Thermometer Constructions
Table of Contents
1. Introduction
We will construct a thermometer, or give several different constructions.
CAUTION: these are purely "intellectual" and abstract. These are NOT intended to be instructions for constructing an actual thermometer.
2. Greiner's Dilute Gas Thermometer
Consider a glass container, which intuitively looks like a volumetric flask: a large reservoir with a thin glass boundary, and a long thin neck with a thick glass boundary. We place some dilute gas inside the flask, then "cap" it off with a "blob" of mercury. (This is very dangerous, please do not try this at home.)
This summarizes the construction found in Thermodynamics and Statistical Mechanics by Walter Greiner, Horst Stöcker, and Ludwig Neise. (See page 10.)
2.1. Calibration
The mercury acts as a "pointer". We calibrate this thermometer with the following steps:
- measure ice's temperature (as 0 degrees) and place a "tick" on the neck of the flask where the pointer rests;
- measure boiling water's temperature (as 100 degrees) and place a "tick" on the neck of the flask where the pointer rests; and finally,
- divide the distance between these markings into equal parts according to the temperature scale used.
2.2. Physics Underlying This Thermometer
Why does this work? Well, for a dilute gas, it turns out to be approximated by ideal-gas behaviour very well. In particular, we would have
\begin{equation} pV = nRT \end{equation}If we make the neck thin enough, and the reservoir large enough, then pressure \(p\) would be approximately constant. We then have
\begin{equation} \frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}} \end{equation}for volume \(V_{j}\) and temperature \(T_{j}\) for the system in two states \(j=1,2\).
The pointer (blob of mercury) then tracks the volume of the gas, which is directly proportional to the temperature of the environment (or whatever the thermometer is in contact with).