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

Introductory statistical physics
TABLE 1. Some entropies
Molar entropy at room temperature
atmospheric pressure / JK-’ mol-’
diamond
platinum
le ad
laughing gas
2.5
42
65
220
These numbers suggest that entropy is related to hardness. Indeed, as a rule hard gem-like abrasive
and refractory materials such as diamond, garnet, topaz, quartz, fused zirconia, silicon carbide,
and boron nitride, in which the individual atoms are bound to each other in nearly infinite three
dimensional lattices by genuine chemical bonds that severely limit random thermal motion, have
small measured entropies.’ Bent goes on to discuss gases, melting, evaporation and the closeness
of the entropy of water of crystallization to that of ice.
Qualitative discussions of this sort are not uncommon (Angrist and Hepler 1967, Open
University, Course S 100, 197 1). Nor are formal logical accounts. What is unusual is Bent’s inbetween
tactic: quantitative but not deductive, intuitive but not vague or evasive.
SOME FEATURES OF THE BERKELEY APPROACH
Not all the features of Reifs volume Statistical Physics (1965) in the Berkeley series can be
looked at here. But, like Gurney, the tough body of the book is introduced by one or two
preliminary chapters of considerable inferest.
Using computer simulation
Reifs first two chapters exploit the technique of computer simulation which others have also
used: (Alder and Wainwright, 1959; Nuffield Advanced Physics, 1972; Open University Course
T100, 1972; Reynolds, 1965). Of course, similar Monte Carlo methods are a significant research
tool, for example in the thermodynamics of polymers (Hammersley and Handscombe, 1964).
Reifs system is a set of classical particles moving in a box. Four, and then forty, particles are
followed as collisions take them from one half of the box to the other. Numbers in each half,
and the proportion in each half, are followed, showing how absolute fluctuations increase with
numbers, but that relative fluctuations decrease. The exercise is directly comparable with the
PSSC marble machine, and with similar data from the motion of pucks on an air table (Nuffield
Advanced Physics, 1972), and with a dice-throwing paper simulation (Nuffield Advanced Physics,
1972). The purpose is the same: to illustrate the ideas of microscopic state and distribution;
their differences; and how a system of many particles wil tend to an equilibrium distribution
subject to fluctuations but approximating well to stable deterministic behaviour.
Like the PSSC machine, Reif uses his model to show the irreversible nature of the change
towards equilibrium, with the added interest that the motions in his system are all precisely
reversible, being Newtonian motions of elastic particles. He is thus able, by reversing the motions
and making the system ‘evolve backwards’, to pose the reversibility paradox in an acute form.
In the Nuffield advanced physics course, similar ideas are tackled by using film of real events
run both forwards and backwards.
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