[perlgeek]

A mostly unrelated question, in case any metrology geeks are around: why is the Kelvin an SI unit?

Naively, there seem to be multiple approaches to derive temperature from other, more fundamental units. Like using the thermodynamic definition, 1/T = dS/dE, or using Boltzmann's law to approach temperature from the mean kinetic energy of gas particles. Are none of them suitable for precise measurement?

[klodolph]

Maybe we will someday, the kilogram and ampere are a bit higher on the priority list right now. Also remember that S is not a quantity that we can directly measure, so 1/T = dS/dE isn't so useful for measuring T.

The effort to redefine the Kelvin would probably use an acoustic thermometer to measure the speed of sound in a gas. This would fix the Boltzmann constant. It seems a bit silly to do this when the definition of the kilogram is expected to change, though.

In the meantime, triple-point cells are pretty convenient, much more convenient than the international prototype kilogram, or the infinite length of wire used to define the ampere. Also remember that laboratory temperature measurements tend to be much less accurate than voltage or mass measurements. ITS-90 is apparently good to within 100ppm, but 1ppm or better is no problem when you're measuring voltage, mass, or length.

Here's a presentation on thermometry, the acoustic thermometer described is what's used to accurately measure the Boltzmann constant: https://www.youtube.com/watch?v=Irr8fOLtiWc

[Thorondor]

It's not really possible to derive temperature from other more fundamental units. For example, you can't define entropy as an absolute number; it needs to be assigned a unit, and the standard way of doing this is to multiply it by the Boltzmann constant, which depends on a unit of temperature. The mean kinetic energy of gas particles (3/2 kT) also depends on the Boltzmann constant.

[bonzini]

Currently the SI is making the triple point of water fixed. I think his point is to make the Boltzmann constant fixed, like the SI is doing for the speed of light, and derive the Kelvin from there. For example 1K could be the temperature at which an atom of (insert some gas here) has a mean kinetic energy of 1.3806488 * 3/2 * 10^-23 J.

However, you have to make sure the definition can be made into an experiment, unlike the old Ampere definition from the article. A definition that mentions perfect gases wouldn't work, if no actual gas exists that can provide a better precision than the triple-point experiment.

Edit: the Kelvin is changing too: https://www.eurekalert.org/pub_releases/2017-04/pb-rft040517...

[amluto]

> For example, you can't define entropy as an absolute number; it needs to be assigned a unit,

You can define entropy directly without reference to other units, although it's a bit awkward. Entropy is the log of the number of microstates that correspond to a system's macrostate. Concretely, if you put n mols of ideal gas molecules in a box of volume V at a pressure P and temperature T, there is some large number of microstates corresponding to all those parameters. Entropy is the log of this number.

In classical mechanics, there's a normalization problem if you try to get an actual number out of this type of problem -- the microstates and all the macroscopic parameters are continuous. In quantum mechanics, though, this issue is solvable, although it's still awkward.

I can imaging a different type of system in which entropy really can be calculated, though. Imagine a particle that can be in exactly one of two states that are macroscopically identical. Now try to cool the system so that the particle is in one of those states of your choice. To do so, you will need to dump exactly 1 bit of entropy.

1 bit of entropy is tiny, but adiabatic demagnetization refrigerators work kind of like this, albeit in reverse, and I could imagine an experiment that would use a device like an adiabatic demagnetization fridge to remove a calibrated number of bits of entropy from some object. From this, you could, in principle, define entropy directly.

[URSpider94]

While you are right that this is the statistical definition of entropy, there are two issues: first, entropy is a unitless quantity, so defining it exactly doesn't actually move the ball forward in terms of defining units of measure. Second, outside of its theoretical underpinnings, physicists and chemists hardly ever talk about absolute values of entropy, they almost always use differences in entropy -- which factors out the need to define the exact number of microstates present before and after.

[amluto]

> first, entropy is a unitless quantity

The parent post asked about defining temperature in terms of more fundamental units. Entropy is typically written in J/K. If you treat it as dimensionless, then you get a definition of temperature in terms of energy for free. My point is that you can, in principle, actually do an experiment to make this useful.

[BurningFrog]

One answer is that there are SI units for a lot of derived units. A Watt is Joule/second, for example. But that's not what you're really asking.

Kelvin is considered one of the 7 base SI units, as described here: http://physics.nist.gov/cuu/Units/units.html

I think the mean kinetic energy of gas particles is impossible to measure directly. You can compute it by measuring the temperature though :)