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

New Trends in Physics Teaching IV
It should be noted that this simple concept of value is largely in accordance with the usefulness
of the energy forms to man: the higher the corresponding temperature, the more useful is
the thermal energy. Electrical and mechanical energy are good for nearly everything - including
the production of thermal energy at arbitrarily high temperatures.
Examples
A heat engine (HE) may be considered as a device which produces high value electrical or
mechanical energy from low value thermal energy. To accord with the principle of energy
degradation stated above, this can only be achieved if one part of the thermal energy is upgraded
to electrical energy while another part is degraded into thermal energy at a lower temperature
(usually the temperature of the surroundings). This explains the necessity for a cold reservoir
in a heat engine. The quantity of energy transferred to the cold reservoir must be large enough
to ensure that the corresponding degradation exceeds the revaluation involved in upgrading the
thermal energy into the electrical form.’
Further qualitative conclusions may be drawn from this presentation without the need for
special thermodynamic knowledge (of, e.g., the Carnot cycle). If we define the efficiency qHE of
the heat engine as the ratio of the energy in the form desired (here, electrical) to the energy in
the form supplied (here, thermal at a relatively high temperature), one realizes that must
be less than unity, because the electrical energy developed is less than the thermal energy supplied.
Moreover, one may conclude that the efficiency depends on the temperatures of the ‘hot’
reservoir (e.g. steam) and the ‘cold’ reservoir (e.g. condenser): the higher the temperature of the
former and the lower the temperature of the latter the greater the efficiency which is theoretically
possible. For, if the temperature of the hot reservoir is high, i.e. the thermal energy has
already a high value, only a small upgrading is needed to produce mechanical energy. Applying
proposition (I), only a small amount of energy has to be degraded. Moreover, the lower the
temperature of the cold reservoir, the smaller this amount becomes because the effect of degrading
a given quantity of energy is the greater the lower the temperature of the cold reservoir at
which this energy is absorbed.
In apparent contradiction to experience, a heat pump (HP) succeeds in shifting the thermal
energy of cool surroundings to the higher temperatures able to warm a room. This difficult idea
turns out to be simple to understand if considered in the light of the value of the energy involved.
To shift thermal energy to a higher temperature the heat pump uses, say, electrical energy (i.e.
high value energy). The upgrading required for the production of the temperature difference is
compensated by the downgrading of the electrical energy provided. In fact, the quantity of
upgraded thermal energy is closely related to the quantity of electrical (or mechanical) energy
driving the pump: the higher the temperature shift and the greater the quantity of energy
upgraded, the more electrical (or mechanical) energy has to be supplied. If we consider the
efficiency of the process qHp, we see that qHp > 1, because the desired energy (here thermal
energy to heat a room) is greater than the energy supplied to work the pump. As we have seen,
the smaller the temperature shift required, the greater the efficiency which is theoretically
possible. In order to save valuable electrical energy, the temperature to be reached in the heated
room should be as low as possible and the temperature of the surroundings from which energy is
drawn should be as high as possible. This may be achieved by using ground water rather than the
air, for example.
1. Here we make the obvious assumption that the degradation increases with the quantity of degraded energy. This is explained
below.
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