# The exact formula for PV-work in an irreversible process

Chestermiller
Mentor
Yes, I get the same.
Does that mean that friction on its own doesn't make the process irreversible, whereas gas viscosity does?
Both make the process irreversible. But, I think the interesting part of this is that, unlike the case of a frictionless piston with mass, if you have a massless piston with friction, then when the friction is very high (so that the gas expansion is very slow), your concept that the gas experiences an essentially reversible expansion is fulfilled (since the viscous contribution becomes negligible). However, even in this case, there is overall irreversibility to the process (due to friction), since the work done by the gas to push the piston is greater than the work done by the piston to push back the atmosphere. This is really an interesting problem that I think both of us learned something from.

Both make the process irreversible. But, I think the interesting part of this is that, unlike the case of a frictionless piston with mass, if you have a massless piston with friction, then when the friction is very high (so that the gas expansion is very slow), your concept that the gas experiences an essentially reversible expansion is fulfilled (since the viscous contribution becomes negligible). However, even in this case, there is overall irreversibility to the process (due to friction), since the work done by the gas to push the piston is greater than the work done by the piston to push back the atmosphere. This is really an interesting problem that I think both of us learned something from.
I might be over interpreting the result, I guess, however:
If η is zero we get exactly the work for a reversible process based on the internal gas pressure alone and independent of the atmospheric pressure and independent of C. Doesn't that indicate that friction (C) doesn't lead to irreversibilty. For η = 0 we get the maximum (reversible) work no matter how much friction there is.

Chestermiller
Mentor
I might be over interpreting the result, I guess, however:
If η is zero we get exactly the work for a reversible process based on the internal gas pressure alone and independent of the atmospheric pressure and independent of C. Doesn't that indicate that friction (C) doesn't lead to irreversibilty. For η = 0 we get the maximum (reversible) work no matter how much friction there is.
Yes, but it is the precisely the gas viscous behavior that is solely responsible for the irreversibility occurring in the gas. And, even in the ideal gas limit of low densities, the viscosity of gas is not equal to zero.

• Philip Koeck