Carl E. Mungan, Professor
Carl E. Mungan, Professor
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# Letter to the Editor: Why Distinguish Work from Heat?

Forum on Education of The American Physical Society

Carl E. Mungan

Gislason and Craig1 discuss thermodynamic definitions of work (W) and heat (Q) in the Spring 2005 Newsletter. They clearly have been thinking and writing about this topic for some time, judging by the references they furnish. Their examples deal with the irreversible compression of an ideal gas, a situation I also have analyzed.2

As a physics educator, my point of view differs from that of Gislason and Craig who are chemistry educators. I see only two fundamental reasons to invest class time in defining work and heat. The first stems from the way these concepts are typically developed in the first physics course. Work evolves out of the basic mechanics definition of force times displacement into thermodynamics applications such as pressure times volume change or electromagnetic field times change in total dipole moment, while heat is introduced in terms of conduction, convection, and radiation between materials at different temperatures. That is, work and heat represent particular categories of energy-transferring interactions between two systems. The interaction of applying pressure to a piston enclosing a gas is different from that of directing a bunsen burner flame onto the gas, even if the effects on the gas (in terms of changes in P, V, T, etc) are the same. In this view, W and Q are only distinguished insofar as they help a student to properly count and calculate all relevant external effects acting on a system of interest. This is analogous to the way that friction and normal force are separately marked on a free-body diagram, even though a single "surface interaction" force would theoretically have sufficed. But Gislason and Craig define W and Q in terms of concepts such as internal energy (U) and entropy (S), so that an explicit connection to the physical processes is lost. Defining W and Q via abstract equations rather than by two lists categorizing specific interactions is not helpful for introductory students.

A second reason for defining and determining W and Q is to subsequently use them to calculate changes in thermodynamic potentials such as S and U. However, if ∆U and ∆S can first be computed in some other way, as they are in the examples Gislason and Craig discuss such as Bauman's problem,3 then what possible reason is there to next deduce W and Q? This seems a case of closing the barn door after the horse has already escaped!

Based on the preceding considerations, as I have remarked elsewhere,4 it is my opinion that distinguishing W from Q is not useful in general for irreversible processes. An exception is an irreversible process (such as a free expansion or the problem discussed in Ref. 2) in which W and/or Q (for each external agent) is a priori known to be zero, whereby each sum W+Q in the first law of thermodynamics happens to reduce to a single term. In contrast, for example, if a block slides over a rough table, one cannot cleanly distinguish a portion of the energy transferred between the block and table due to W because of the contact forces between protrusions on their surfaces, and a portion due to Q as their surfaces warm up. In both this and Bauman's example, mechanical and thermal effects are intimately convolved with each other.

References

1) E.A. Gislason and N.C. Craig, "The proper definition of pressure-volume work: A continuing challenge," APS Forum on Education Spring 2005 Newsletter, pp. 9-11.

2) C.E. Mungan, "Irreversible adiabatic compression of an ideal gas," Phys. Teach. 41, 450-453 (Nov. 2003).

3) R.P. Bauman, "Work of compressing an ideal gas," J. Chem. Educ. 41, 102-104 (Feb. 1964). My question upon reading this problem is: Would it not have been better to have asked for U and S rather than for W?

4) C.E. Mungan, "A primer on work-energy relationships in introductory physics," Phys. Teach. 43, 10-16 (Jan. 2005); C.E. Mungan, "Radiation thermodynamics with applications to lasing and fluorescent cooling," Am. J. Phys. 73, 315-322 (Apr. 2005).

Carl E. Mungan is an Assistant Professor of Physics at the U.S. Naval Academy in Annapolis, Maryland. He can be reached via email at mungan@usna.edu.