Why must reversible process proceed slowly?

[daudaudaudau]

Hi.

I'm beginning to study thermodynamics. I'm told that an adiabatic process is a process that is thermally insulated and which is reversible. For instance if a piston is thermally insulated and we compress the gas inside, this compression (I'm told) has to be slow. But why must the compression be slow? What happens if you just hammer the piston to the bottom? Why is this not reversible?

 

[Andy Resnick]

The requirement for 'slow' is artificial, and in this specific case is invoked to allow the gas within the piston to maintain equilibrium at all times. In the same way, sometimes it is claimed that a particular process must be 'fast' to prevent the flow of heat from occurring.

Part of this reasoning reflects the fact that what is really being taught is thermostatics, not thermodynamics.

 

[daudaudaudau]

But then I can ask again, why must equilibrium be maintained for the process to be reversible? The way I see it, the process is reversible if I can get the work back that I put in when I compressed the gas. I can't see why this depends on the speed at which I compress the gas.

 

[Prologue]

Look at the kinetic theory model for gases, say ideal gases, where they are merely billiard balls. If you put the gas into a cylinder with piston, then the additional energy that the gas receives when you compress the gas is given from the gas hitting the moving piston and bounces back with more speed than it had before the collision. This is the work being done. Now by the same token, when you pull out the piston, the piston will steal energy from the bouncing particles, having work done on it. There is a problem with the pull though. If you pull on the piston soooooo fast that no molecule ever touches it, and you expand the volume by, say, a factor of two, then you have changed the state without changing the energy. If you were to then compress back to the original volume, it would have a lot more energy than it did initially. So, the action of 'pulling' the piston must move at a very slow rate when compared to the motion of the molecules if you want it to be reversible.

I made it sound like this only happens for a pull, but that is not true. If you were to push the piston in, only at times where the particles are NOT touching the piston, you could do the same with pushing - i.e. change volume without changing energy.
Edit: There is a neat program written for vpython (visual python), that demonstrates this nicely. They have the temperature of the gas given, and then a bunch of balls zinging around in a cylinder, then you move the piston up and down, etc. But all of the quantities are simulated, and not calculated. And you can pull the piston faster than the speed of the balls and 'pump up' the temperature. It is a really cool demo. Ruth Chabay, and Bruce Sherwood came up with the simulation if I remember correctly.

 

[daudaudaudau]

Excellent explanation. So when I do it too quickly, I am in fact not performing any work on the gas.

But I am just wondering: Can this be explained without thinking about atoms and molecules? Wasn't thermodynamics developed before people really knew about these things?

 

[Prologue]

Probably either: They new experimentally that if you go too fast you screw stuff up, or there is some mathy tool that they used that required it. I don't really know though.

 

[DocZaius]

Excellent explanation Prologue! I wish the "giving the piston a chance to do work on the gas" explanation had been told to me when this "slow" necessity was first introduced to me.

 

[Andy Resnick]

But then I can ask again, why must equilibrium be maintained for the process to be reversible? The way I see it, the process is reversible if I can get the work back that I put in when I compressed the gas. I can't see why this depends on the speed at which I compress the gas.

Because the definition of a reversible process is one that means an infinitesimal amount of energy is able to reverse the process; this can only occur if we have well-defined concepts like 'equilibrium' and 'state'. Then, a reversible process is one that takes a material from one equilibrium state to another equilibrium state that is infinitesimally close in state space.

You are correct that the speed is (formally) irrelevant! In practice, the limitation arises from the requirement that energy is not dissipated during the process (similar to a conservative force).

It's clear that if I compress a gas so fast that shocks develop, there will be dissipative processes leading to sound, heating, etc. The idea of 'slowness' for a reversible process is simply to state that the working substance is never too far from equilibrium.

 

[daudaudaudau]

What about reversible heating then, this also has to take place slowly. Say I want to heat a pot of water reversibly from 1C to 2C (1C=274Kelvin, 2C=275Kelvin). I have two great heat reservoirs at 1C and 2C. I put the pot on the 2C and it heats up. Then to get this heat back I move it to the 1C reservoir. Now the state of the pot is unchanged, but the 1C has gained energy and the 2C has lost it. So the environment has changed.

Now if I have reservoirs at 1C, 1.5C and 2C I can repeat the above process, first heating to 1.5C and then to 2C. I then cycle the pot back through the 1.5C and 1C to restore it's original state, but now the change in the environment is less than before, because the 1.5C reservoir is unchanged and the 1C and 2C are only changed by a heat corresponding to 0.5C, whereas before they where changed by heat corresponding to 1C.

If I continue this subdivision ad infinitum the process becomes reversible. Is this the "reason" for the slowness requirement?

 

[Gary P]

Adiabatic processes need to operate relatively quickly or the temperature changes occurring in the gas will result in flow of heat to the outside. The need for it to occur slowly is in terms of the the velocity of sound in the gas and the longest dimension of the volume. If the piston moves "fast" then there will be a pressure wave traveling though the gas and heat will flow irreversibly from the warmer high pressure zone to the low pressure zone on the other side of the pressure wave. This would occur even with "perfect" insulation in the cylinder walls.

 

[DocZaius]

Adiabatic processes need to operate relatively quickly or the temperature changes occurring in the gas will result in flow of heat to the outside.

My understanding was that adiabatic processes are ones that do not result in the flow of heat to the outside.

 

[jtbell]

I think that's what he means. His meaning would have been clearer if he had said "else" or "or else" instead of simply "or".

 

[DocZaius]

"Otherwise" might work, as well. But I actually understood his sentence. I just had viewed adiabatic processes as processes that are incapable of resulting in a flow of heat to the outside, not ones that need quick operations so as not result in a flow of heat to the outside. I think it's that type of simple-model thinking that has caused me to have trouble understanding the reasons for the speed of processes being important.