Lecture T4: First Law of Thermodynamics

The lecture reviewed several of the same concepts introduced in T3. This included discussing the distinction between quasi-static processes and other process as well as the importance of quasi-static processes for modeling engineering systems. Relative to the latter point the first PRS question (which you will see more of on homework T5) was used to illustrate first that work depends on path and further that quasi-static processes derive the most work from a system and thus are useful idealizations to benchmark the performance of real systems against. We then discussed the use of the first law of thermodynamics and did a PRS problem that was intended to highlight the importance of getting the signs right when using the first law (even for simple problems it can be confusing until you get more comfortable with the material). We also talked about the importance of cyclic processes for modeling heat engines. A third PRS question was used to emphasize that heat and work are path dependent processes, whereas internal energy is a property (and thus a function of the state of the system). This has important implications for cyclic processes. We finished the lecture with an introduction to enthalpy. For now you should consider this only as a useful combination of properties of the system (and thus a property itself). As we work more problems its utility will be clearer.

Responses to 'Muddiest Part of the Lecture Cards'

(47 respondents from 72 students attending)

1) Why is the sign convention for heat Q positive when heat goes into the system? (2 students) Why is -W in the equation? (1 student) Consider the equation DE=Q-W. If we add heat to the system we want the energy to go up (so Q and E should have the same signs since they appear on opposite sides of the equal sign). Similarly, if the system does work (energy flowing out of the system) we expect the energy to go down--hence the minus sign in front of the "W", since we define positive work as that which the system does on the surroundings.

2) I am still confused on concept question 1. (2 students) Also in the piston cyclinder when the piston falls and the volume decreases, I see why P goes up, but not why T goes up. (1 student) Relative to the concept question, you will get the chance to think about it more when you do homework T5. If it is still unclear at that time, let me know and we can talk about it. Relative to the temperature change in a piston-cyclinder under compression, it can either go up or down or stay the same, depending on the amount of heat trnasfer that occurs during the process. If there is no heat transfer, we will see the temperature goes up. You don't have all the tools to see this yet (in particular the relation between internal energy and temperature), but you do have the tools to say the internal energy goes up (DU=Q-W, if Q=0 then U increases when work is done on the system).

3) What was the equation for work used in concept question 2? (1 student) Work =power x time = voltage x current x time.

4) Does a quasi-static process always have to be adiabatic? (1 student) No.

5) Is it possible forthe surroundings to return to their initial conditions after a cyclic process? (1 student) Specifying any two independent properties of the system (they need to be independent, e.g. density and specific volume will not work because they are simply reciprocals of each other) fully specifies the thermodynamic state of the system. So returning to those two values means that the system has returned to the same thermodynamic state. It does not mean however, that the surroundings have returned to the same thermodynamic state (although in an ideal world this is theoretically possible (a perpetual motion machine), in the world we live in it has never been observed--we will talk more about this when we get to the Second Law of Thermodynamics). Consider an automobile engine for example. The pistons go up and down over and over again, continually returning to the same state. But the surroundings do not return to the same state (fuel and oxygen are burned, waste heat is produced, etc.).

6) How do we know the internal energy of a system is always zero for a cyclic process? (2 students) The internal energy of the system is not zero. The net change in internal energy is zero since the system returns to the same thermodynamic state (the definition of a cyclic process) and internal energy is a property and therefore only a function of the state of the system. So for a cyclic process, Q=W. A little unclear on why DU is path independent and Q & W are path dependent. (2 students) The above should address the first part. Relative to why Q and W depend on path -- it is just a reflection of the way things work in the world around us. All it says is that the net energy change of a system must balance the sum of that which crosses the system boundaries (Q-W); beyond that, some processes (paths) lead to more or less energy change, more or less energy transferred as heat at the boundary and more or less energy transferred as work at the boundary. Hence they are path dependent.

7) In a cyclic process, how is the surrounding affected? (2 students) Typically for heat engines we convert one form of energy to another in the surroundings (say fuel into potential energy when we raise a weight, or fuel into waste heat, etc.)

8) What benefit is there to modeling a heat engine as a cyclic process? (2 students) You will see the answer to this in about two lectures (feel free to read ahead).

9) Is the total work done by expanding the piston the same as the work to raise the piston weight plus the work to expand against the atmosphere? (1 student) Yes (unless there are additional forces like friction).

10) What is the difference between DE=Q-W and DU=Q-W? (1 student) The latter equation assumes that changes in potential and kinetic energy are small relative to changes in internal energy. So is E= U + KE + PE? (1 student) Yes--you could also add nuclear energy for problems in which it changes significantly. When can PE and KE be neglected? (1 student). Strictly speaking, you should ask when can changes in KE and PE be neglected since the first law deals with changes in the state of a system. Changes in PE and KE can be neglected when they are small relative to changes in internal energy.

11) It would be nice to have a clearer definition and understanding of how to use enthalpy. (6 students) We will get to this over the course of the next several lectures. For now just consider it to be a property which is a useful combination of other properties.

12) I am still having trouble with the concept of differential q-s where psys=pext, when over a non-differential psys may change, but pext remains constant. Related: if q-s process is slow, how do you get power even if you get max work? (1 student) I don't understand your question. Read over the notes and the previous mud responses if you haven't already and then come talk with me if it is still unclear.

13) Can you clarify what free expansion is and what those processes might look like? (1 student) Free expansions (and compressions) are all expansions (and compressions) that aren't quasi-static (so all abrupt motions relative to the speed at which the system equilibrates).

14)What is a typical efficiency for a common heat engine, such as a car engine? ( 1 student) 25%. You will learn to estimate this in a lecture or two.

15) You can determine the energy of a system by knowing 2 state properties. Can you determine the others or do they just not matter in terms of energy? (1 student). Internal energy is a property and is a function of the state of the system. You can use it with any other one independent property to find another property (it only takes two properties as long as they are independent).

16) No mud (16 students). Good!