# Thermodynamics: work done when a gas is leaking into atmosphere

1. Feb 22, 2013

### Avi Nandi

I have a gas container which contains gas at high pressure. The gas container is fitted with a capillary tube which opens into the atmosphere. Now we have a stopcock fitted to the capillary tube. We opens the stop cock slightly and allows the gas to leak outside. The process will go on till the pressure is equalized on the two sides. Is the gas doing any work??

My second question features the same arrangement. Only now the container is vacuum. now the stop cock is opened slightly and the gas is allowed to enter. Now is this process involve any work???

2. Feb 22, 2013

### Jano L.

This is very good question! When you expand the gas into atmosphere, the gas is moving against the atmospheric gas with atmospheric pressure, so it performs work on the atmospheric gas. As a result, the original atmospheric gas decreases its volume and thus accepts some energy due to this work and the gas inside the container gets colder. For example, when you open the bottle of beer, you will hear sss and see little fog above the liquid, which is the condensed water fog due to sudden decrease of the temperature inside.

When the expansion is into vacuum, the expanding gas does not act on anything, so it does not perform work. If the gas is ideal, the gas will not change its temperature.

3. Feb 22, 2013

### Buckleymanor

Not so sure it does no work.Imagine if your vacuum is at ground level and the presumption is that air is allowed to rush into the container.
The air is in effect moveing from a higher level within the atmosphere to lower level and thus doing work.

4. Feb 22, 2013

### Staff: Mentor

If air is allowed to rush into the container... Then it isn't a vacuum any more, and you're back to the first situation in which work is done.

5. Feb 23, 2013

### Avi Nandi

can i consider it as a free expansion?

6. Feb 23, 2013

### Jano L.

What is free expansion?

7. Feb 23, 2013

### Avi Nandi

free expansion is an irreversible process when a gas expands into an evacuated chamber. No work is done in the process. no thermodynamic equilibrium is maintained in the process.

8. Feb 23, 2013

### Jano L.

Wait, I misunderstood you. Regarding the second scenario, initially the gas is present in the atmosphere, but in the container there is vacuum. Then you let the gas to come in. In this case, since you perform it slowly, the gas in the container will increase its pressure so that there will be no vacuum any more. The gas in the atmosphere will expand into the container and perform work. When the pressures are equalized, the gas in the container will be most probably hotter than the gas in the atmosphere. So it is not free expansion - because the container is finite, there is no vacuum in it during the process.

9. Feb 23, 2013

### Avi Nandi

we cannot tell a gas is doing work if there is no displacement of any piston or if we cannot realize it by lifting or falling of a weight. is this true???

10. Feb 23, 2013

### 256bits

If you consider the whole of the atmosphere and the container as your control volume then you might be able to say that no heat nor work crosses the boundary. Refer to the famous gas on one half of a container and a vacuum on the other seperated by a membrane. Here the control volume is the whole container and no work nor heat is stipulated to cross that boundary.

In this case, if you consider the container with a vacuum as the control volume, then the post by Jano. L is absolutely correct.

11. Feb 23, 2013

### 256bits

consider flow work.

12. Feb 23, 2013

### jartsa

Capillary tube is a very thin tube, right?

The gas in the container is doing the work of pushing the gas that is in the capillary tube. The gas in the capillary tube and the capillary tube are heated by drag.

The athmosphere is pushing to the opposite direction, so the energy of the athmospehere increases.

The gas in the athmosphere is doing the work of pushing the gas that is in the capillary tube. The gas in the capillary tube and the capillary tube are heated by drag.

The gas in the container is pushing to the opposite direction, so the energy of the gas in the container increases.

13. Feb 24, 2013

### Avi Nandi

many many thanks to all of you for your help.

14. Feb 25, 2013

### Avi Nandi

can you please tell me what is flow work?