Lecture T4: First Law of Thermodynamics

The objective of this lecture was to present all of the tools required for you to tackle homework problems T2-T5. We began with a review of the first law of thermodynamics. Then I talked about the importance of cyclic processes for modeling heat engines. A 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 followed this with a discussion of specialized forms of the first law, in particular for the case where changes in kinetic and potential energy are small relative to changes in internal energy and the only work is p-v work, and that work process is quasi-static. Then we arrive at du=delq-pdv. We will use this expression frequently.

We then introduced a new property called enthalpy (h=u+pv). Enthalpy is a useful combination of properties of the system. Physically, it represents the energy that would be carried across a system boundary if you were to push a chunk of gas into the system (as occurs in many aerospace devices with flows in and out). The chunk of gas carries with it some amount of internal energy per kilogram (u), and there is a certain transfer of energy to the system as work to push the volume of gas, v, (per kilogram) into the system at pressure p. As we work more problems the utility of enthalpy will be clearer.

Then we expressed the first law in terms of enthalpy for the case where changes in kinetic and potential energy are small relative to changes in internal energy and the only work is p-v work, and that work process is quasi-static. Then we arrive at dh=delq+vdp.

Finally I said that if we are working with an ideal gas that du=cvdT and dh=cpdT where cv and cp are the specific heats -- constants that are only a function of temperature. These relationships were presented without any development. More on the details for these will be presented in the next lecture. They are important relations because when combined with the other relationships shown in red above, you can relate temperature, pressure and volume changes to heat and work and energy change -- the whole objective of applying the first law. It will take some practice for you to see how this all fits together. We will work problems on the homework, in lecture and in recitation.

I concluded the lecture with a second PRS question about how many parameters you need to estimate the temperature change in the room if someone throws something from the top row. This was basically an energy exchange problem, but the point was that you need some relationship between internal energy and temperature (e.g. du=cvdT). Thus, the intention was to motivate the importance of the specific heats. But more on all this in the next lecture...

Responses to 'Muddiest Part of the Lecture Cards'

(38 respondents from 76 students attending, but I ran a few minutes over and was late handing out the cards, so many had to run to class)

1) Unclear about cv and cp--and related questions (9 students) My objective today was only to show what they are and that they are important for relating energy changes to changes in other system properties (like pressure and temperature). But I didn't show you where they come from. I will do this tomorrow in class.

2) It would be nice to have a clearer understanding of how to use enthalpy--and related questions. (8 students) We will spend more time on this in the next several lectures.

3) Confused about cyclic properties -- and related questions. (7 students) For a cyclic process 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. I confused some people by saying there was net work if the loop was open. What I meant by "open" was that there was some area between the lines so when you integrated pdv around the whole process you were left with some finite number of Joules. Some people interpreted this to mean that the loop wasn't continuous, but had a break in it. This isn't what I intended. If it has a break in it, is is not a cyclic process. Why is work path independent for an adiabatic process? (2 students) For an adiabatic process DU=-W, and U does not depend on path since it is only a function of the state of the system.

4) Why did you divide the kinetic energy by the efficiency of the person in the last example? (2 students). The key is that I want to know how much chemical energy (blood sugar) was converted in the process of throwing the object. Humans are about 25% efficient converting blood sugar to mechanical energy. So if the object was given 10J of mechanical energy, 40J of blood sugar would be used. The additional 30J would be released as body heat. The problem at the end of class was pretty muddy. (3 students) Please read over the answer to this problem (from a previous year).

5) How is internal energy different from chemical energy? Aren't both stored in the molecules inside the gas? (1 student) It depends on how you wish to define internal energy. Sometimes it is useful to define separately the energy associated with the random motion of molecules in a homogeneous gas, from the energy that would arise in new molecules that would be formed if one were to allow two reactants to mix. But if you look over the readings in the T3mud, you will see that it is also common in some applications to lump them together into internal energy.

6) Why those three assumptions? (1 student) By the three assumptions, I assume you mean: 1) changes in kinetic and potential energy are small compared to changes in internal energy, 2) the only work is pdv work, 3) the pdv work process is quasi-static, and there was a 4) ideal gas. For many engineering devices these are appropriate simplifying assumptions that enable us to model the performance of the system. You will apply these for instance, to modeling an internal combustion engine and a jet engine.

7) Could you explain that pdv thing again for quasi-equilibrium processes? (1 student) For a quasi-equilibrium process, the system pressure is very nearly equal to the external pressure so work is equal to the integral of psysdv over the process (versus pextdv).

8) Could you define what is meant by a property? (1 student) Please read the excerpt from Fenn (it also appeared in the bottom of the T3mud).

9)Why no partials in dh=du+pdv+vdp? ( 1 student) I started with h=u+pv. Then dh=d(u+pv)=du+d(pv)=du+pdv+vdp by the chain rule.

10) Can you just relist all of the major equations and variables given in lecture today? (1 student).A pretty good list is in the general comments above.

11) No mud (5 students). Good!