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

It felt like this class had a little better balance between the PRS (2 questions) and turn-to-partner (1 question) activities and the chalk-talk than last class (6 PRS questions). It allowed more time for discussion and explaining concepts on the blackboard.

Please go back and think about some of the answers to the PRS questions if they were unclear to you in lecture (I inserted the questions into the web page thermo notes).

Responses to 'Muddiest Part of the Lecture Cards'

(69 respondents)

1) In the gas turbine problem, how can we describe the state of the gas at various points in the engine if the gas is not in thermodynamic equilibrium (e.g. the gas is clearly moving)? (1 student) Good question. It depends on what you consider your system to be and in particular how big it is. Consider a very small chunk of gas (say 1E-6 m on a side) as it moves through the 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 relative the speed at which 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 the gas to reach equilibrium.

2) Not clear on the explanation between psys and pext (12 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.) The important point to realize is that they are not always equal to one another. For example, if you were to rapidly remove the weights, it takes some time for the gas in the cylinder to respond (see response #1 above). Second, it is important to remember that pext is the relevant parameter for evaluating the work done by the system. Only under situations where the time rate of change of the state of the system is slow relative to the time it takes for the system to reach equilibrium can we assume that the system pressure is the same as the external pressure. We call this "quasi-static".

3) Why do we say that work is done by the system when it is an outside force (i.e. a person) that removes the weights? and related questions about "by", "on", etc. (4 students) The uses of the words "on" and "by" and the associated signs for the work are a long standing convention that focuses attention on what the system does to the surroundings (e.g. how much work an engine produces) rather than vice versa. In your question, I think you may be confusing the removal of weights (work done by person) with the lifting of weights by the system (work done by system).

4) When reading a graph, or doing a problem, how do we know if "v" is volume or specific volume? (1 student) Read this. Uppercase is volume (an extensive property that depends on mass), lower case is specific volume (an intensive property that doesn't depend on mass).

5) If the piston is in a vacuum, won't some work still be done when psys increases and moves the piston? Because doesn't it take force to move the piston? (2 students). If the pressure external to the piston is zero, then the piston can do no work (it isn't pushing against anything). This does not mean that the state of the system does not change (it does), the system just doesn't do any work on the surroundings.

6) Please spend more time on the p-v diagram sketches for the last problem (3 students). Take a look at this. When all the weights are removed instantaneously, the minimum amount of lifting is done. If you incrementally take off a little bit of weight, you end up lifting the most weight through the largest distance. Does "quasi-static" describe the third piston in question #5? How does this gradual change relate to psys & pext? I think psys Å pext ... (not completely sure). (1 student). You've got it exactly right.

7) With the piston problems I have trouble understanding how the weights effect the problem. Are they effectively increasing Pext? (1 student) Yes!

8) Are you allowed to fix the position of the piston for the ice-bunsen burner experiment, or do you just have to do the quasi-equilibrium thing? (1 student) Yes. One could stick a pin in to hold the piston in place, but then the force on the pin would vary in the same way that the weights would to keep the piston at a fixed position. So it is the same thing. But it is easier to develop a physical feeling for the pressure by keeping track of the weight on top of the cylinder rather than the force on the pin.

9) In the last question, how do you know that the pressure drops first rather than the volume increasing first? (1 student). Good question. I know because I am interested in pexternal not psystem. As soon as I instantaneously remove the weights, pexternal changes (psystem and volume will take longer to respond).

10) (On the piston-clylinder, ice, bunsen burner question) why wouldn't you remove weight while heating to double the volume at constant pressure? (3 students) If I removed weight, the pressure wouldn't be constant since it acts in direct opposition to the weight. Constant weight=constant pressure.

11) I dunno. I have learned in 5.11 that the change in energy in a thermodynamic system is irrespective of the path you took to get there. Now (I think) I am learning the opposite. Of course I'll try to accept this one. I just have to let it sink in. (2 students) NO YOU DON'T! Good question. The folks in 5.11 are right. Energy is a state variable ( a function of the state of the system, not how it got there) and does not depend on path (same for pressure, temperature, etc.). Work and heat depend on path. One of the miraculous things about the First Law of Thermodynamics is that the difference between two path dependent parameters (heat and work) equal the change in a path-independent parameter (energy). We just haven't gotten there yet.

12) Are work and heat always path dependent? (2 students) Yes, but that doesn't mean that you can't have a multiple of paths that give the same work/heat. Think of two curves on a p-v diagram which are different but have equal area underneath them.

13) Unclear on the two p-v graphs for the first PRS question (4 students). Remember two things about these. i) The magnitude of the work is the area under the curve. ii) If the system expands against a force (v increasing) work is done by system.

14) Explain the derivation of the work equation (1 student). Please read section 4.3 of S, B, & VW. If it is still unclear let me know.

15) Why does work depend on path? (1 student). Remember the path is our representation of a physical process. It reflects the behavior of the world around us. It turns out that in our world you can take a system from thermodynamic state a to thermodynamic state b in many different ways and as a result produce different amounts of work. (This is my professorial way of saying "It just does.")

16) Could we do some problems that show the sign distinction with work? (1 student) Yes. We will have lots of practice with this as we proceed through the lecture material.

17) The graphs of thermodynamic properties (p-v, p-T, etc.) are still unclear to me. (3 students) These graphs are representations of a three-dimensional space (p, T, v) describing the behavior of a pure gas-phase substance. Take a look at section 3.7 of S, B & VW, it may help.

18) Does positive work correlate with endothermic or exothermic? (1 student) Neither. Endo/exothermic refer to the change in enthalpy of a mixture as a result of a chemical reaction. We haven't gotten to enthalpy yet, but we will. It is possible to have an endo/exothermic reaction and no work done by the system (e.g. no volume change).

19) The wording on some of the PRS questions. I know I got #2 wrong because my eyes inverted "work done on" and "work done by" even though it was right in my head.(1 student) I am not sure I know how to fix this.

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

21) Is a black border in the schedule a recitation and the subject is inside the box...? (yes) Are all the problem sets handed out on the web or are some handed out in class? (1 student) We intend to hand all of them out over the web, but I assume that occasionally we will hand things out in class if we don't get them up in time.

22) No mud (23 students). Good! I am improving.