Lecture T2: Changing the State of the System with Heat and Work

After a short review of the important concepts from lecture T1, I discussed changing the state of a thermodynamic system and how this is represented on various thermodynamic diagrams. On the blackboard I did an example of a piston-cylinder arrangement being heated at constant pressure. Then the class did an example for a small chunk of gas passing through a gas turbine engine. The results on this problem were very good. I then commented on the distinction between heat and work and noted that for a particular situation, determining whether it is heat or work sometimes depends on where you draw the system boundary. I then briefly revi ewed the formulation for work presented in the notes. Two of the more difficult things to understand about the material are 1) the signs to use for work (please review this), and 2) the distinction between thermodynamic equilibrium and quasi-equilibrium processes (or quasi-static processes) -- in particular when it is appropriate to assume a system is "close" to equilibrium. There are some useful notes on the latter item below and in the old mud responses. I have also asked Professor Greitzer to discuss this again at the beginning of lecture T3. I finished the lecture by noting that work was a path dependent quantity. That is, it is a function of how you get from state 1 to state 2 (the area under a pext-V curve) not on the difference between state 1 and 2. To reinforce this we concluded the lecture with a turn-to-your-partner exercise where I asked you to move along two different thermodynamic paths using ice, a bunsen burner and weights. Note in the example that the amount of weight lifted (the work done) depended on which thermodynamic path you took even though the initial and final states for the two paths were identical.

Responses to 'Muddiest Part of the Lecture Cards'

(53 respondents out of 70 attendees)

1) Could you explain more about quasi-equilibrium and quasi-static? (6 students) Whether you can consider a process to be a quasi-static (same as quasi-equilibrium) depends on what you consider your system to be and in particular how big it is, and how quickly it comes to thermodynamic equilibrium. Only under situations where the time rate of change of the process is slow relative to the time it takes for the system to reach equilibrium can we assume that the process is quasi-static. Consider a very small chunk of gas (say 1E-6 m on a side) as it moves through an engine. We would like to say that one unique set of properties defines its thermodynamic state and that all the forces balance one another (i.e. everything is equal--thus equilibrium). Changes in the state of the system (the chunk of gas) must take place slowly relative to the time it takes for the chunk of gas to reach equilibrium. Now consider a change to the chunk of gas (say the pressure changes on one side because it bumps up against something). How long does it take for the information to travel from one side of the chunk of gas to the other and by what mechanism does it travel? Pressure information travels at the speed of sound through molecular collisions propagating as a pressure wave. For such a small chunk of gas, it is not hard to imagine that this time to reach equilibrium is very short indeed (go ahead and calculate it--the speed of sound is about 300m/s for air so it is about 3E-9s). So as long as the changes in state of the small chunk of gas are slow relative to this time we can consider the gas to be in thermodynamic equilibrium. One can make similar arguments for adding energy by heat transfer to a small chunk of gas, but the propagation speed is much slower as it occurs by molecular diffusion (you can look up the thermal diffusivity for a gas and figure out what the time is). Now how does this differ from the piston-cylinder example? In that case, we considered the entire volume of the cylinder as the system. If the cylinder was say 1m in length, it would take about 0.3s for a pressure wave to propagate the length of the piston (and even longer for temperature differences to be felt since they propagate by molecular diffusion). So our criterion for how slow the changes to the system have to be to consider it in equilibrium depends on the scale of the system or more appropriately, how quickly it achieves equilibrium. A nice discussion of this appears in the middle paragraph of p. 19 S, B, & VW. The residence time of a chunk of gas in a gas turbine engine is about 0.05s, and thus most of the processes that impact it occur much slower than the time it takes a small chunk of gas to reach equilibrium.

2) How close to pext must psys have to be for them to be set equal? (2 students) It depends on what level of fidelity you require from your engineering model. In some situations, if it is within 10% it would be sufficient for you to get a rough estimate. In other situations, you might prefer it to be within 0.01%.

3) Are there real-world examples where the volume increases but work=0 (the thin massless piston seems pretty theoretical)? (1 student) This process is called a free expansion. Anytime gas is expelled into a vacuum (like space) a free expansion occurs. Note however, that free expansions also occur quite regularly but under conditions where the external pressure is not zero (and the corresponding work is not zero, but it is less than what could be achieved if the expansion happen through a slow (quasi-static) process. You will learn more about these non-quasi-static or free expansions in the next few lectures. If no work is done when pext is zero, doesn't it take work to return the system to the original state? (1 student) Yes! And you will see more about this later when we discuss reversible and irreversible processes.

4) From a graph, how do you know work = 0? (1 student) If the integral of pext-dv is zero for the process (e.g. a vertical line on a p-v diagram, or v=constant).

5) Still unclear on why psys = pext if quasi-equil (5 students). In the case of the piston-cylinder arrangement the former is the pressure of the system and the latter is the pressure applied by the surroundings (weights, the atmosphere, etc.). When moving slowly relative to the time it takes the system to equilibrate, the two are approximately equal. But the important point to realize is that they are not always equal. For example, if you were to rapidly remove the weights, it takes some time for the gas in the cylinder to respond. Second, it is important to remember that pext is the relevant parameter for evaluating the work done by the system.

6) Need more examples of where + and - work is done. (1 student) We will have plenty. Unclear about no useful work done on the surroundings when pext = 0. Why is the work not useful? Why is work classified as useful or not? (1 student) I should have been clearer, remove "useful" from your sentence. There is NO work done when pext = 0.

7) Does the piston in a quasi-equilibrium system move at constant velocity or does it not matter? (1 student) It doesn't matter.

8) Does work always involve some degree of mechanical motion? Maybe at the molecular level ?!! (1 student). Could you give a more precise definition of work than "everything else"? (2 students) Work is a flow of energy across a system boundary by other than a difference in temperature. This can occur by a flow of electricity across a boundary, or a spinning shaft with a torque on it across a boundary, or a force which moves the boundary.

9) Suppose you have hot air going into a dashed-line system of cold air. Where do you draw the boundary? (1 student) The short answer is "wherever it is most convenient for solving the problem". In practice it takes some experience to know the most convenient places to draw system boundaries--it is not always obvious. We will have a few examplesthis semester and more next semester (in both fluids and thermo/propulsion).

10) In choosing path a (in the turn-to-your-partner exercise) is there any reason to complete the second leg of the path? (1 student) You will see in Chapter 5 that we represent many processes as cycles (closed loops on thermodynamic diagrams) in order to estimate work and efficiency. Still don't understand how to travel path a and path b using our tools. (1 student) Please read over the explanation of the correct answer (link above) and then see me if you still have questions. Consider path a: to travel across the graph, we heat up the air. Doesn't that increase the pressure of the air too? (1 student) Not is the combined force of the weight and the atmosphere is constant -- it balances the pressure in the cylinder.

11) Why would we want to approximate pext with psys? (1 student) Then we can use relationships between properties of the system to help us calculate the work done. How do we bring in psys into a problem involving the state of the system? (1 student) We will have many examples of this in further lectures and the homework.

12) At what point do the experimental laws of thermodynamics cease to apply (i.e. how wide a nozzle would a jet engine have)? (1 student) There is a nice response to this from Einstein on the front page of the thermo web material.

13) Why doesn't combustion increase the pressure? (2 students) It can, it depends on how the system is designed. In a gas turbine engine the combustion occurs at roughly constant pressure. A candle sitting on a table burns at constant pressure. Combustion inside a closed box increases the pressure.

14) How do we know a pressure wave propagates at the speed of sound? (1 student) By definition, the speed of a pressure wave is the speed of "sound". Since what we call "sound" is the ear's response to pressure waves.

15) I thought heat was defined as the internal kinetic motion in a substance (1 student) That is not correct. Internal energy (U or u), which we will learn about in the next lecture, is related to the internal kinetic motion in a substance. Heat is the transfer of energy across a system boundary by virtue of a temperature difference only.

16) What do the LO#'s refer to on the problems? (1 student) Those are references to the different measurable outcomes that the problem addresses (I guess it would be clearer if I used MO# but ...)

17) No mud (18 students). Good!