Lecture T13: Irreversibility and Entropy

This was the last thermodynamics lecture. I discussed the differences between reversible and irreversible processes and provided the equations necessary to calculate entropy changes for a system. A few notes: We define an irreversible process as one that cannot be reversed without some change to the surroundings (typically, work going to heat). Reversible processes are useful idealizations and we use them for comparison to measure how well we are doing with real (irreversible) processes. When we measure the entropy changes of both the system and the surroundings, the sum tells us how much irreversibility we have (how far from ideal we are). The amount of irreversibility is directly related to a lost opportunity to do work. Entropy is a convenient combination of thermodynamic properties (and is thus a thermodynamic property itself). On the final homework, you will get some practice calculating changes in entropy for a system. You have not been given the tools to calculate the change in entropy for the surroundings. You will get to this in 16.05.

Final note: I very much enjoyed teaching you over the last month. I look forward to seeing you all again during the spring when I teach the propulsion material. In preparation for the quiz, if you have any questions at all, please contact me. I would be happy to set up a meeting to go over the material with you.

Additional opportunities to talk with me:

4-5pm Monday during office hours

9-10 and 10-11 on Thursday during recitation.

Responses to 'Muddiest Part of the Lecture Cards'

(43 respondents out of 66 students attending class)

1) Do we need to derive the entropy equation? Could you please post an entropy type question on the muddy responses?--and related questions (2 students). No, you do not need to be abe to derive the entropy equation. What I would like you to know about entropy is that it is a property--a function of the state of the system. It is useful to us because we can use it to measure the degree of irreversibility in a process (by looking at entropy changes of the system and surroundings). And the amount of irreversiblity is related to the work we get out of a process (compared to an ideal process). An "entropy type" question would either be to describe what entropy is and why it is useful to us, or to calculate the entropy change of a system during a process (like homework T12). You will not learn how to calulate the entropy change of the surroundings until you get to 16.05.

2) What about heat exchangers? We didn't cover them explicitly, but are we supposed to put 2 and 2 together on the quiz? (1 student) They are covered explicitly on homework T11. You are expected to understand the basics of the energy exchange processes in a heat exchanger for the quiz. If you have questions, please contact me.

3) Could you demonstrate a problem using entropy and show a graph of T-s? -- and related questions (3 students). You will have an opportunity to do this on homework T12. That is about as much as I would expect you to know at this point. I would be happy to do another example in the next recitation.

4) How will entropy be used in an engineering field? (1 student) We will use it as a measure of irreversibility or lost work, i.e. to compare the efficiency of our processes to ideal processes.

5) Are there any other useful equations that I should know for entropy? I thought there was some way to calculate s using H and delta T? (or was that Gibb's free energy?) (1 student) For now, stick with the equations given in the notes. My objective in this lecture was just to introduce a useful new property and note that we could use it as a measure of irreversibility. When you get to 16.05 and start solving many problems using entropy, you will see there are some other very useful relations.

6) I didn't understand how entropy is defined. Isn't it the loss of energy due to natural dissapation? (1 student) No. Energy is a property, entropy is a property. Energy is not lost, but conserved (the first law). Entropy changes are related to how much work we can get out of a system (an energy transfer across the system boundary) compared to the maximum possible work for an ideal process. These concepts may be a little obscure right now, because you don't quite have all the tools necessary to use entropy changes to measure the lost opportunity to do work.

7) I have read that entropy is always increasing and that at maximum entropy...nothing will be able to happen (no change)...will we learn about this in 16.05? Also, wouldn't all REAL systems/processes have some entropy or else we could create a pertetual motion machine? (1 student) In response to your first question, yes entropy is always increasing. I think the maximum would have to coincide with no more opportunity to do work -- e.g. the entire universe at the same state. We are a long way away from this however. And while it is interesting to think about, there are other more practical purposes for measuring entropy changes, i.e. to assess the performance of devices. You will learn about doing this in 16.05, but probably not about what happens at the end of the universe. In response to your second question. All systems have entropy (it is a property and a function of the state of the system. All real processes produce entropy changes (when summed up for the system and the surroundings). And yes, an ideal energy exchange process with no change in entropy (again, when the change is measured for both the system and the surroundings) would allow a perpetual motion machine.

8) A system is reversible if delta w=0, even though delta q not equal zero? Why? (1 student). A process (not system) is reversible if the system can be taken from state 1 to state 2 and then back to state 1 with the surroundings returning to the intial state as well. The process may have heat transfer, work, both or neither. The key is that when the system is brought from state 1 to 2 to 1 again, the net heat transfer and net work transfer are zero.

9) For an isothermal compression, how do you find the heat and work? I keep getting it wrong. (1 student) Qualitatively, you can obtain the sign for work by noting that the specific volume decreases during the process (negative work). Then applying the first law for an ideal gas, if delta T = 0 (since isothermal), then q=w. So you know that heat and work are numerically equal. In terms of finding a numerical answer, the details are given in the notes.

10) Does the turbine extract work from the gas and the compressor do work on the gas so that the shaft work for a compressor is positive and the shaft work for a turbine is negative?-- and related questions (2 students) The turbine extracts work from the gas (our system). So the system does work when passing through a turbine (positive work). The opposite is true of a compressor. The system has work done on it (negative work). To avoid confusion, remember that the system is the gas.

11) Can you describe the work and heat transfer of the engine failure (with water and blades) to give us some experience with what to look for? (1 student) Sure. Here it is.

12) Is there any chance of holding a quick review session Wed. or Thurs.? (1 student) The recitations on Thursday are intended to serve this purpose.

13) So what is the deal with entropy and religion? (1 student) Entropy is a very useful property with broad applications in many fields. It also is rather obscure to many people. It can also be confusing to many people because it isn't a property that is commonly measured and quoted on the news every day (like temperature). It also has implications for many of the broader processes we observe in the universe. As a result of all of the above, the concepts of entropy, entropy changes and implications for processes we observe around us have been embraced to varying degrees and with varying interpretations by many people--all independent of the connection to religion. The connection with religion is secondary, but tends to find its way into the news. There are many expert thermodynamicists with very strong faith throughout the world, and other people of very strong faith who don't embrace some of the implications of the second law of thermodynamics.

14) No mud. (26 students) Great.

1) When two different temperature bricks are put together, how is the process reversed? How does net work become zero? (1 student) I assume you are asking how to make this process reversible. The way to do this is with a whole series of reserviors that are each only a small delta T different in temperature. Then it is possible to gradually transfer the heat from one brick to another and then go in reverse. You will learn more about this in 16.050

2) I didn't exactly understand the difference between the two processes (rev. and irrev.) on the board. Was the difference that the piston was included in one so you're not changing the surroundings to reverse? (1 student) First, review the notes. The difference is that in the reversible case when the system is returned to its initial state, the surroundings are too. In the irreversible case, even though the system is returned to its initial state, the surroundings have been changed.

3) A good example to use in the future is two pistons with a shaft connecting the two. It shows that work is saved in the other piston when one expands. (1 student) Very good suggestion. Thank you. It is like a thermodynamic pendulum.

4) If all processes conserve energy, then why aren't all processes reversible? (1 student). Conservation of energy is not a sufficient condition for a process to be reversible. It is rather the other way around. All real processes are irreversible. In our world, physical processes like friction etc., lead to additional work being required to return systems to their initial state.

5) Would like more examples on entropy and reversible processes. How do you measure inefficiency of a system analyzing entropy? (1 student) I can give you more examples in recitation. Relative to measuring efficiency using entropy, this is a topic for a later course (16.050).

6) What parts of entropy will be covered on the test? (1 student) There will be very little emphasis on entropy. For guidance read the subject learning objectives. I would like you to understand the difference between reversible and irreversible processes and why the difference is important for engineering devices. You should be able to state that entropy is a property and a function of the state of the system and is used to measure how irreversible various processes are (as you will see in homework T12).

7) T-s diagram -- How is it used to understand efficiency? (1 student) That is beyond the scope of this course. If you are interested you can read ahead in one of the textbooks on reserve in the library or wait for 16.050.

8) No mud. (26 students). Very good.