I began the lecture with a fairly extensive review of the material from lecture T2. I thought this would be helpful since a weekend fell between lectures T2 and T3. Based on the mud responses, it seemed like people appreciated this. I won't go over the material again here since I think it is adequately covered in the T2 mud responses. As part of this review I gave the first concept question. The objective of this question was to highlight the relationship between work and area on a p-v diagram, and to test your understanding of the sign convention for work. I began the new material with a discussion of the various formulas for work for different processes (constant volume, constant pressure, constant temperature, and adiabatic). Then we started the first law with the second concept question. This was designed to test your understanding of the first law. The class did very well on this question. I then wrote the first law on the board and discussed the meaning of internal energy. This is the energy associated with the random motion of molecules. To highlight the difference between this and kinetic and potential energy, I drew three boxes on the board, each containing molecules in random motion. Each contains internal energy. If I move the box at a velocity (i.e. superpose this velocity on the random motion of the molecules), then I have kinetic and internal energy. If I change the position of the box in a potential field, then I have changed the potential energy. I concluded the lecture by beginning to look at various forms of the first law -- these are each specialized for particular situations (e.g. negligible changes in kinetic and potential energy, etc.). We will continue to specialize the first law for various situations as we progress through the lectures. I have provided a compendium of equations that may help you keep them all straight.
Responses to 'Muddiest Part of the Lecture Cards'
(64 responses out of 76 attendees)
1) Unclear on the meaning of internal energy--and related questions. (9 students) Several people were unclear about the distinction between potential energy and internal energy, the relationship between temperature, pressure and internal energy. We will specifically discuss the relationship between internal energy and T and p in later lectures, so I will not address that here. But there are two readings which may be helpful for you in understanding the various forms of energy, heat and work. The first is Chapter 1 of Understanding Thermodynamics, by H. C. Van Ness (1983 by Dover Publications, New York, NY). The second is from Understanding Engineering Thermo by Octave Levenspiel (1996 by Prentice Hall, Upper Saddle River, NJ, pp18-19).
2) The last bit on path dependence/independence, and the use of "d", and "delta" was confusing. And how can the difference between two path dependent functions result in somehting that is independent of path and a function of the state of the system? (11 students)
3) The black box problem was unclear. (4 students) First, is this situation possible? Can you think of a scenario in which you could produce this? Sure, we could put an electric motor and a battery inside a rigid cooler (thermally insulated) and allow it to pull the weight up. Now what about the energy in the box? Why does it have to be decreasing? The First Law ( DE=Q-W) tells us it must. Whatever is in the box is doing work to raise the weight (so if we consider the black box our system, work is crossing the system boundary via the fine thread). And by the statement of the problem, the box is in every other way isolated from its surroundings, so heat transfer to the box is zero. So DE=-W where W equals the work done by the system, which in this case is positive (it lifts a weight). So DE is negative, the energy in the box must be decreasing (at the same rate that the potential energy of the weight increases since the energy of the entire box + weight system is constant). Finally, the second answer (heat transfer down the thread) was just a red herring. Your intuition should tell you that it is very difficult to transfer heat down a very fine thread. The waste heat produced by whatever is doing the work in the box would go towards heating up the contents of the box. There was a good question about the scenario where it is a magnet in the box lifting the weight. This still satisfies the first law (of course). The magnetic potential energy (associated with the distance between the two objects) would be converted into gravitational potential energy (the raising of the weight).
4) How can you calculate DU is DKE and DPE aren't negligible? (1 student). You would have to be given additional information about the system (like the velocity, mass and relative height in a potential field. Will we always assume DKE and DPE are negligible? (2 students) No, for many situation we are very interested in the change in these quantitites.
5) For constant volume, why is w=0? (1 student) When the work is done by a gas expanding against something work is the integral of pdv (as derived in the notes). So if there is no change in volume, work = 0. However, there can be other kinds of work (electrical work for example), that have no relationship to the change in volume. From the integral, how is work negative if the volume is reduced? (1 student) Calculate a sample case and see.
6) If you are using infinitessimlly small systems, is everything consisdered quasi-static? (1 student) I think so, as long as you are still assuming it is a continuum (versus individual molecules).What do we need to know about quasi-static processes? (1 student) See T2 mud.
7) Would like more examples of the first law (2 students). You will get them!
8) Can you go over what units correlate with what quantity? (2 students).We will have problems that ask for Joules, J and/or Joules per unit mass, J/kg. To distinguish one variable from the other, it is common to write extrinsic variables in capital letters (e.g. U, W, Q) and intrinsic variables in lowercase (e.g. u, q, w). The relationship, for exampl, is that q=Q/m where m is the mass of the system.
9) In a combustion engine isn't the greatest change in energy a result of change in chemical energy, not internal energy? -- and related questions (2 students).Some texts (see excerpt from Levenspiel above) don't distinguish between the two, although I like to. The main point is they are a form of energy carried in the material that is not potential or kinetic. A nice discussion of this appears in the excerpt from Van Ness (.pdf) also mentioned above. But yes, as I have stated it, chemical energy in the fuel + oxidizer is converted into thermal energy (high temperature) or internal energy in the product gases.
10) How does all this apply if you have a flow in and out of a system (1 student). We will get to this in a few lectures.
11) What is the difference between heat and temperature? (1 student). See T2 mud.
12) I still don't feel that I could explain what the state of a system is. (1 student). Refer to Fenn, Engines, Energy and Entropy (1982, by W. H. Freeman and Company, San Francisco, CA, p. 53) for more help.
13) Where can I learn more about rockets? (1 student). I like Rocket Propulsion Elements by Sutton and Bilbarz and Mechanics and Thermodynamics of Propulsion by Hill and Peterson.
14) What is w for an adiabatic, quasi-static process? (1 student). See this section of the notes.
15) No mud (20 students). Good!