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