FOURTH LECTURE.

The Equation of State for a Monatomic Gas.

My problem today is to utilize the general fundamental laws
concerning the concept of irreversibility, which we established
in the lecture of yesterday, in the solution of a definite problem:
the calculation of the entropy of an ideal monatomic gas in a
given state, and the derivation of all its thermodynamic proper¬
ties. The way in which we have to proceed is prescribed for us
by the general definition of entropy:

S=^ klogW.                             (13)

The chief part of our problem is the calculation of W for a given
state of the gas, and in this connection there is first required a
more precise investigation of that which is to be understood as
the state of the gas. Obviously, the state is to be taken here
solely in the sense of the conception which we have called macro¬
scopic in the last lecture. Otherwise, a state would possess
neither probability nor entropy. Furthermore, we are not
allowed to assume a condition of equilibrium for the gas. For
this is characterized through the further special condition
that the entropy for it is a maximum. Thus, an unequal dis¬
tribution of density may exist in the gas; also, there may be
present an arbitrary number of different currents, and in general
no kind of equality between the various velocities of the molecules
is to be assumed. The velocities, as the coordinates of the
molecules, are rather to be taken a priori as quite arbitrarily
given, but in order that the state, considered in a macroscopic
sense, may be assumed as known, certain mean values of the
densities and the velocities must exist.    Through these mean

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