Definition of an irreversible process

Question

I'm a little bit confused as to why quasi-static process cannot lose energy to friction in order to be reversible. This is how I'm thinking: Suppose you have a container of gas with a piston, and on top of the piston you have a pile of infinitesimally fine powder. Removing the powder, one grain at a time, defines a path $\gamma$ from state $A$ to $B$ in state space.

Here's where I'm confused: Does irreversible mean that you can't get from $B$ to $A$ by ONLY adding each of the grains you removed, or does it mean that if you're at $B$, then there is no way to figure out a process that would define $-\gamma$ ending at $A$? If irreversible means the former, then I'm fine. If it means the latter, then I don't understand. If you just went from $A$ to $B$, you know what it took to get there, and in theory, you even know the amount of energy lost to friction at each infinitesimal step of the way in the path. So to define $-\gamma$, you would have to add a certain amount of heat at each stage to compensate, but the amount is something you could in theory determine.

Answer 1

Does irreversible mean that you can't get from B to A by ONLY adding each of the grains you removed, or does it mean that if you're at B, then there is no way to figure out a process that would define −γ ending at A?

There are several different concepts of reversibility. In the context of the 2nd law of thermodynamics the important one is thermodynamic reversibility, which means one can return from the final state of the system+environment to the original state, getting everything, including the environment, into the same thermodynamic state. So it is not enough that the system gets back to the original thermodynamic state; the environment needs to get to the original thermodynamic state as well.

If some path $\gamma$ in the thermodynamic state space of the system is given, then in principle there is a reversible process that can realize such path. But the path can be also realized in an irreversible process, provided it is quasistatic so the representative point of the state of the system moves along $\gamma$. This happens, for example, when friction is present while the system changes quasistatically, or something else irreversible is occurring outside the system.

Answer 2

Entropy can increase, but not decrease. If you reverse a process that increases entropy, you'd be decreasing entropy, which is impossible. So reversible processes are processes that conserve entropy. Friction increases entropy. It turns kinetic energy into heat. Turning the heat back into kinetic energy would decrease entropy, and is impossible.

You can't just remove the powder. Matter cannot be destroyed. You have to move it somewhere else. If you want the process to be reversible, you have to move it somewhere the same height or something like that. If you just drop it, the gravitational potential energy will be transformed into kinetic energy, which will then be transformed into heat. You can drop a grain of sand and have it hit the floor and stop and heat up a bit, but you can't have it cool down a bit and jump back into your hand. It's not reversible.