# Free expansion

1. Nov 4, 2005

### asdf1

what happens in a free expansion?

2. Nov 5, 2005

### Danger

In my girlfriend's case, I sent her to Weightwatchers.

Sorry, guys; I'm bored.

3. Nov 5, 2005

### Staff: Mentor

How would that be free, danger?

asdf1, could you be more specific as to what you want to know?

4. Nov 5, 2005

### Danger

The expansion was free. Recompressing her took a few bucks. :grumpy:

5. Nov 5, 2005

### HallsofIvy

In other words, asdf1, would you please explain what you mean by "free expansion"?

6. Nov 5, 2005

7. Nov 6, 2005

### asdf1

in thermodynamics, what conditions does free expansion have?
what kind of energy is constant? is it the energy absorbed? the work done? internal energy?

8. Nov 6, 2005

### Q_Goest

Hi Asdf1. A "free expansion" is generally described as the expansion of a gas inside a container in which a portion of the container is isolated from the rest by a diaphragm or wall of some kind. So on one side of the wall you have some gas at a pressure and temperature and on the other side you have a vacuum. The wall is then magically removed and the gas allowed to fill the entire container. Note also this process presumes the contents of the container come to some equilibrium but this is rarely mentioned in the literature but is important because you'll find folks miss this point and redesign the experiment using a valve to separate the two containers. If this happens, such a process really isn't "free expansion" it's a bit different. I'll get to that in a minute.

One can define the process as being adiabatic, though in reality there is always heat transfer but we'll neglect that here. There is also no work done by or on the gas. So if you apply the first law of thermodynamics to this situation, the initial internal energy of the gas is equal to the final internal energy. No energy leaves or enters the volume, so if you wrote the equation for the first law, you'd have dU on one side and all the terms on the opposite side would be zero making dU=0. Not very exciting really. There's an increase in entropy but that's not much fun either. I think the whole point is to get students to consider how to apply the first law, because in reality there's not much you can do with this. I haven't once in almost 20 years come across a case where I'd use it.

There are plenty of cases though where gas might be taken from one container to another through a valve. And I've seen people talk about this in the same terms as the "free expansion" I just explained above, take this one for example: http://www.taftan.com/thermodynamics/FREEEXPA.HTM
Although it is true that the total internal energy is the same in this once the pressures equalize, it is not true that the internal energy for each side is the same. They would have to mix completely and come to equilibrium after the pressures equilized in order for that to occur, so this very misleading. One wouldn't expect mixing to occur very effectively between these two volumes because of the restriction between them. What we find in this case is the gas on the high pressure side (side A) has actually expanded isentropically and all the entropy change is occuring on side B. If you apply the first law to each side independantly, you'll find that to be the case.

9. Nov 6, 2005

### asdf1

wow!!! thank you for the very clear explanation!!! :)