To the Editor of The Physics Teacher,
Energy is one of the most pervasive and useful concepts in physics. Students surely deserve a clear definition of it, just as they deserve clear definitions of mass, acceleration, etc. But many physics textbooks, along with a recent article in these pages,1 prefer to leave energy undefined.
It is not difficult to define energy. It’s the ability to do work. Quantitatively, a system’s energy is the amount of work it can do. Some have objected to this definition on the grounds that mechanical energy is partly transformed into thermal energy in all real processes, and the second law of thermodynamics tells us that thermal energy cannot be entirely used to do work.2 But, as has been correctly pointed out by others,3 the definition should be understood as referring to the amount of work a system could do under ideal conditions. In the case of thermal energy, the idealized conditions include the limit of heat engine exhausts approaching 0 K. Other physical laws involve similar idealizations. For example, no material object in the real universe experiences absolutely no external forces, although this is precisely the situation imagined in Newton’s first law.
Quantum zero-point energy might be an exception to the “ability to do work” definition, although in light of the accelerating universe and dark energy this situation is murky at present. In any case, this exception can be pointed out to students of quantum physics.
Although most introductory textbooks specializing in energy define energy as the ability to do work,4 my own quick survey of 22 introductory physics textbooks tallied only 6 that defined energy this way, and 16 that provided no general definition.5 Several of these 16 even emphasized that “there is no completely satisfactory definition of energy,” and that we can only “struggle to define it.” Such statements are likely to discourage students. These 16 textbooks that provided no general definition gave, instead, formal definitions of the specific individual forms of energy, for example “kinetic energy is defined as (1/2)mv2.” This reduces the principle of conservation of energy to some equivalent of the following statement: “Every physical system has associated with it some conserved quantity having the dimensions of (1/2)mv2.” This statement is true enough, but for sophomores it is not physically very meaningful.
The “ability to do work” definition gives students something to hang their hats on, so that specific energy forms take on a physical, as opposed to a formal, meaning. This definition unifies energy’s various forms while highlighting its societal importance: It can do work!
References:
1 Eugene Hecht, “An Historico-Critical Account of Potential Energy: Is PE Really Real?” Phys. Teach. 46, 486 (Nov. 2003); endnote 14.
2 Robert L. Lehrman, "Energy is not the ability to do work," Phys. Teach. 11, 15 (Jan. 1973).
3 Mario Iona, "Energy is the ability to do work," Phys. Teach. 11, 259 (May 1973).
4 Harold H. Schobert, Energy and Society (Taylor and Francis, New York, 2002); Robert A. Ristinen and Jack J. Kraushaar, Energy and the Environment (Wiley, New York, 1999); Roger A. Hinrichs, Energy, 2nd edition (Saunders, Philadelphia, 1996); Gordon J. Aubrecht, Energy (Prentice Hall, Englewood Cliffs, NJ, 1995).
5 Including Richard Feynman, Robert Leighton, and Matthew Sands, The Feynman Lectures on Physics, Vol. I (Addison-Wesley, Reading, MA, 1963); see pages 4-1 and 4-2.
Art Hobson
University of Arkansas
ahobson@uark.edu