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

New Trends in Physics Teaching IV
(4) How to build a ‘Scenario’. This section starts with an assumption that is discussed later:
that both the rate of increase of GNP and the coefficient of elasticity (see footnote above)
can be considered approximately constant. This leads immediately to exponential growth, which
is presented here in a very elementary way, as a geometric increase. It is very easy to derive the
formula:
C, = (1 +k), CO
where CO = initial consumption, Cn = consumption after n years, k = yearly rate of growth, as a
fraction of total consumption. Possible values of k are taken from IEA (1980) data and the
students are informed that these are official data, on which international policies are based. They
are also warned that the use of such data for long term forecasts does not make much sense, but
it can be useful in order to see what would happen if nothing changes (this is the concept of this
scenario). They calculate data up to year 2000, and if they wish they can try other values for k.
Then they compare the figures with the actual proven oil reserves, and the proven oil plus coal
reserves. To evaluate the total consumption over the whole period, additional mathematics is
needed (essentially the formula for the sum of a finite geometric series which can be derived
without difficulty or accepted as ‘black box’ formula).
For calculations, various possibilities are suggested: since programmable calculators are not
usually available, the best choices are calculators with yx keystroke, or the use of logarithmic
paper. The use of a plain arithmetic calculator alone proved feasible but rather boring.
This part of the work is, in practice, quite exciting and students are astonished to see how little
difference in the exhaustion time is caused by a different estimate of reserves, as long as we
accept the exponential growth assumption. (See also pp. 20-37 above.)
The conclusion is that there are two possibilities: either new reserves, in unlimited quantity,
are made available, or the growth of energy consumption must slow down. This can be done by
limiting the growth of GNP (zero growth model) or by decreasing the elasticity coefficient, that
is, by using less energy for the same production (economy of energy). It is suggested that all these
possibilities should be explored at the same time, and that no one of them alone can solve the
problem.
The second unit, ‘Energy Resources’, should not become a summary of information. What we
try to do is to give an idea of how data about energy reserves and resources are established, and
underline the fact that they are by no means fixed quantities. The contents of this unit can be
summarized as follows: (a) Definition of energy ‘reserves’ and ‘resources’: how much can be
recovered, under what conditions, at what cost? (b) Some indications about the way resources
are estimated: the geology of fossil resources. (c) Actual and past data about energy reserves
and resources. (d) Energy content of resources: the connection between technological choices
and energy content of resources. In this unit, we deal mainly with fossil resources: renewable
resources are discussed in another unit.
Nuclear energy
While the units on energy consumption and resources introduce few energy concepts - the
problems related to final uses and therefore to conversion efficiency are dealt with in other units
- the two ‘nuclear energy’ units introduce many relevant ideas in physics.
The aims of both units can be summarized as follows. Students should learn to: (a) apply in a
new context some important ideas of classical physics (e.g. apply the kinetic theory of gases and
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