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Why do tanks get hot when you fill them from higher pressure tanks?

Discussion in 'Basic Scuba Discussions' started by jimmyw, Feb 21, 2013.

  1. jimmyw

    jimmyw Angel Fish

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    This is sort of a geeky physics/gas law question, but I thought someone here might be able to answer it for me or at least point me in the right direction. I've been diving for over 40 years, but I've never really understood why tanks get hot when you fill them from other tanks. I signed up here just to ask.

    I understand why tanks get hot when filled directly from a compressor, or at least I think I do. You start with a lot of air out in the atmosphere - a large volume V1. You compress that air with a compressor and it gets hot as you stuff it into the small tank - a smaller volume V2. I looked up "adiabatic heating" and I understand it. I even went through the equation for an ideal gas (PV=nRT). That equation has two unknowns if I stick in the volume change. I was able to figure out that a second equation comes from the effect of the number of degrees of freedom of nitrogen N2 and oxygen O2 diatomic molecules (PV**gamma is constant). Those two equations allows one to solve for temperature T and pressure P given the change in volume V. Gamma is derived from the number of degrees of freedom of the molecules and is also equal to the ratio of heat capacity at constant pressure to heat capacity for constant volume - roughly 1.4 for air.

    Another way of looking at why the tank gets hot (when filled directly from the compressor) is just to notice that you are running a pump and putting energy into the system by compressing the air. At least it makes sense that adding energy makes it hot. You could get that energy out again by running a pneumatic motor from the scuba tank. I'm pretty sure that one could (at least in theory if we imagined perfect compressors, no frictions, no heat gain/loss, etc.) let the hot filled tank expand out into the atmosphere and get back to where you started with all the gas at room temp and atmospheric pressure.

    But that's as far as I got. Why does the scuba tank also get hot when filled from a higher pressure tank (or a bank array of higher pressure tanks? This has always bugged me. When the array of tanks was filled by the compressor, they got hot. At that point it's just like the first case of directly filling the scuba tank from the compressor. At least in theory it could expand out and the whole thing would return to the starting temp/pressure/volume.

    So when you let the air out of a high pressure tank to fill a scuba tank, you are going from the initial high pressure small volume in the fill tank to lower pressure, larger volume, in the volume making up the fill tank plus the scuba tank. You aren't adding any energy like you did with the compressor in the first case. In fact, since the fill tank was allowed to cool after it was filled, it makes sense that it cools off below room temp. But why in heck does the scuba tank get hot? You're doing the opposite of the first case - you are now going from high pressure small volume to lower pressure larger volume. Shouldn't the air cool off? Why does the scuba tank get hot in both cases when you are doing the opposite thing in those two cases?

    I've looked on the web and found some stuff, including some questions just like the one I asked, but I'm pretty sure the answers are wrong.

    I know it's not because the remaining air in the scuba tank being filled gets compressed. The tank gets hot even if it was at a a vacuum when filled.

    Thanks, in advance, for any help on this.
     
  2. JohnN

    JohnN Solo Diver

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    You need a bit more physics/physical-chemistry.

    If the gas were ideal (remember PV=nRT is the "Ideal Gas Law"), there would be no heating/cooling on compression/expansion. Almost all gases are not ideal. The deviation from this (how much they cool when they expand or heat when compressed) is called the Joule-Thompson coefficient (Joule?Thomson effect - Wikipedia, the free encyclopedia) and is the basis of how your refigerator/air-conditioner work.

    Back to filling tanks, you should expect to see a cooling of the tanks doing the filling (their pressure is reduced) and an increase in temperature of the filled tank (its pressure is increasing).

    FWIW, Helium has a negative Joule-Thompson coefficient at 1 atm (it warms when it expands and cools when it compresses)
     
  3. awap

    awap Solo Diver

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  4. jimmyw

    jimmyw Angel Fish

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    I've been working on this for a while and I've gone through a dozen or more wikipedia articles. :) I'm certain that even an ideal gas gets hot when compressed. It's called adiabatic heating. The equations I referred to are both ideal gas law equations and if you solve them they show that you always get heating, although the amount of heating depnds on the type of gas. A monatomic gas heats more, while a diatomic gas heats less. That's where the degrees of freedom come in.

    But the gas laws apply to a complete system. The complete system is the gas in the original fill tank, and the volume of the gas in that tank is increasing. The gas flowing into the scuba tank being filled starts at high pressure in the fill tank and ends at lower pressure in the scuba tank. The gas laws apply to the gas, and when I look at the gas, the gas is expanding, not compressing.

    The J-T coefficient for air (N2, O2) is always positive, so compressing that gas makes it hotter and expanding that gas makes it colder.

    I've been looking at many web pages and physics/chemistry info, but somehow the answer evades me.

    ---------- Post added February 21st, 2013 at 11:37 AM ----------

    What friction? I don't see "friction" referred to in any of the wikipedia pages on gas laws - ideal or otherwise.

    ---------- Post added February 21st, 2013 at 11:46 AM ----------

    Let me try to explain what bugs me. Take two 1 cc cubes of the high pressure air in the fill tank. One of them stays in the high pressure tank and the other goes over into the scuba tank. To make it simple, we'll let the pressure equalize so both tanks have the same final pressure. The 1cc cube of air in the fill tank expands and cools. The fill tank gets colder. I understand that, or at least I think I do. The 1 cc cube of air that went into the scuba tank also expands. It expands the same amount as the same 1cc cube of air that stayed in the fill tank, but it ends up hotter, not colder. Why?
     
  5. PeterNBiddle

    PeterNBiddle Manta Ray

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    Tank A = 50 PSI
    Tank B = 5000 PSI.

    If you connect Tank A to tank B, you now have one tank, called tank C.

    Tank C has some significant differential pressure issues to resolve. As they resolve the air heats up (from bumping into air) and the metal heats up (from bumping into metal).
     
  6. awap

    awap Solo Diver

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  7. jimmyw

    jimmyw Angel Fish

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    I know this is right. It's got to be since I know the smaller tank gets hot when I actually do this, but think about my two 1cc cubes of air above. It looks like they both expand the same amount and both should cool. Instead, one gets hot and one gets cold.
     
  8. JohnN

    JohnN Solo Diver

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    If you stopped the filling with that 1cc of air in a tank with a 0 pressure (OK, I know that isn't possible, but this is a hypothetical case), you are correct, you would see cooling. That is not an interesting case, because what are going to do with 1cc of gas :D

    As you continue to fill the tank, you continue to compress the gas (the tank started with less pressure than the fill tank) inside of it and the heating predicted by the J-T Coefficient is observed. If you look at the Wikipedia article I linked, you'll see the J-T Coefficient of O2 is greater than that of air and this is empirically what is observed when you fill a bottle with deco gas (high O2 content). It gets hotter than a bottle filled with air.

    There is some heating of gas by a compressor, but if you went to the trouble to cool the compressed air to ambient temperature before filling the fill bottle, you would still see heating of the fill bottle. The increase comes from gas compressing, not any friction associated with making the compressed gas
     
  9. Johanan

    Johanan ScubaBoard Supporter ScubaBoard Supporter

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    Oops, I should have read the OP more carefully.
     
  10. jimmyw

    jimmyw Angel Fish

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    Well, we could have made it 100,000 cc's of gas. :) It can't be the volume of the gas that's important. Each 1cc should act the same. If one cc cools, then 2 should cool, and 100,000 should, too. I'm certain that the 1cc in the fill tank does cool and the 1 cc in the scuba tank does heat up.

    I thought this was the answer, at first, but it's not. The answer can't lie in the fact that the air in the scuba tank is getting compressed. It's true that it does get heated slightly after it expands as it gets recompressed (as the scuba tank continues to fill), but that heating is always less than the amount that gas was cooled as it expanded from its compressed state in the original fill cylinder. It always ends up expanded and and lower pressure colder. I actually worked through the math on that. I can't go through all the equations and research I did here, but here's the bottom line: It's just not possible to get away from the fundamental fact that all the gas in the scuba bottle started at high pressure in the fill tank in a smaller volume than the volume of the scuba tank and it ends up at a lower pressure in the scuba tank taking up a larger volume than it started with.

    All the gas in the scuba tank started at a higher pressure in a smaller volume and ended up at a lower pressure and a higher volume.

    I'm pretty sure the answer lies in how the gas is transferred from the fill bottle to the scuba bottle, but I don't quite have it figured out. Sometimes it just helps to post your thoughts and listen to the comments of others to try to figure out where you are going wrong.

    I really do appreciate the comments of anyone here who is trying to help me work through this. Some of the comments on the special characteristics of deco gas or helium filling operations are particularly appreciated as they've given me some new leads even though I'd already been through the J-T effect page in Wikipedia several times.
     

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