Answer to Question #20017 in Molecular Physics | Thermodynamics for Ujan Chakraborty

Question

Temperature is the average of the kinetic energies of all molecules of a body.Then, why do we consider it a different fundamental physical quantity altogether [K], and not an alternate form of energy, with dimensional formula derived from 3 initial fundamental quantities length[L], mass[M] and time[T]?

Answer 1

Temperature is nothing else than energy per degree of freedom. It is purely for historical reasons that energy per degree of freedom is measured in Kelvin, and not in, say, micro-eV. It is just that these systems of units got fixed and became widely used before the statistical meaning of temperature became clear.
For the same reason, mass measured in kg and not in, say, Tera-eV.
If you would correct all of this, and apply more rational choices of units, you would end up with a natural system of units. This is what many physicists do in their professional lives. In such a system constants like the speed of light and Boltzmann's constant end up as being defined equal to unity. This makes it clear that these are not constants of nature, but man-made artifacts caused by the use of clumsy systems of units. In that respect Boltzmann's constant k is no different than the constant measuring the number of cubic inches in a gallon.