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

New Trends in Physics Teaching IV
A different computational approach is used by Reynolds (Reynolds, 1965; see also Open
University, Course TI 00, 1972). He uses an artificial system of ten particles each with access to
five equally spaced energy levels, so that all possible distributions (there are 23) and all possible
microstates (there are 72 403) can be enumerated. The computer is given appropriate transition
probabilities, and then follows the system to equilibrium, showing that there is a stable equilibrium,
with the system spending time in each distribution proportional to the number of microstates it has.
Two-state systems
In chapters 2, 3, and 4 Reif exploits to some degree the valuable isomorphism between such
different examples as particles in two halves of a box and two-state systems such as a paramagnetic
solid. The arguments above (Unit changes, pp. 165 et seq) about mixtures are also of the same
form, giving a whole class of useful simple problems which are physically different but use the
same simple analysis. Reif does not use the unit-change method in his account of paramagnetism.
If one does, it becomes quite simple. Regarding the two states (parallel or antiparallel to the field)
as A and B states as before, a transition from B to A changes 52, with
52 after 152 before = NB /NA
If energy e is borrowed from a heat bath for the transition, there is another change to Cl:
so that the equilibrium value is
52 after/n before = exP(*/kr)
NB INA = exp(e/kr)
-
Putting E = 2pB, and the magnetization asp (NB-NA)
yields the usual results for a paramagnetic
solid, and the Curie law as a good approximation at small pB/kT.
The same style of discussion serves to handle such problems as the proportions of Zuevo and
dextro forms in a sugar, the ionization of a gas or of water, and so on, with minor modifications
each time.
THE NUFFIELD ADVANCED PHYSICS APPROACH
The Nuffield Advanced Physics (1972) approach reflects many of the conclusions that seem to
me to follow from the previous analysis.
First, informal, intuitive teaching of the sort examplified by Bent is likely to be important.
In the Nuffield course there is a good deal of it: film shown forwards and in reverse; simulations
using dice; and (with other values of its own) discussion of fossil fuel resources. We also borrowed
from Bent the idea of using numerical values of entropies.
Second, arguments using the total number of microstates 52, getting from changes to 52 an
average distribution, have advantages over the more usual calculation of the number of states
W,,, in the most probable distribution. The latter is less useful in the end, and involves more
work. In the Nuffield work we only use 52.
Third, calculations using unit changes offer an important simplification, and can even avoid the
need to calculate 52 (or W,,,) at all, since ultimately only changes to them are of interest. But
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