What is a Kelvin?

I admit to a perverse fascination with metrology, specifically with the question of how fundamental units of measure are defined, so I enjoyed this article on the possibility of redefining the kelvin.  (Among my other forms of geekiness, I also like knowing about grammar and usage trivia, so yes, it is “kelvin,” not “Kelvin”.)

In the old days, of course, the unit of temperature was defined by setting 0 and 100 celsius to be the freezing and boiling points of water.  That’s far from ideal, since those temperatures (especially the boiling point) depend on atmospheric pressure.  We can do much better by defining the temperature scale in terms of a different pair of temperatures, namely absolute zero and the temperature of the triple point of water.  The triple point is the specific values of temperature and pressure such that liquid, gas, and solid phases coexist simultaneously.  Since there’s only one pair (T,P) such that this happens, it gives a unique temperature value that we can use to pin down our temperature scale. That’s how things are done right now: the kelvin is defined such that the triple point is exactly 273.16 K, and of course absolute zero is exactly 0 K.

So what’s wrong with this?  According to the article,

“It’s a slightly bonkers way to do it,” says de Podesta. According to the metrological code of ethics, it is bad form to grant special status to any single physical object, such as water.

This is certainly true in general.  For instance, the kilogram is defined in terms of an object, a particular hunk of metal in Paris whose mass is defined to be exactly 1 kg.  That’s clearly a bad thing: what if someone lost it?  (Or, more likely, rubbed a tiny bit of it off when removing dust?)

But this doesn’t really make sense to me as a problem with the kelvin.  Water isn’t an “object”; it’s a substance, or better yet a molecule.  At the moment, the unit of time is defined in terms of a particular type of atom, namely cesium-133, and that definition is regarded as the gold standard to which others aspire.  Why is cesium-133 OK, but H2O bad?

Although the objection-in-principle above doesn’t seem right, apparently there are some important pragmatic reasons:

‘Water’ needs to be qualified further: at present, it is defined as ‘Vienna standard mean ocean water’, a recipe that prescribes the fractions of hydrogen and oxygen isotopes to at least seven decimal places.

OK, I’ll admit that that’s a problem.

The proposed solution is to define the kelvin in relation to the joule, using the familiar relationship E = (3/2) kT  for a monatomic ideal gas.  This is fine, as long as you know Boltzmann’s constant k sufficiently accurately.  Researchers quite a while ago found a clever way of doing this, and they’re so confident about it that they wrote in their paper

If by any chance our value is shown to be in error by more than 10 parts in 10⁶, we are prepared to eat the apparatus.

This boast is all the more impressive when you consider that the apparatus contains a lethal quantity of mercury.

The method involves ultraprecise measurements of the speed of sound, which is proportional to the rms speed of atoms and hence gives the average energy per atom of the gas.  The original work wasn’t precise enough to justify changing the definition of the kelvin, but the hope is that with improvements it will be.

Of course, then the kelvin will be defined in terms of the joule, which is itself defined in terms of the kilogram, which depends on that hunk of metal in Paris.  People are working hard on finding better ways to define the kilogram, though, so we hope that that problem will go away.