2.1 Thermometers

A thermometer measures changes in mechanical properties, or changes in electrical properties, or other changes in the material at different temperature reference points. Examples include the expansion of mercury in the iconic mercury thermometer, or the platinum resistance thermometer shown in class. The values of these material properties are simply labels for the different temperature reference points.

The Boltzmann factor

has a universal parameter called $k_{B}T$ that we want to measure¹¹ 1 Later we will see that this parameter is defined as the change in the entropy with respect to energy $(\partial S/\partial E)\equiv 1/T$. The notion of entropy is independent of any particular substance or property. . To make this measurement we need a simple system where the probabilities can be translated into the material properties of the substance. We used the Boltzmann factor to calculate the pressure of an ideal gas at constant volume. This pressure is proportional to precisely the $k_{B}T$ parameter appearing in the Boltzmann factor. Thus a mechanical property of ideal gasses, i.e. their pressure, can be used to measure the $k_{B}T$ parameter. The readouts of all other thermometers were calibrated against the ideal gas pressure-thermometers²² 2 Today there are other systems which can provide additional absolute temperature calibrations, but the ideal gas still plays an important role. .