The kelvin

The kelvin (K) defines thermodynamic temperature (pāmahana wera ahupūngao).

The kelvin used to be defined in relation to the triple point of water – the specific thermodynamic temperature at which the three phases of water (solid ice, liquid water and gaseous water vapour) co-exist (0.01°C or 273.16 K at a pressure of 611.73 Pa).

Now, the definition of temperature is linked to the Boltzmann constant (k), which relates the average relative kinetic energy of particles in a gas with the temperature of the gas. It has a fixed value of 1.380 649 x 10^–23 J K^–1. The joule (J) is a unit equivalent to kg m²s^–2, and all of these units (the kilogram, metre and second) are traceable back to fundamental constants. By fixing k, we can be confident that our definition of temperature will remain consistent.

One kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy k T by 1.380 649 x 10^–23 J.

Discussion point: Temperature scales can be relative or absolute. A relative temperature scale measures amounts that are more or less than a reference amount, using positive and negative numbers. An absolute temperature scale uses the value zero as the lowest limit of temperature. How do the commonly used measurements of Celsius, Fahrenheit and Kelvin fit into this?

NOTE: This video was filmed prior to the change to SI definitions. As of 20 May 2019, kelvin is now defined in terms of the Boltzmann constant rather than the triple point of water.

Transcript

FARZANA MASOULEH

At the moment, we use the triple point of water to define the temperature. That is defining the temperature based on three states of water, which is solid ice, water vapour and liquid water. If all these states of water co-exist in an equilibrium, the temperature at that point would be 0.01°C or 273.16 K.

This is a very reliable method and reproducible, so that’s why we have been using it for a long time. But the fact that it only relies on one point of temperature to define the whole spectrum, it’s not very accurate, especially for extreme high and low temperatures.

So we need to use another method to be able to get more accurate readings for temperature. What we use is the Boltzmann constant, which is shown with that number at the bottom [k = 1.380 649 x 10^-23 J K^-1].

In 1800, Boltzmann was a scientist who was monitoring temperature and really found out that temperature is nothing but monitoring the energy so there is a relation between energy and temperature. Later Planck, another scientist, gave a ratio to the energy and temperature and defined that ratio after Boltzmann and called it Boltzmann’s constant.

So now, in this slide, I’m going to describe a very interesting fact that shows us how we are ready now to use Boltzmann’s constant to define our temperature. If you see from 1900, we have the accuracy of the measurement for the Boltzmann constant, and this scale is logarithmic so it shows a very accurate measurement at the moment because the accuracy is going on certainty of – the measurement is going from a bit over 1 to less than 0.001. So the first two measurements of Boltzmann’s constant were done by Planck and Einstein, and one of those last ones there is done by one of our colleagues at MSL. Meanwhile, temperature has – the accuracy or the uncertainty measurement of temperature has not changed a lot, and we see that, at the moment, we can measure Boltzmann’s constant much better than we can do temperature. So now is the right moment to try to do, to try to define temperature based on the Boltzmann constant, because if we use the Boltzmann constant now, we don’t upset any temperature measurements which have been done at the past.

Acknowledgements

This video clip is from a recording of a presentation by the Measurement Standards Laboratory of New Zealand (MSL) in celebration of the redefinition of the International System of Units (SI), which happened on 20 May 2019. The presentation by Peter Saunders and Farzana Masouleh of MSL was filmed at Unleash Space, Faculty of Engineering, Auckland University.