# The second law of thermodynamics

Imagine you are watching a film of waves lapping a beach and as they recede a sandcastle slowly rises up from the flat sand. You would immediately deduce that the film is being run backwards. Likewise if the film was of an infrared scan of a metal bar and a hot spot appeared to be growing spontaneously at one point on its length, you would make the same deduction. Thus we all have an instinctive understanding of the nature of the second law, even if we have difficulty with some of its implications. In its original simplicity, the law is stated as:

Heat will not pass spontaneously from a body to a warmer one.

However, as we have seen in our first example of the sandcastle, it has much wider implications than the purely thermal case. Other ways of stating the law could be:

Sandcastles do not arise spontaneously.

The improbable rarely happens.

Entropy increases.

Entropy is the arrow of time

The word spontaneously in the law implies that heat can only be made to travel up a temperature gradient if work is done. Thus the motor in your refrigerator does the work to pump heat out of the cold space into the warmer one. Likewise when heat is allowed to flow down the thermal gradient it allows work to be done. In an old fashioned steam engine the heat from the burning coal passes via the condenser to the outside world and the intermediate agent (steam) does work to rotate the wheels. It is a small step of reasoning to deduce that the amount of energy available depends upon the temperature difference, since one is zero when the other is.

This is a major restriction on the use of heat energy. A joule of electrical energy is totally available to do work, but a joule of heat is only available insofar as there is a temperature difference. Indeed, a law due to Carnot states that no heat engine can be more efficient than a reversible one, whose efficiency is:

(TH-TC)/TH where TH and TC are the higher and lower absolute (°K) temperatures respectively.

Make no mistake, this is a massive restriction on the utility of heat energy. Even a heat engine working between the boiling point and freezing point of water cannot exceed an ideal efficiency of about a quarter, and all real engines are considerably less than ideal.

It is necessary to explain the use of the term Entropy used above. Entropy roughly means disorder. The sandcastle was unexpected order among the disorder of the beach; disorder here meaning that you cannot distinguish one area from another. The sandcastle is also unlikely, so another and better definition of entropy might be likelihood. In the real world entropy always increases, with one exception. We might define life as a localised temporary region of decreasing entropy. Life builds up the improbable structure of its cells from the disordered materials around it. It does this, however, at the expense of increasing the entropy around it, and it always eventually decays back to the disorder from which it came. A molecule, a crystal or  a planet form because they represent a lower potential energy than the alternative and are therefore more probable. A bacterial culture does not have this property and when life is extinct it returns to chaos .

The small boy who built the sandcastle reduced the entropy in a localised area by doing work. In expending the energy to do the work he increased the entropy of his surroundings.

A partial analogy is found in the case of hydro-power. It is useless to have a lake full of water if you do not have a lower water course for it to discharge into, and the power available depends on the difference in height. The analogy breaks down because in the thermal case you can to some extent choose the height difference. You can burn your fuel unmixed at low temperature and get little energy from it or you can premix it with the appropriate quantity of air and achieve a higher temperature and hence more power, as in a steam locomotive or internal combustion engine.

Ignoring the laws of thermodynamics results in all sorts of misunderstandings and misrepresentations. It allows the free energy and perpetual motion scams to exist. It is a mainstay of the renewable energy policies of the environmentalists.

The three laws of thermodynamics in their simple forms are

1.      Energy can be transformed but not destroyed.

2.      Heat cannot spontaneously flow from a body to a hotter one.

3.      The entropy of a substance approaches zero as its temperature approaches absolute zero.

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