# What is a reversible cyclic process?

1. Dec 8, 2012

### harjyot

I know carnot's cycle is an example. but what is it exactly? a cycle in which ever part of process has a 'counter-process' please elaborate.

2. Dec 8, 2012

### Darwin123

There are only two things that can be done to entropy. It can be moved and it can be created. "Reversal" refers only to reversal of the motion of entropy.

In a reversible cyclic process, entropy is not created. However, a reversible cyclic process can move entropy from one spatial point to another.

The reverse cycle moves the entropy in the opposite direction of the original cycle. The reversal refers to motion of entropy. Since no entropy is created anyway in the original cycle, the reverse cycle doesn’t create entropy either.

In an irreversible cyclic process, entropy is created as well as moved. An irreversible cyclic process both moves some entropy from one point to another and creates extra entropy.

It should be note that irreversible engines also have a counter cycle in irreversible refrigerators. If you run the irreversible engine backwards, the direction of motion of the entropy is reversed.

The irreversible engine does work on the surroundings. However, the irreversible engine can be run backwards as a refrigerator. Then, the surroundings do work on the irreversible refrigerator. The important difference is that entropy is created in both directions. Although the motion of the entropy can be reversed, the creation of the entropy can not be reversed.

When entropy moves from a high temperature point to a low temperature point, it releases energy in the form of work. A good analogy would be in electricity. Moving an electric charge from high potential to low potential releases energy in the form of work.

The energy can be stored by any method. If no entropy is created, then moving the entropy in the opposite direction requires only the same amount of work. However, if entropy is created then more entropy has entered the low temperature point then was taken from the high temperature point. Then, more work is required to move all the entropy from low to high temperature. The energy stored is not enough to reverse the process.

A Carnot cycle is one example of a reversible cyclic process. The Carnot cycle moves entropy from one spatial point to another without making any entropy. When a scientist calculates the change of entropy per cycle in a Carnot engine, he is talking about the entropy moved from one heat reservoir to another.

Entropy can spontaneously move a certain quantity of entropy through the Carnot engine from the high temperature reservoir to the low temperature reservoir. The Carnot engine does a certain amount of work TO the surroundings in the mode. If the surroundings do the same amount of work ON the Carnot engine, the same amount of entropy will move from the low temperature reservoir to the high temperature reservoir.

The “counter cycle” to a Carnot engine cycle is a Carnot refrigerator cycle. No entropy is created.

It is important to emphasize that the Carnot engine does not create any entropy at any time. The Carnot cycle moves entropy from one reservoir to the other. If the Carnot cycle spontaneously moves entropy from hot to cold, the cycle acts as an engine by doing work on the surroundings. If work is done by the surroundings to move entropy from cold reservoir to a hot reservoir, it is working as a refrigerator.

Real engines are irreversible. They both move entropy and make entropy.

“Spontaneous” means to happen without work being done on the cycle. Entropy can spontaneously move from a region of high temperature to a region of low temperature. Entropy can not spontaneously move from a region of low temperature to a region of high temperature.

Here is a link and quotation stating that a reversible engine does not make entropy.

http://web.chem.ucsb.edu/~genchem/Chem1BW03/moreinfo/ch.10-entropy.pdf
“In a reversible, cyclic “process both the system and the surroundings are returned exactly to their original conditions. In an irreversible process, even if the process is cyclic (state 1 —> state 2 —> state 1), the surroundings are changed in a permanent way. Work is converted to heat in the surroundings. All real processes are irreversible. A reversible process gives us the maximum work obtainable from the gas.

1) In a reversible process the total entropy of a system plus its surroundings is unchanged, Suniv = 0.
2) In an irreversible process the total entropy of a system plus its surroundings must increase, Suniv > 0.
3) A process for which Stot < 0 is impossible. (The process is spontaneous in the opposite direction.)”

Last edited: Dec 8, 2012
3. Dec 8, 2012

### Rap

Excellent summary.

4. Dec 9, 2012

### Studiot

For any cyclic process

$$\oint {\frac{{dq}}{T}} \le 0$$

Now if we reverse the direction of the cycle then

$$- \oint {\frac{{dq}}{T}} \le 0$$

The only way this can occur is if

$$\oint {\frac{{dq}}{T}} = 0$$

This is known as a reversible cyclic process.

Care must be taken with this since T is undefined in some cases for the system (working fluid).
The cyclic integral can be evaluated if T is the temperature of a suitable heat supply process.

5. Dec 9, 2012

### Rap

Is this always true? Can't entropy simply be created in an irreversible process? I'm thinking of two gases like hydrogen and oxygen in a container of fixed volume and isolated. They will react irreversibly to form water vapor, creating entropy, yet no entropy has been moved.

6. Dec 10, 2012

### Darwin123

Of course. I should have made it more clear.

An irreversible process is a process where entropy is created. Entropy may or may not be moved in an irreversible process.

Many irreversible process both make and move entropy. I was thinking of biochemical processes in which both happen. When a plant absorbs sunshine and grows, it makes entropy. However, it also moves entropy. The plant has a high degree of order not because entropy was destroyed, but because entropy has moved out of the volume occupied by the plant. The total entropy of the universe has increased, but most of the increase occurs outside the volume of the plant.

7. Dec 11, 2012

### Rap

This is only true for reversible processes, right? If I thermally connect two fixed-volume systems, entropy will flow from the high temperature system to the low temperature system, yet no work will be done. Entropy will also be created.

8. Dec 12, 2012

### Darwin123

My mistake. I should have said:

If entropy flows from a high temperature region to a low temperature region, work MAY be done on the surroundings.

For both reversible and irreversible processes, the work done on the surrounding may or may not be returned to the hot reservoir. That depends on the processes going on in the surroundings. However, energy transferred to the cold reservoir can't become work done on the surroundings.

In an irreversible process, the entropy that is created goes into the cold reservoir. The energy associated with the entropy that is created can not go into the work done on the surroundings.

Distinguishing between irreversible processes may be useful. Some processes are more irreversible than others.

A completely irreversible process is one that can do no work on its surrounding. A completely irreversible process creates the maximum amount of entropy possible consistent with conservation of energy. None of the internal energy taken out of the hot reservoir can be used as work on the surroundings. The internal energy taken out of the hot reservoir can be said to have been absorbed by the entropy that has been created.

A partially irreversible process does some work on its surroundings. A partially irreversible process creates entropy, but less than the maximum amount of entropy consistent with conservation of entropy. Some of the internal energy taken out of the hot reservoir can be used as work on the surroundings. The internal energy taken out of the hot reservoir that doesn't become work on the surroundings can be said to have been absorbed by the entropy that has been created.

A reversible process is one that can do the maximum amount of work consistent with conservation of energy. Since no entropy is created, no internal energy can be absorbed by newly created entropy.