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Wikipedia's article on the recent change to the definition of the SI base units states, as the reason for changing the definition of the kelvin:

A report published in 2007 by the Consultative Committee for Thermometry (CCT) to the CIPM noted that their current definition of temperature has proved to be unsatisfactory for temperatures below 20 K (−253 °C; −424 °F) and for temperatures above 1,300 K (1,030 °C; 1,880 °F).

Sure, I understand that tying temperature to a physical artifact, even a highly-reproducible one like the triple point of water, is unsatisfying. But the way it's worded implies there's some more significant problem, as if temperature measurements outside that range are less accurate or less reliable. What is that problem?

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The best resource I've found that describes the shortcomings of the previous definition of the kelvin is

The kelvin redefinition and its mise en pratique. B Fellmuth et al. Phil. Trans. R. Soc. A 374, 20150037 (2016).

Basically, the pre-2018 kelvin, defined via the triple point of water and propagated to the full range of temperatures via the ITS-90 scale, is the best we have for most temperature ranges, but it can be improved at very low and very high temperatures:

While the redefinition of the kelvin will have no impact on the status of the ITS-90 or PLTS-2000, there will be significant benefits, particularly for temperature measurements below approximately 20 K and above approximately 1300 K, where primary thermometers may offer a lower thermodynamic uncertainty than is currently available with the defined scales.

Here primary thermometry refers to the direct measurement of thermodynamic temperature, as defined in statistical mechanics (but see the paper's §3 for a more precise definition). This can be done via a variety of methods but, with current technology, those methods are only able to achieve better stability, precision and reproducibility at the < 20K and > 1300 K ranges mentioned above. In the middle interval, the change in definition does not affect practical thermometry:

In particular, the most precise temperature measurements in the core temperature range from approximately 25 to 1235 K will, at least initially, continue to be traceable to standard platinum resistance thermometers calibrated according to the ITS-90.

This leaves us, then, with two ranges where there are primary-thermometry methods that beat the ITS-90 precision:

  • At very low temperatures you can use Acoustic Gas Thermometry, where you have a dilute gas that you can treat as an ideal gas, which is an extremely well-characterized system. Here you measure the speed of sound, which depends on the temperature in well-understood ways.

  • At very high temperatures, radiometric thermometry uses Planck's spectral law to infer the temperature of a glowing object from the spectrum of the electromagnetic radiation that it emits. This is again a well-characterized system where the thermodynamic temperature enters only via $k_BT$ to the measurable observables.

Looking forward, there also seems to be an expectation among metrologists that the pace of improvement in precision and reproducibility in primary thermometry will continue to beat that of practical temperature scales, which means that $k_B$-based thermometry will eventually displace ITS-90 in other temperature ranges. This future-proofing is an important aspect of the change to a universal-constant-based definition.

For now, though, only those two extreme temperature ranges are affected.

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It is difficult to determine Boltzmann's constant from the temperature of the triple point. That is easier at extremely low temperatures (with statistical mechanics) or at very high temperatures (from radiation).

At ambient temperatures, the connection to Boltzmann's constant is by using gas thermometers. Very cumbersome, and not as precise as in the other ranges.

ITS-90 will remain in effect. For calibration of thermometers at ambient temperatures, the triple point of water will continue to be used.

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I think that the problem is that the temperatures that you quote are a long way away from the triple point of water and no one thermometer can accurately span to your quoted temperatures from the triple point of water.

A definition of the kelvin that fixes the value of Boltzmann’s constant makes it possible to design thermometers to suit the temperature range of interest without being compromised by the need to function well at the TPW. The new kelvin definition, in principle, enables all equations of state that include temperature to be used to make traceable temperature measurements.

Taken from The Boltzmann constant and the new kelvin which was written in 2015 and gives a nice overview.

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