*Black body curves.(Modified Wikimedia Commons image by Darth Kule.*

One interesting thermometer I used to measure very high temperature was a hot wire pyrometer that used the Planck radiation law as its working principle. This pyrometer was essentially a telescope through which you could view your crucible, and in the same eyepiece you also saw a metal wire internal to the pyrometer. The procedure was to increase current through the wire until it glowed with the same color as your crucible, read the current, and then convert to temperature. Since what was being viewed, and the metal wire, were not strictly black bodies, there were necessary corrections based on material emissivity. All this didn't give you much confidence in your final temperature reading. The problem with all thermometers is that they needed to be calibrated, and that's where the fundamental definition of temperature, the thermodynamic temperature, enters the discussion. The gas thermometer, one manifestation of a thermodynamic thermometer, makes use of Charles' Law, which states that the volume occupied by an ideal gas at a fixed pressure will be proportional to the absolute temperature.

*Principle of a gas thermometer.While atmospheric pressure is a convenient working pressure, it's not quite constant. Helium, however, functions as a good ideal gas, since it's inert, monoatomic, and it remains a gas to very low temperatures.(Created using Inkscape.*

The physical properties of nearly everything are highly temperature-dependent, so you can build a thermometer in many ways. Some principal methods are listed on the website of the US National Institute of Standards and Technology: Acoustic thermometry (based on the speed of sound in argon gas), photonic thermometry (based on the thermal expansion of a Bragg grating in an optical fibers), radiation thermometry (based on the Planck radiation law), and Johnson noise thermometry. Since electrical current is the movement of electrons, it's reasonable to conclude that the thermal motion of electrons would create a current; and, since these motions are random, the current is a noise current. In 1928, John B. Johnson of Bell Labs was the first to measure this noise, often called the Johnson-Nyquist noise.[2] Physicist, Harry Nyquist, also of Bell Labs, did a theoretical study of these currents,[3] and his equation for the root mean square (RMS) noise voltage

where

*NIST quantum voltage noise source (QVNS).The QVNS provides a noise signal that can be compared to the Johnson noise of a resistor.(NIST photo by Dan Schmidt.*

The reason for wanting a precise value of the Boltzmann constant is that this constant will be given a fixed value in 2018 in order for the unit of absolute temperature, the kelvin, to be defined based on the Boltzmann constant. Presently, k

"By defining the kelvin in terms of the Boltzmann constant, you don’t have to have these variations in uncertainty, and you can use quantum-mechanical effects."[8]There are some restrictions on the Boltzmann constant measurement for it to be good enough to redefine the kelvin. There must be one experimental value with a relative uncertainty below one part per million, and there needs to be at least one measurement from a different technique that gives a relative uncertainty below three parts per million.[8] At present acoustical measurements have given the best accuracy.[8] Great confidence is given to a value when it's derived from different methods, multiple times.[8] In 1999, NIST developed the QVNS as a voltage reference for Johnson noise thermometry. The QVNS is based on a superconducting Josephson junction, and it provides a fundamentally accurate noise voltage signal, since it produces quantum mechanical noise. The resistor noise voltage is measured in comparison to the QVNS noise, allowing a very accurate temperature measurement, and a measurement of the Boltzmann constant when the resistor is held at a known temperature.[8]

- Thermometry Web Page, NIST Web Site.
- J. Johnson, "Thermal Agitation of Electricity in Conductors", Phys. Rev. 32 (1928), pp. 97ff.
- H. Nyquist, "Thermal Agitation of Electric Charge in Conductors", Phys. Rev. vol. 32 (1928), pp. 110ff.
- Johnson Noise Thermometry, NIST Web Site.
- Jifeng Qu, Samuel P Benz, Alessio Pollarolo, Horst Rogalla, Weston L Tew, Rod White, and Kunli Zhou, "Improved electronic measurement of the Boltzmann constant by Johnson noise Thermometry," arXiv, December 31, 2014.
- J. Qu, S. Benz, K. Coakley, H. Rogalla, W. Tew, D. White, K. Zhou and Z. Zhou, "An improved electronic determination of the Boltzmann constant by Johnson noise thermometry," Metrologia, vol. 54, no. 4 (August, 2017), https://doi.org/10.1088/1681-7575/aa781e.
- N.E. Flowers-Jacobs, A. Pollarolo, K.J. Coakley, A.E. Fox, H. Rogalla, W. Tew and S. Benz, "A Boltzmann constant determination based on Johnson noise thermometry," Metrologia, vol. 54, no. 5 (October 2017).
- NIST 'Noise Thermometry' Yields Accurate New Measurements of Boltzmann Constant, NIST Press Release, June 29, 2017.