Lecture T11: Reversible and Irreversible Processes

Today I discussed reversible and irreversible processes. I started this with two PRS questions (first, second) that asked about whether certain processes obey the first law and/or are observed to occur spontaneously in nature. This brought us to the key points from the lecture. In nature we observe processes going in one direction spontaneously. The first law allows both the forward and the reverse direction (as long as energy is conserved). The second law will tells us which processes occur in nature spontaneously. All processes can be reversed, but it takes work. A process is irreversible if it cannot be reversed without changing the surroundings (the change to the surroundings is typically that energy is given up in the form of work and energy is received in the form of heat). In other words, the test of reversibility is that both the system and the surroundings are returned to their initial state (it is not enough to put Humpty Dumpty back together again, the whole world has to go back together again too). Forms of irreversibility are friction, free expansion, mixing of gases, and heat transfer across a finite temperature difference. There is a direct relationship between energy and lost work (recall homework problem T4, more work was required to compress the gas when it was done instantaneously versus quasi-statically).

I then introduced two processes using third and fourth PRS questions. The first process was an adiabatic free expansion. There is no heat and no work, so the temperature is constant (it really is). The second was a quasi-static, isothermal expansion (so q=w). We will finish our discussion of these two example processes in the next lecture. This will lead us to a definition of the property called entropy and to the second law of thermodynamics.

I'm going to Mars. (1 student) Cool.

Responses to 'Muddiest Part of the Lecture Cards'

(45 respondents of 73 students in class)

1) How was there no work in the free expansion example if there was a change in volume? (1 student) Work is force multiplied by distance. The volume change suggests distance, but there was no force (the gas expanded into a vacuum). So pext=0.

2) Do reversible processes only occur when the net effect on the surroundings is zero? (1 student) If the system goes from state 1 to state 2 and then back to state 1, AND the surroundings returns to its initial state also, then the processes is called reversible. How is there no work in a free expansion? If you drew a p-v diagram, even though you don't know the exact curve, it still will contain area underneath it. (1 student) There are two misinterpretations in this line of reasoning. First, work is defined as the integral of pextdv. Second, in order to plot a p-v diagram, the system has to be in quasi-equilibrium so a state can even be defined. I still don't fully understand how we can have an instantaneous change to the system (the free expansion into a vacuum) without any change in temperature -- and related questions. (2 students) As I said in class, this is not intuitively obvious to most people, but it is a) consistent with the first law and b) what is observed in experiments. For the free expansion, I thought of it as pv=RT, p gets smaller, v increases and RT stays the same. (1 student) That is what happens when you compare the initial and the final states (since in any equilibrium condition for an ideal gas, this equation holds). However, during the process, the properties of the system can not be defined since it is not in equilibrium.

3) Are there any thermodynamics books I could reference to better understand this material? (1 student) I recommend starting with Sonntag, Borgnakke and Van Wylen. It is on reserve in the library along with a few other thermo texts.

4) Sometimes it is said that when the temperature doesn't change the process is adiabatic. I thought it was isothermal and adiabatic meant no q added. (1 student) I am not sure I understand your question. Isothermal means constant temperature. Adiabatic means no heat transfer. These two are very different statements. You can have an adiabatic process with a change in temperature and you can have an isothermal process that has heat transfer. In the special case of no work, you can also have an adiabatic process with no change in temperature (the example we did in class of the free expansion).

5) What examples would it be more difficult to see whether it is reversible or not? (1 student) Most of the examples are fairly straightforward -- because we have a lot of experience in our lives watching things occur in one direction only.

6) Is entropy another part of the change of system state equation? (1 student) We will talk about entropy in the final lecture. It is a property and a function of the state of the system. Confused with the connection of entropy and also reverse processes. (1 student) We haven't gotten there yet. But we will.

7) Irreversibility is related to lost work? I don't understand how this is true. (1 student) You will not get a lot of experience with this concept in Unified, but it is a major topic in 16.05. But think more about the Mars examples. Irreversible processes (putting a hot brick next to a cold brick, allowing a gas to expand without doing work, etc.) all represent energy that could have been used to do something useful, but was not -- it was just allowed to be converted to heat without extracting work.

8) In the piston example with the volume increasing and the pressure constant doesn't it require heat to maintain constant temperature? So then wouldn't you need heat to go to work and maintaining T? (1 student) I am not sure I understand the question. In neither of the two examples was the pressure constant -- it was reduced as the system expanded. In the adiabatic example with the rigid walls, there was neither heat nor work. In the quasi-static isothermal expansion there was q=w.

9)If you mix gases of different densities, wouldn't they separate spontaneously? Of course not to the left and right sides of the container, but to the top and bottom? (1 student) No. You are breathing oxygen, nitrogen, a little carbon dioxide, etc. These gases don't separate with some ending up at the bottom of the room, yet they have different molecular weights. The reason? The space between the molecules in a gas is so large that it doesn't impede the expansion of both gases to fill a container.

10) Does the second law come with an equation? (1 student) Yes it does. It says that if you calculate the change in entropy for both the system and the surroundings and then sum these two changes, the net change in entropy is always greater than or equal to zero. (It is equal to zero for an ideal, reversible process. All other processes (the real ones) lead to an increase in entropy.) The only trick is that you can't only evaluate it for the system. You have to calculate it for the surroundings too. You will have practice with the former on the last homework. The latter you will learn about in 16.05.

11) No mud (29 students). Great.