# Why is there a separate SI unit for temperature?

Assuming I got the below facts correct:

• There are 7 SI units - mass (kg), length (m), time (s), current (A), temperature (K), luminous intensity (cd), amount of substance (mol).
• Thermal energy is essentially nothing but kinetic energy.
• Temperature is a measure of thermal energy (hence measure of kinetic energy).
• Kinetic energy can be expressed in $$[M^1 L^2 T^{-2}]$$ (a function of mass, length and time).

Per these facts, is kelvin (SI unit for temperature) also a function of mass, length and time. If so, why do we need a separate SI unit specially for temperature? Am I missing something?

• physics.stackexchange.com/questions/166568 and physics.stackexchange.com/questions/231017 may already cover your question. Jan 9, 2021 at 12:16
• Does this answer your question? Is the Boltzmann constant really that important? Jan 9, 2021 at 12:53
• I don't think this question is a duplicate of the linked question, since on the surface one is asking about the units of $T$ and the other is asking about the value of $k_B$. (The OP might be able to answer their question by reading that duplicate, though.) Jan 11, 2021 at 16:54
• Though the answer / reasoning might be the same, but the questions were different. I am a physics noob and am hearing Boltzman constant for the first time. I don't care about the constant, my question was more to understand the reason for choosing a separate SI unit for temperature. @MichaelSeifert Jan 17, 2021 at 16:56

Good question. In any system of units the proportionality factor between the unit of temperature and the unit of energy is the Boltzmann constant. If we set the Boltzmann constant to $$1$$ - as it is in the system of Planck units - then in effect we are measuring temperature and energy in the same units.
However, using Planck units in everyday life would create practical difficulties, because the Planck temperature is so very large - the temperature of a cup of tea is approximately $$2 \times 10^{-30}$$ Planck units. You can think of this as being a measure of how small atoms are - an everyday object contains a large number of atoms, so its average thermal energy per atom is very small compared to its macroscopic kinetic energy, potential energy etc. So to produce a set of units in which both typical macroscopic energies and temperatures have reasonable values (not too large, not too small) you need to set the Boltzmann constant to a very small value.
• To be fair, you could use a system of units where $k = 1$ while not going all the way to Planck units. For example, if you used a version of SI where $k = 1$, the temperature of a cup of tea would be $5 \times 10^{-21}$ J. That's not nearly as numerically small as it is in Planck units, but your broader point of course remains true: it's inconveniently small. Jun 14, 2021 at 19:57