Lecture T5: First Law of Thermodynamics, Cv, Cp

The lecture started out well and ended in a train wreck. I began with a presentation of some of the many forms of the first law of thermodynamics. Included with this discussion was a PRS question regarding the applicability of a particular form of the law. It is important that you recognize the various assumptions implicit in the different forms of the equations and that you use the appropriate equations when solving problems. The compendium of equations lists most of the common forms along with their applicability. We then did a second PRS question to motivate the need for specific heats. The point was to show that in order to use the first law to calculate changes in temperature, pressure, etc. of a system, we need to be able to relate changes in internal energy (or enthalpy) to other properties. We do this using the specific heats. All this went well (except for Andy who didn't win the \$5 bill) and then the train wreck started. I tried to go through the derivation of the relationships for cv and cp too fast in too little time. We will begin with this tomorrow and I will try to sort out the confusion.

Responses to 'Muddiest Part of the Lecture Cards'

(53 respondents out of 66 students)

1) Unclear on Cv, Cp, the derivation, etc. (45 students) Please read the section of the notes to familiarize yourself. Here are the most important points: 1) cv and cp tell us how many Joules of heat transfer are required to change the temperature of a material by 1 Kelvin via a constant volume or constant pressure process, respectively. 2) These are properties of the material we are dealing with (that is they are different for different gases, solids, etc.). 3) In general, u is a function of two properties of the system (as is h), however, if u=u(T) only and h=h(T) only then du=cvdT and dh=cpdT. If this gas also obeys pv=RT (a thermally perfect gas), then the gas is called an ideal gas. 4) cv and cp allow us to relate changes in h and u to changes in T. As to which to use when, if you want to calculate the change in internal energy use cv, if you want to calculate the change in enthalpy, use cp. 5) Generally, cv and cp are functions of temperature (that is, the specific heat of a material changes with temperature), but for most of what we do in this class we will assume they are constant. For air for example, du=cvdT with cv=716.5 J/kg-K implies that if the temperature of 1 kg of airs changes by 1 K, then its internal energy has changed by 716.5 J. Similarly, since cp=1003.5 J/kg-K for air, its enthalpy (u+pv) would change by 1003.5 J.

2) I am still not clear on why you don't need an ideal gas to use dU=delQ-pdV. (1 student) All that is required for this is that the work equal the integral of pdV, it does not require a particular relationship between p and V--like pV=RT--could be pV^2=RT for example (but then it wouldn't be an ideal gas).

3) Is it a fundamental aspect of thermo that you can have an indeterminate # of necessary variables? (1 student) I am not sure what you are asking. Please see me and I can try to help you sort it out.

4) In the equations for the first law, when can we use psys? Is it only for quasi-static processes? (1 student) Yes.

5) When you fold DEblood sugar = DKE/hAndy, does this ignore his blood sugaar moving his arm? (2 students) It depends how hAndy is defined. The 20% number I quoted is roughly the efficiency of a human at producing a unit of mechanical work output -- so I think it would include moving the arm.

6) I know that adiabatic processes do not mean that the temperature is constant, but it is difficult to conceptualize. Can you give some examples of adiabatic processes where DT<0, DT = 0, and DT> 0? (1 student) I hope the discussion in the recitation helped with this. If not, please see me and we can discuss it more.

7) How is an adiabatic process represented on a p-v diagram? What makes an adiabatic process definite when both p and T change? (1 student) An adiabatic process is represented on a p-v diagram with a curve pv^g = constant as shown in this section of Chapter 4. Both T and p change in an isothermal process also, but just in a different way as you will see in homework T4.

8) What is the point of modeling an adiabatic process when it can never exist? (1 student) It is a useful idealization and many processes indeed are closely approximated as adiabatic (we will use this frequently for example for engines and rockets).