Thermo - PV work and mechanical work

[Chestermiller]

Chestermiller: So, do you know whether the statement holds?
And moreover, why does/doesn't it?
["He is saying that, even if a (closed) system experiences an irreversible process, it is possible to identify one or more reversible paths for the surroundings that imposes the exact same irreversible path on the system."]

No, I really don't know. I've never thought much about the path that the surroundings experiences. In my judgement, the focus should always be on the system. And, to get the entropy change of the system, I think we can always dream up a reversible path to get the entropy change. I guess I've never had much motivation for looking at the process experienced by the surroundings.

Maybe you can pick a specific example of an irreversible path for the system, and we can see whether we can dream up a reversible path for the surroundings that puts the system through the exact same irreversible path.

Chet

 

[ffia]

No, I really don't know. I've never thought much about the path that the surroundings experiences. In my judgement, the focus should always be on the system. And, to get the entropy change of the system, I think we can always dream up a reversible path to get the entropy change. I guess I've never had much motivation for looking at the process experienced by the surroundings.

Maybe you can pick a specific example of an irreversible path for the system, and we can see whether we can dream up a reversible path for the surroundings that puts the system through the exact same irreversible path.

Chet

I also have a difficult time believing that this should always be the case.

But perhaps this should be viewed as just a "trick"/approximation to "at least be able to calculate something". [For example, I'm pretty sure my lecturer thinks that this is an "ok approach", and I just feel cognitive pain trying to understand/motivate it to myself.]

I believe there tries to be a philosophy like this:
If the system undergoes an irreversible change, some of its thermodynamical variables are not well-defined, right?
However, in the process the energy of the system changes, and work and heat are transferred between the system and its surroundings. And what leaves the system, enters its surroundings.
Now if the environment is big, one can approximate that its thermodynamic variables don't change much (at least the convenient ones...).
On the other hand one has to think that the environment behaves reversibly, but at the same time the environment should have super fast "relaxation times". This would allow me to make a macroscopic change in the system at a finite rate while only making reversible changes in the surroundings.
And, with this logic I get the changes in the system indirectly from the changes that happened in the surroundings.

I'm not sure, this is just how I've tried to understand it, now having read thermodynamics from a few different sources. Although most sources don't explicitly talk much about this. Some just use this and some just don't introduce problems where this kind of approach could be used.

For example, this seems to give ok results (well, at least results) in the adiabatic, irreversible compression of an ideal gas in a cylinder. In the problem we only know the initial state of the gas, the pressure of the surrounding air (and the area of the piston and the weight we suddenly put on it), and want to calculate work and the change in height.
[I've understood that the relation PV^{γ}=constant only works for reversible processes, which is why this is not straightforward.]

[Sorry about my bad english, btw.]