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

[jimmyw]

Another fundamental error. The volume of gas in the two tanks doesn't change.

I don't see how you can say that. I quote from the article:

Description

We consider n moles of an ideal gas at pressure P_i and temperature T_i, confined to the left-hand side (as drawn) of a thermally-isolated container, that occupies a volume V_i = V₀. The right-hand side of the container, also with volume V₀, is evacuated. The tap (solid line) between the two halves of the container is then suddenly opened and the gas fills the entire container of volume V_f = 2V₀.

The volume of the gas clearly doubles from V₀. to 2V₀.


---------- Post added February 22nd, 2013 at 06:22 PM ----------

Yup. The OP wants to follow a cc of gas from one tank to the other? He should do that... and think of the pressure/volume/temperature changes that occur at each and every step of the way. I think he believes that each cc of gas goes from being at 3000psi and X° in one tank, directly and immediately to being at 1500psi and Y° in the second tank.

I don't think it changes instantly, but the gas laws don't really care how quickly the change occurs. If you think about the Joule Expansion being described, it's very close to what we're talking about, except that the whip connecting the tanks is very large in diameter so the two gases can freely mix and the pressure drops exactly in half due to the doubling in volume. The hot gas from the scuba tank mixes freely with the cold gas from the donor tank and the result is that the heat from the scuba tank gas exactly balances out the cooling of the donor tank, leaving no net change in temperature. With the smaller diameter whip, the gases don't mix freely and the donor tank cools, while the scuba tank gets excess heat.

 

[RJP]

I don't see how you can say that. I quote from the article:

The volume of the gas clearly doubles from V₀. to 2V₀.

I was editing while you were typing. Read my edited post above, especially...

You're confusing the "amount of gas" (how many molecules, or moles) with the "amount of space" (how much volume) those molecules occupy.

The volume hasn't changed unless the size of the tanks changed. The amount of gas (number of molecules) in each tank has changed, but the volume they occupy is the same.

This is another fundamental error, perhaps. You seem to be looking at the American "volume" of 80cf when thinking about the tank. You should be using the absolute volume of the tank - 80cf tank = 11.1 liters.

EDIT - note this phrase in your article citation: "The right-hand side of the container, also with volume V₀, is evacuated." This means it is a vacuum. There are no molecules of gas in one of the containers in the citation. Therefore there is zero volume occupied by gas. In the real world scuba tank example, the receiving tank is NOT evacuated. It contains 11.1 liters of gas 14psi. The other tank contains 11.1 liters of gas at 3,000psi. At the end of equalization the gas you have still occupies a volume of 22.2 liters - 11.1 x 2.

The volume of gas has clearly NOT doubled.

 

[Ghanguss]

The "overall net pressure" is not dropping. The overall net pressure IN THE SYSTEM is the same. This is why we say that tanks "equalize" - pressure in one is dropping, pressure in the other is rising. The one dropping cools, the one rising heats up.

The only thing constant in this system is the number of moles/molecules of the gas/s

The overall net pressure has reduced. This has resulted from an increase in volume.

Consider also that work must be done to push the air back from the second cylinder into the first cyclinder to restore the system to its original state (from a compressor for example)

 

[rjack321]

The "overall net pressure" is not dropping. The overall net pressure IN THE SYSTEM is the same. This is why we say that tanks "equalize" - pressure in one is dropping, pressure in the other is rising. The one dropping cools, the one rising heats up.

Jimmy, at least a half dozen of us have told you the same thing in various words. You have been watching too much Big Bang Theory or Nature. This is not quantum physics. Its strictly adiabatic cooling and heating. There is absolutely no energy being added or subtracted by the transfill whip.

 

[RJP]

The only thing constant in this system is the number of moles/molecules of the gas/s

The overall net pressure has reduced. This has resulted from an increase in volume.

Ughhhh...

Please point out which tank became larger. I'm dying to understand how a system that started with a fixed volume of two 11.1 liter tanks and ended with a fixed volume of two 11.1 liter tanks had an increase in volume due to the fact that some of the gas molecules moved from one tank to the other.

Please further explain how the net pressure in this closed system has decreased... keeping in mind that pressure is the ratio of force to the area over which that force is applied. HINT: Neither the force (amount of gas) in the system, nor the area (surface area inside the two tanks) has changed.

 

[Ghanguss]

Ughhhh...

Please point out which tank became larger. I'm dying to understand how a system that started with a fixed volume of two 11.1 liter tanks and ended with a fixed volume of two 11.1 liter tanks had an increase in volume due to the fact that some of the gas molecules moved from one tank to the other.

Please further explain how the net pressure in this closed system has decreased... keeping in mind that pressure is the ratio of force to the area over which that force is applied. HINT: Neither the force (amount of gas) in the system, nor the area (surface area inside the two tanks) has changed.

From my original example (which was used to simplify things somewhat, while keeping the OP's problem relevant)- the original gas is in one cylinder of certain volume. Now another cylinder is added and the gas allowed to flow into that additional cylinder, hence the gas now is spread across double the volume.

Whether the cylinders are partially filled or not, by allowing gas to flow out of the first cylinder, that gas now exists across a larger volume than it initially occupied. Does that make sense?

It really depends how you approach the problem. If you consider that both cylinders are initially connected together, then a pressure differential cannot exist. So your reasoning that the two cylinders are the starting volume is not the best approach IMO.

The initial system is one closed tank containing x amount of gas, to which you add additional volume in the form of a second cylinder.

The second half of your question can be answered after grasping the first part of my answer.

 

[RJP]

It really depends how you approach the problem. If you consider that both cylinders are initially connected together, then a pressure differential cannot exist. So your reasoning that the two cylinders are the starting volume is not the best approach IMO.

I couldn't "reason" any other approach. You, and the other poster, used the word "net" which was your problem. Looking at "net" change would by definition take into account the "two-tank system" and include offsetting increases in pressure in one tank and decreases in pressure in the other. Therefore, that was the "approach" I took. If you meant, "the pressure in the donor tank decreased when half the gas was let out" that's what you and the other poster should have written. That is of course a correct, and unassailable statement.

Of course none of this changes the fact that the receiving tank will - in both PRACTICE and THEORY - be warmer after being filled, whether from a compressor or another tank.

:d

 

[Ghanguss]

I couldn't "reason" any other approach. You, and the other poster, used the word "net" which was your problem. Looking at "net" change would by definition take into account the "two-tank system" and include offsetting increases in pressure in one tank and decreases in pressure in the other. Therefore, that was the "approach" I took. If you meant, "the pressure in the donor tank decreased when half the gas was let out" that's what you and the other poster should have written. That is of course a correct, and unassailable statement.

Of course none of this changes the fact that the receiving tank will - in both PRACTICE and THEORY - be warmer after being filled, whether from a compressor or another tank.

:d

You shouldnt struggle when your in quicksand!

 

[RJP]

You shouldnt struggle when your in quicksand!

When my "what" is in quicksand?

 

[jimmyw]

The only thing constant in this system is the number of moles/molecules of the gas/s
The overall net pressure has reduced. This has resulted from an increase in volume.
Consider also that work must be done to push the air back from the second cylinder into the first cyclinder to restore the system to its original state (from a compressor for example)

Yes. This is exactly how it should be analyzed. We don't even have to say "net pressure." We can just look at the initial pressure and volume of the gas and the final pressure and volume. The volume of the gas has doubled. The fact that there was an empty cylinder adjacent to the initial tank doesn't affect the volume of the gas. It's only after the gas is allowed to expand into the empty tank that it has any effect - the volume of the gas has doubled.

And Ghanguss is also correct that work would have to be done to get the gas back into the initial state. During the expansion, the stored energy in the compressed gas was released as heat. The amount of heat released exactly counteracted the cooling that would have occurred if the gas had expanded reversibly (if we'd captured the stored energy from the compressed air.)

Again, I thought about it quite a bit last night. The physics all makes sense.