# Power and Entropy

An ideal pendulum, which is not subject to air friction (e.g., pendulum in a vacuum), and which also possesses frictionless hinges (perfect bearings), would oscillate in perpetuity, if allowed to do so, with perfect transference of energy between the potential and kinetic forms. The total energy (the sum of the instantaneous potential and kinetic energies) for the ideal isolated pendulum is, however, fixed. No matter how long it is in motion there is no change in the total energy for this closed system formed by the ideal pendulum. The system can be described as

'closed' in a case like this, since it has no influence on the outside world, and the outside world has no influence on it. A bit like a prisoner on Robben Island! Such a system neither delivers nor absorbs power, since power entails an increase or decrease in total energy. Power is defined as the time rate of change of energy [3], and we define an energy change of one joule in one second as a watt in the m.k.s. system of units.

In practice a pendulum system can never be perfect and entirely closed. As the ball travels through the air, friction (collisions between the ball and air molecules) will cause the ball and the surrounding air to warm up. The suspension hinges, if they are not perfect bearings, will also heat up. This heat is an indication that power is being expended by the system. The drag of the air on the ball causes it to lose speed and hence kinetic energy, which in turn means a loss of potential energy. On each swing the pendulum ball will climb less high and eventually the oscillations will cease. A child on a rusty swing will be pretty familiar with the effect. The loss of total energy in the pendulum system can be equated to the heat generated, and power transfer occurs from the pendulum to its surroundings.

The decay in the pendulum motion with time, and the consequential loss of total energy, is a manifestation of the second law of thermodynamics, which simply put states that all systems are subject to increasing disorder or decay and in decaying they lose energy. The technical term that has been coined to encapsulate the process is entropy. Increasing entropy equates to increasing disorder and decay. The original expression of the law, enunciated first by Lord Kelvin, is:

A transformation whose only final result is to transform into work, heat from a source which is at a single temperature, is impossible.

It really gives expression to a common-sense principle, which, as Steven Weinberg [4] graphically puts it, 'forbids the Pacific Ocean from spontaneously transferring so much heat energy to the Atlantic that the Pacific freezes and the Atlantic boils'.

Few people would bother to ascribe a meaning to the well known nursery rhyme of Humpty Dumpty, but it is really a quite potent, if subliminal, lesson in entropy. The increased disorder of the broken egg that was poor Humpty, could not be restored to order - 'put back together again' even by 'all the king's horses and all the king's men'! If you are an infant or primary school teacher, get your charges to sing it as often as possible, so that one day they may become scientists or engineers! We may desperately need them as fossil fuels vanish.