Entropy and the Kinetic Theory: the Molecular Picture
Michael Fowler 7/15/08
Searching for a Molecular Description of Entropy
Clausius introduced entropy as a new thermodynamic variable to measure the “degree of
irreversibility” of a process.
He believed that his two laws of thermodynamics (conservation of
energy and that entropy never decreases) were profound and exact scientific truths, on a par with
Newton’s laws of dynamics.
Clausius had also made contributions to kinetic theory, publishing
work as early as 1857, although unlike Maxwell he did not adopt a statistical point of view—he
took all the molecules to have the same speed.
(Actually, this work inspired Maxwell’s first
investigations of kinetic theory and his discovery of the velocity distribution.)
Clausius was the
first to attempt a semiquantitative analysis of the effects of molecular collisions (see later).
Obviously, if the kinetic theory is correct, if heat
motion of molecules, the fundamental laws
of thermodynamics must be expressible somehow in terms of these molecular motions. In fact,
the first law of thermodynamics
easy to understand in this way: heat is just kinetic energy of
molecules, and total energy is always conserved, but now instead of having a separate category
for heat energy, we can put the molecular kinetic energy together with macroscopic kinetic
energy, it’s all ½
with the appropriate masses.
: What about potential energy?
For the ideal gas,
energy terms between molecules are negligible, by
definition of ideal gas.
Actually, potential energy terms
important for dense gases, and are dominant during
phase changes, such as when water boils.
The extra energy needed to turn water into steam at the same temperature
is called the
It is simply the energy required to pull the water molecules from each other working
against their attraction—in other words, for them to climb the potential energy hill as they move apart.
“latent heat”— still standard usage— is actually a remnant of the caloric theory: it was thought that this extra heat
was caloric fluid that coated the steam molecules to keep them away from each other!)
But how do we formulate
in terms of this molecular mechanical model?
age 22, in 1866, wrote an article “On the Mechanical Meaning of the Second Law of
Thermodynamics” in which he claimed to do just that, but his proof only really worked for
systems that kept returning to the same configuration, severely limiting its relevance to the real
Nevertheless, being young and self confident, he thought he’d solved the problem.
1870, Clausius, unaware of Boltzmann’s work, did what amounted to the same thing.
claimed to have found a function of the molecular parameters that increased or stayed the same
with each collision of particles and which could be identified with the macroscopic entropy.