## Sunday, October 3, 2010

### Reversible Processes

This post is part of a series, Nonsense and the Second Law of Thermodynamics.  The previous post is entitled:  Entropy is Not a Measure of Disorder.

To understand the macroscopic thermodynamic definition of entropy,  it is important to understand something called a reversible process.  A reversible process is just what it sounds like: a process that is reversible.

A reversible process should be thought of as an ideal case. In a reversible process, the system is in equilibrium for every infinitesimal step of the process.  Imagine a balloon filled with gas, and imagine that the balloon is perfect, i.e., we need not concern ourselves with the properties of the balloon itself: we care only about the gas inside the balloon and the gas outside the balloon.

At equilibrium, the pressure on each side of the balloon is equal.  If the pressure outside of the balloon is reduced, the balloon expands until the pressures are equal again.  In a reversible process, the balloon is allowed to expand continuously by infinitesimal steps.  The reversible process acts as a  limit to any real process.

When a reversible process is reversed, it leaves both the system and the surroundings in the same state they started in.  If we define the universe as the system plus the surroundings, the universe remains unchanged after a reversible process has taken place.

Compare a reversible process to an irreversible process.  Consider climbing a mountain, climbing back down and returning to the original position at the base of the mountain.  The climber is at the same place that he or she started, but the surroundings have changed.

The climber gave off heat during the ascent and descent, and the surroundings are now an unnoticeably little bit warmer.  The climber has changed as well, having burnt calories.  One need not go into all of the details to understand that this process is not reversible.

Consider a perfect frictionless pendulum: as it falls it converts potential energy into kinetic energy, as it rises it converts the kinetic energy back into potential energy and the cycle continues indefinitely.

Again, notice that the reversible process is an ideal, but unattainable process.  The next post discusses a cyclical reversible process used to convert heat into work. The next post is entitled The Carnot Cycle.

Sources
• Atkins, P. W. Physical Chemistry, W. H. Freeman and Company, New York, 3rd edition, 1986
• McQuarrie, Donal d A., Statistical Thermodynamics,  University Science Books, Mill Valley, CA, 1973
• Bromberg, J. Philip, Physical Chemistry, Allan and Bacon, Inc., Boston, 2nd Edition, 1984
• Anderson, H.C., Stanford University, Lectures on Statistical Thermodynamics, ca. 1990.

Sambaran said...

For a reversible process, why does a system need to be in equillibrium for every infinitesimal step of the process?
I would prefer to define reversible process as a process where we can return the system and surroundings to a previous state. I do not understand how equillibrium-at-every-infinitesimal step is a prerequisite for that. Can you please explain?

Sambaran said...

dummy comment to keep track of responses via email

Rich said...

Think about the balloon example, and suppose that a step is not reversible, for example, there is more pressure inside the balloon at that step than there is outside. That pressure will cause the balloon to expand. Now we want to reverse the process and shrink the balloon, but when we get to that step, there is more pressure inside the balloon; so it will expand when we are trying to shrink it.

The only way to make each and every step reversible is if the pressure is equal for each and every step. If it is increased by infinitesimal steps, this will be the case. Again such a process is a theoretical limit and not practically achievable.

Rich said...

In my first sentence, I meant to say, not at equilibrium.

Sambaran said...

@Rich,
Thanks for your explanation. Now I understand the importance of equillibrium at every infinitesimal step if we want the process to be reversible at every infinitesimal step.
However, does a process need to be reversible at every infinitesimal step for the entire process to be termed reversible. Taking your balloon example, assume 3 states.
State-A: Balloon radius is 3 cm
State-B: Balloon radius is 5 cm
State-C: Balloon radius is 7 cm
At state-A and state-C, there is equillibrium. However while going from A to C via B, there was no equillibrium at B. Assume that at B the pressure inside the balloon was greater than outside (meaning it was on its way of expansion).
After reaching state-C, can we now not bring back the balloon to state-A such that the balloon and the surroundings are at exactly same state as before? Of course the 'path' from A to C is not the same as that from C to A (we will take an alternate route excluding B on return 'path). However can we still not term the process reversible considering only the start-point(A) and end-point(C)?

Rich said...

@Sambaran

That is a great question and gets at the question in a way that you may not even realize yet.

If you cannot reverse the path, then the path is not reversible by definition.

The interesting thing is that Entropy is a state function. That means that the value of the entropy is independent of the path taken (but only reversible paths lead back to the same state). That means that if your path is not reversible, then there is no path that can reverse your path.

If my explanation does not hep, you might try searching the Internet for the phrase "Clausius equality," which should point you in the right direction.

Sambaran said...

I have a doubt regarding vibrations-and-waves. To be precise it is a statement in the book by A.P.French. Will you be interested in answering the doubt?

If yes, can you please email me. My id is: baransam at the rate of hotmail dot com