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Re: [Phys-L] thermometry

Interesting - the version I offered used to be the 'target' knowledge in the English examinations widely used as university entrance qualifications, and was in the textbooks. I've been around long enough not to assume curriculum models should be unquestionably treated as authoritative, but that was a treatment which made inherent sense to me. You could measure a temperature with a thermocouple and a liquid-in-glass thermometer, in effect interpolating between the fixed point values that were defined as scales, and not expect they would precisely agree (i.e. in principle, not in terms of measurement error) except at the fixed points.

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

Makes sense, but I would have assumed that only applied if they were using the same scale, so if my liquid-in-glass thermometer does not entirely agree with my thermocouple I would not sat that was because one was wrong but because the mercury(say)-in-glass scale is not identical to the thermocouple scale.

The point in the earlier post that a scale may not be linear assumes of course that one has another scale with which to compare that thermometric property with an independently measured temperature (or how could you know?) So the temperature measured using a mercury-in-glass thermometer is linear on a mercury-in-glass scale (by definition) but may not be on thermocouple scale or an ethanol-in-glass scale, etc.  To avoid this one needs a practical scale which can be confidently assumed to match a thermodynamic (theoretical) scale, and I guess at one time no one had one of those: thus the treatment in the school textbooks.


Best wishes

Keith


On 13/02/2018 20:42, John Denker via Phys-l wrote:
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.
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