Today, we ask what temperature is. The University
of Houston's College of Engineering presents this
series about the machines that make our
civilization run, and the people whose ingenuity
created them.
Very early in any
thermodynamics class, I ask students to tell me
what they think a thermometer measures. Think about
that: A thermometer gives us a number that we call
temperature, but what have we really measured? All
the reasonable answers seem to crumble in our hands
when we try to hold them in the light.
One student asks, "Isn't temperature a measure of
heat?" That sounds reasonable, but suppose we're
boiling water. We heat it and heat it until we've
turned all the water into steam. But now the steam
is the same temperature the water was. All that
heating and no temperature change.
Another student asks, "Doesn't temperature measure
the speed of molecules?" That turns out to be true
as long as the molecules form a very thin gas. It
doesn't work at all for complicated materials.
So take another tack. Maybe temperature just
measures the length of a mercury or alcohol column.
Okay, suppose we fill a capillary tube with mercury
or alcohol, dip it in a glass of ice water, draw a
line, and call it zero degrees Celsius. Then we dip
it in boiling water, and we mark off a hundred
degrees Celsius.
Finally, we ask where we should mark off fifty
degrees Celsius. The answer is not right
in the middle of the column. Neither mercury nor
alcohol expands exactly the same amount for each
degree of temperature change. The two thermometers
would read a little bit differently. We need some
independent means for finding out where the
fifty-degree mark would fall.
Not until halfway through the course can we finally
define temperature so all the many pieces fit
together. And when we do, the definition is too
technical for me to say on the air.
Voice: No, wait a minute. You
can't leave us hanging.
Really, you don't want to know.
Voice: Sure we do. Tell
us.
Okay, okay.
"The temperature of any material is the partial
derivative of its energy with respect to its
entropy while you hold its volume constant."
Voice: You're joking!
No, I told you it'd sound arcane. And yet, science
has to be about making sense. In the end, our
senses tell us what temperature is, at least
between the freezing point of our bodies and about
140 degrees Fahrenheit, where our nerves begin to
burn out.
Temperature is a measure of intensity. The
higher the temperature of anything, the greater
that intensity is, and the more heat it will drive
into colder bodies. Temperature can really be
thought of as a measure of the ability to drive a
flow of heat.
And I'm reminded once more that, objective as we
try to be, our subjective selves always inform
science. Let me leave you with a fine insight into
temperature and intensity by poet Christopher
Morley:
I bid you, mock not Eros;
He
knows not doubt or shame,
And, unaware of proverbs,
The
burnt child craves the flame.
I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
work.
(Theme music)
For proper discussion of temperature, see any
undergraduate thermodynamics text. I especially
recommend W. C. Reynolds, and H. C. Perkins,
Engineering Thermodynamics. Garden City, NJ:
Doubleday and Co., Inc., 1966.
For a discussion of temperature in relation to
molecular velocity, see, e.g., C. L. Tien, and J.
H. Lienhard, Statistical Thermodynamics.
Revised ed. Washington, D.C.: Hemisphere, 1979.
The Christopher Morely quotation is from his poem,
Of a Child That Had a Fever.
(Photo by John Lienhard)
The Engines of Our Ingenuity is
Copyright © 1988-2003 by John H.
Lienhard.
