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Re: [Phys-L] thermometry



On 02/13/2018 01:21 PM, Prof Keith S Taber wrote:

My understanding (and what I used to teach when I was real science
teacher) is that "the property change of a thermometer which
corresponds to a temperature change" is linear by definition.

I wouldn't have said that.

Is that still the convention?

I don't think that was ever the convention. There are
some super-fundamental properties that you want "the"
temperature to satisfy.

1) A equilibrium, all parts of the system must be
at the same temperature.

That means that if you have two thermometers in
equilibrium, and they disagree, at least one of
them is wrong.

2) At a more fundamental level, temperature is
defined as ∂E/∂S at constant volume.

Note that property (1) is an immediate corollary
of this definition, assuming the various parts
can reach equilibrium by exchanging energy and
entropy. Moore&Schroeder have lovely diagrams
to show why this must be so.

This definition may not be directly usable in
the introductory algebra-based course, but it
is something to keep firmly in mind.

================

I've seen plenty of thermometers based on properties
that are nowhere near linear.
-- diode current is exponential in temperature
-- diode voltage is logarithmic in temperature
-- at millikelvin temperatures, people use carbon
comp resistors as thermometers. The resistance
is exponential in the square root of temperature.
Don't ask me why, but it is, quite nicely, over
a wide range.

It's up to the thermometer maker to calibrate the
device so that it upholds the fundamental principles.
If that means the calibration curve is nonlinear,
so be it.