represents, for every state of the gas, the given space and velocity distribution of the gas molecules. The permanent, stationary, state of the gas known as thermal equilibrium is only a special case of the general case (18), this special case being widely known as MAXWELL'S Law of Distribution of Velocities.
Step c
Special Case of (b), Namely, Determination of Entropy S for the Thermal Equilibrium of a Monatomic Gas
This case PLANCK derives very easily from the general case represented by (18). As the desired result has already been found in another way in pp. [48]-[53] when dealing with MAXWELL'S Law (of distribution of molecular velocities), we will not repeat PLANCK'S derivation of the law from (18). It will suffice here to give the results: The law of distribution is given by function
where
and
are constants and
