being the same, the 2000psi tank contains 2/3 the gas that the 3000 psi tank has.

if yo transpose the formula to p1/v1 = p2/v2 you find that the answer to both halves is the same, and therefore p1/v1 = p2/ v2. You use this to determine if your tank has enough gas to do the dive. if you need 50 cuft to =do the dive then a full 80 will do it but will another al 80 with 2000 psi be enough??? 2000/3000*80=??? You can do this only because the empty water volumns are the same. so lets look at what the v's are in a al 80 the V is equal to working volumn devided by working pressure. or 80/3000*15 = water volumn of tank. to make it easier lets use 80/ 200 bar and that gives you a water volumn of .4 cuft. So 200 bar of .4 vulumn is 80 cuft. if you have 200 bar and a water volumn of .6 then you have 120 cuft when pressurized to 200 bar. So that is how to compare 2 tanks compressed content. The formula goes much further than this limited use. Now the v's used before was teh v of water volumn. Lets change teh v's used to be the amount of copressed gs in the tank.

That gives us p1 equaling the pressure of a tank & v1 is the cuft at that pressure. or 200 bar and 80 cuft for a full al80.
So p1v1= p2v2 only if we are talking about 2 tanks with the same water volumns or the same tank at different pressures.

With that understood then its is clear to see that p1v1=p2v2 when 2 al80s are involved when one tank has 3000 psi in it and the other has 1500 psi in it does not work. However if the formula p1v1 computres compressed volumn then the formula is true for the given that compressed volumn is also equal. so p1v1=p2v2= same compressed volumn. That drives the transpositon to become p1/p2=v1/v2= compressed volumn given water volumn is the same.
You use this when computing how much gas you have when you do not have a full tank. so with a 3000 psi tank filled to 1500 you have 3000/1500 or 2. with the seme tank both water volumsn are the same so the compressed contents of teh 3000 tank is 2 times teh 1500 tank.

All presty basic so far. but now... lets compare 2 different tanks. Now this sounds a bit screwwy but this has hapened ot me. the boat dropped my tank overboard ans teh valve cracked open . it was a lp95 ans they recovered it with 150 psi in it still venting. They gave me a al100 s a replacement and it had say 2700 in it. which tank had more air in it. The 95 was at working pressure so it had 95 cubes in it. the al100 @3000psi had 2700 in it should be computed by 2700/3000*100 or 90 cuft. I have 5 cuft less than with the lp95 so the dive plan needs to be reviewed. I did not have to because i was diving with others that were diving al80s and limits on the dive were based on thier smaller tanks. as the formula goes

lp95 vs al100 pressure in bar* water volumn in cuft

lp95 180 * .53 cuft or 95 cuft
al100 bar * .5 cuft or (95 cuft to match the lp95)


180*.52cuft= bar*.5 or 95/.5=al100 bar or 190=al100 bar

the al 100 must have 190 bar to be equal to the lp95 at 180 bar
bar to psi is 190*14.7 or 2793 psi the al100 had 1700 adn it needed 2793 to be equal to the lp95.

another way to look at this to transpose from the start to p1/v1 = p2/v2 or 180/.53= ???/.5 diferent tanks have different v's so the p's must be different also.

I have always thought the PV stuff as lame cause when taught it always uses one aspect of hte pv formula to a specific use and leave the rest untalked about. IE "in a tank ,,,,the gas contained is directly proportional to the pressure it is subjected to." Which is used to teach one tank varying pressure effecting on the cuft contained ni the tank. It is great teaching phylosophy so long as all tanks are the same.

I recently had to have this very discussion with my other half who recently certified OW because she thought she had more gas than me because she had 3000 and i had 2500 in my tank. Normally she would have been right but i was diving my lake tank which is a lp120 and she was diving a al80.

 

[mrdre]

Im not sure i understand what you are getting at. BUT. the formula does not look right. It should be P1/V1=P2/V2....

No, Boyle's-Mariotte Law is P1V1 = P2V2, which means 1500 * 80 = 3000 * 40.