A First Course in String Theory
2.1 Exercises with units
(b) Explain the meaning of the unit K (degree kelvin) used for measuring temperatures, and explain its relation to the basic length, mass, and time units.
where is the internal energy.
The units of and are the same.
In other words, the Boltzmann constant translates the temperature unit to the language of energy unit .
However, although the temperature unit and the energy unit have the relation
just would not give the correct value of energy , not to mention that we have not yet specified of which the energy is.
For an ideal gas,
and the average translational kinetic energy is
for 3 degrees of freedom. In 3D space, if there are only translational motions, there are only 3 degrees of freedom.
In other words, just the value of itself gives no physical meaning. Instead, can be interpreted as the average translational kinetic energy of the particles in an one dimensional space. Equivalently, gives that in our three dimensional space.
Another main difference is that although energy is an extensive property, temperature is an intensive property.
We define the temperature unit Kelvin by requiring the water triple point temperature,
Once this value is fixed, the Boltzmann constant value can be estimated by using, for example, the ideal gas law
because always comes with .
— Me@2020-02-16 11:14:24 AM
2020.02.16 Sunday (c) All rights reserved by ACHK