PChem Question: pV work reversibility/irreversibility

[theLHR]

Hi,

Here's an idea I can't quite figure out the answer to.

If we were to set up a container of an ideal gas (say He) that had a movable lid such that the lid did not interact with the walls to generate friction or the like. On top of the lid we place a brick which is able to hold the lid in place against the pressure of the gas inside the container. Now, if I remove the brick as fast as I can, the lid shoots off because the external pressure is no longer enough to contain the gas. The work done here (by the gas on the surroundings) is less than that if I had removed the brick by an infinitesimal distance at a time.

However, if I were to videotape myself doing this, and then slow the video down to 1 frame per second or something rediculous like that, it would appear that I was slowly removing the brick. Thus, it would appear that I was moving the brick an infinitesimal amount each time in an attempt to maximize the pV work that the gas could do on the surroundings.

My question is why is this then not reversible? I get the concept but it seems like there is an element of time in here. And I understand that we have to wait for the gas to equilibrate mechanically with the surroundings each time I move the brick the infinitesimal amount, but the gas is moving so much more quickly than I could possibly remove the brick that it seems like equilibrium would occur the whole time I was removing the brick until I managed to remove the brick from the lid entirely.

So I guess part b to this is what property of the gas makes it so it's not reversible even though the time scale of equilibrium of the gas is so much smaller than the time scale it takes me to move the brick?

My physics friend says that the only property in the universe that cannot be "video recorded" like this is the entropy. Thus he thinks it has to do something with the entropy.

Any ideas?

Thanks,
theLHR

 

[Mapes]

Hi theLHR, welcome to PF!

No real process is truly reversible. Your thought experiment of lifting the brick comes close, since--as you point out--the gas equilibrates quickly and the frictionless piston will rise under the brick as you remove it. But just the fact that the gas pressure needs to equilibrate in the container means that some waste heat is being generated, and this is energy that you wouldn't get out as work. No matter how fast or slow you watch the video of the process, you'll see a process that is close to--but not exactly--reversible. Does this answer your question?

 

[theLHR]

Hey Mapes,

Sorry for the slow response - I had to mull over what you said. It definitely makes sense what you're saying. Essentially the gas will always equilibrate slower (even if only a picosecond) than me removing the brick. Due to this, the gas will need to use some of it's internal energy to accomplish the mechanical equilibrium and expand.

Here's a twist though. Let's take the same exact expansion thought experiment. As I lift the brick off the internal energy of the gas decreases because work(pV) is negative. Now, the molecules are still traveling at the same exact average speed, no? Which is the definition of temperature. I would expect the temperature to decrease when the brick is lifted.

I guess what I'm getting at still is this time dependence. If I take an infinite amount of years to lift the brick off infinitesimal amounts at a time then it is reversible. Yet if I do it as fast as I can, even though the gas equilibrates on a time scale that is way faster than I can lift the brick off, it is not reversible. I guess I'm just wondering where this time dependence comes in.

theLHR

 

[Mapes]

Now, the molecules are still traveling at the same exact average speed, no?

No. Every time a molecule bounces off the receding piston, it loses momentum (and speed). The temperature of the gas is lower at the end of the process because you've removing energy via work.

 

[theLHR]

Hey Mapes,

I see what you're saying. Now it all makes sense. Thanks!

theLHR