New trends in physics teaching, v.4; The ... - unesdoc - Unesco

Introductory statistical physics
one could not convert any of its heat energy into work’; ‘. . . if we could obtain work by extracting
the heat out of the ocean’. Such remarks can only be read as speaking of heat as the energy
inside things. Feynman is perfectly aware of the difference between heat and internal energy,
and frequently draws all the necessary distinctions. But it is, I think, a property of many
approaches to statistical mechanics, which emphasize particular microscopic models, that they
tend to make it natural to blur the distinction: to talk at one moment of heat as flowing under a
temperature difference and at another of heat as internal energy, usually ‘random’ in some
sense. Indeed, in the exponential atmosphere argument, one is left with some impression that the
molecules climb the gravitational hill at the expense of the ‘random’ internal energy or heat in
the gas.
What is the Feynman’s temperature scale?
Feynman offers the excuse to raise another matter.
In the expression exp(- EIkT), what is T? In his approach to the Boltzmann factor, it appears
that T is the temperature on the ideal gas scale, because the argument derives from the gas laws
and kinetic theory. More fundamentally, of course, it is not that at all, but is a temperature
defined statistically ; defined by a relation of the form
T = E/kA lnn
in which k functions, not as R/N, but as an arbitrary scale constant linking an energy E and a
change in the logarithm of a number of microstates to the Kelvin scale on which the triple point
of water has a chosen value.
Of course the ideal gas temperature is the same thing, but it is the same because of what ideal
gases are, not because of what temperature is. Similarly k = R/N because of the nature of ideal
gases; the relation says nothing about k.
THE PSSC’ APPROACH
The PSSC Physics: Advanced Topics Supplement (1 968) and College Physics (1968) propose a
quite different, equally radical and equally simple approach, now mainly focused on the second
law from a statistical point of view.
The overall strategy
The PSSC strategy is startlingly simple. Perhaps the easiest case of all to argue statistically is that
of the spreading out of N independent particles into double the previous volume. Arguing that
each has a probability of 50 per cent of being by chance in the original half, the probability that
all the particles wil so do is YP or 2-N. The logarithm -N In 2 of this quantity appears in the
expression NkT In 2 for the work done in changing the volume (isothermally). In this case, the
work done is equal to the heat exchanged with a heat sink, so
AQ = NkT In 2
1. Physical Science Study Committee.
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