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

Introductory statistical physics
Counting states in one system using another
Fundamental to the PSSC approach is the attribution of the change in the number of microstates
to the heat bath. This raises a number of new issues and has important consequences for the rest
of the structure of the PSSC teaching programme (see figure 3).
Having argued that the change in In 52 (though they use ‘probability’) of a gas is NkT In 2
when it doubles its volume isothermally, they need to find a way of saying that the same change
of In 52 occurs in the heat bath that delivers heat AQ to the gas, so that the value of AS that
really matters, that of the heat bath, is brought out. The point is that the entropy change of the
gas is easy to calculate but is not what is wanted; while that of the heat bath is hard to calculate
and is what is wanted.
The trouble is that AQ/T is only equal to NkT In 2 if the change is reversible. PSSC thus have
two major problems: to explain what a reversible change is; and to explain why, in a reversible
change, 52 for the whole system is unchanged so that changes in 52 for the two parts of it are
equal and opposite. As with Feynman, these problems arise out of trying to do statistics without
doing statistics (or doing, as here, very little).
PSSC’s reversible and irreversible oscillations
It cannot be said that PSSC’s solution to the necessity to say what reversibility is lacks ingenuity
(figure 4). A filmed demonstration (Ferretti) shows gas being made to oscillate in volume, by
being coupled to an inverted pendulum. The decay of free oscillations is studied, with varying
amounts of aluminium foil surface exposed to the gas, so that oscillations are nearly adiabatic
(no foil), nearly isothermal (much foil) and in between. At the two extremes, the damping is
least, so suggesting that isothermal and adiabatic changes could both be reversible.
VY
masses
rnerr
vo-
Figure 4. PSSC gas oscillator.
Figure S. PSSC marble machine.
Necessary and unnecessary statistics
The PSSC strategy not only needs reversibility and irreversibility, but it needs to present them
statistically. This they do mainly through the use, again on film,of another special pedagogic
device, the marble machine (figure 5). The marble machine is a pair of channels which can carry
marbles, each leading to a larger space with a gap between the two, all mounted on a tilting
board. If marbles are started in one channel, they slowly become distributed between the two,
as the board is tilted many times. Conceptually, much hinges on the machine. It has to illustrate
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