Prism Magazine September 2001



Web Extra


- By Kenneth R. Jolls

I doubt if there is an area of science or engineering where we do a poorer job of teaching than in thermodynamics. As long as people have been aware of the subject and in spite of the countless students who have studied it and textbooks that have been written about it, we still produce scientists and engineers who, for the most part, dislike thermodynamics, distrust it, and are unable to use it for more than the most rudimentary of applications.

I believe that much of the problem is our overemphasis on operations. Having students do the procedures of thermodynamics may fill the time, give useful results, impart some confidence, and satisfy course descriptions, but it doesn't forge the link between theory and practice that promises mastery of the subject.

I taught thermodynamics in what I call the "robotic" style for a number of years before a reviewer suggested that I read Gibbs. I wasn't a thermodynamicist by training, and I had heard that "Gibbs is too abstract" and "Gibbs is impossible to understand," so I was apprehensive. But what I found in Gibbs' papers was a way to use geometrical models to represent thermodynamic ideas at both the theoretical and practical extremes of the subject. Since I had studied mathematics with teachers who used visual models, I didn't find Gibbs' words incomprehensible.

But they did make me rethink what I was doing. How many times had I written on the board: U = f(S, V, N1, N2,...); without explaining clearly what those symbols represent in physical terms? How many times had I -- the teacher -- focused on operations myself without teaching students what they were operating on?

When we think of a thermodynamic process we imagine a system (perhaps a working fluid) and a series of steps through which it passes. The steps may involve work and heat effects and the addition or withdrawal of mass, but taken jointly they define a process that takes the system from an initial to a final state. If the initial and final states are identical, we call the process a cycle, such as the familiar power or refrigeration cycle.

Most textbooks explain such processes using flat, two-dimensional curves, where each curve represents the change of two thermodynamic variables (temperature-entropy, pressure-volume, etc.) in an idealized model of a particular step. Yet there are very few real processes in which only two variables change, and if there is a mixture of chemical species and multiple phases present, many variables can change. Two-dimensional plots rarely show thermodynamic processes completely -- yet we usually ask students to learn the subject ons that basis alone.

The figure shows a computer-generated, three-dimensional PVT (pressure (P), volume (V), temperature (T)) diagram on which is dashed a Rankine cycle -- a series of steps in which water is compressed, heated, boiled, superheated, expanded, and finally condensed back to its original state. The cycle absorbs energy at a high temperature, produces mechanical work, and discharges the unused energy at a low temperature. If it is seen only in two dimensions (on any of the 2-D projections of the surface), one or more steps are lost and the viewer gets an incomplete picture of the process. There are also other thermodynamic surfaces on which power cycles may be viewed, but in every case three dimensions are needed to show the full process. Indeed only the simplest of thermodynamic operations can be shown completely using flat curves.

Shouldn't we be teaching this way? Modern computer graphics can generate still and animated images that show engineering systems far more clearly than do their mathematical descriptions alone. Seeing the Rankine cycle on the complete PVT surface gives the global view - it shows at a glance the effect on the overall process of changes in operating conditions. It allows rapid, qualitative design. Equations, calculations, numbers? Of course they're important, but nothing captures the imagination so quickly as a well-conceived image.

The Rankine Cycle drawing shown here was made using our original graphics software "Equations of State" (EOS) with which students construct a variety of such processes on arbitrarily drawn PVT surfaces. Fifteen years ago, when EOS was first developed, one of our chemical engineering undergraduates, John Morrow, undertook a project to create a users manual for the program. John was one of Iowa State's best students and had a fine GPA that included an A in thermodynamics, taught by another professor. But after working with EOS and seeing how it helped him visualize complex thermodynamic situations, he admitted that his A meant only that he had been able to solve the problems -- not that he had really understood what the problems were about. "If I had been shown the visual models of those processes and been able to see all of the variables changing," John concluded, "my numerical answers would have made more sense to me."

John Morrow was a visual person. He was able to use visual thinking -- his right brain -- in an engineering context. But there is an unfortunate bias against right-brain thinkers in our society. Our educational system places too little emphasis on right-brain methods, particularly in science. Curves and surfaces and slopes and intercepts are for arty types but not for the scientists and engineers who keep the wheels turning. If you've ever said "that's a left-handed way of doing something," or "that's really gauche," or "she plays a sinister role" (sinister is the Latin word for left), then you're a part of that bias also. The left side of the body is managed by the right side of the brain. There is an important segment of our population that thinks more naturally in these subjective, artistic, qualitative, and relational ways, and we are missing their contributions to science and engineering by devaluing their learning style.

What can we do to bring such people into the engineering fold? Probably not very much for those already funneled into a left-brain-intensive mode by left-brain-intensive teachers (who learned from like predecessors). We have to start with grade-school children by varying the way we teach science and by balancing the learning styles that we evoke. Instead of focusing so heavily on calculations and the numbers they produce, let us bring our stunning graphics technology into the classroom and make visualization as much a tool for learning as it is for entertainment. Let us encourage students to use both sides of their brain to comprehend both aspects of the world.

Kenneth R. Jolls is a professor of chemical engineering at Iowa State University and a 1996 recipient of the Responsible Care National Catalyst Award.


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