As a stone flies through the atmosphere, air resistance is always pulling back on it. While reducing the stone’s speed, air friction produces heat. Furthermore, when the stone hits the ground, much of its movement energy is suddenly changed into heat. If movement energy, height energy and heat energy are all added together, that total always remains constant during the upward and downward journey of the stone. Textbooks describe this as the "Principle of Conservation of Energy", but it only serves to disguise an even more important aspect of the story.

This is easiest to grasp if we consider heat energy. First, it must be emphasized that the temperature at which a particular quantity of heat is supplied – determines its "usefulness" (because availability at hotter temperatures means more possible uses). It turns out (perhaps alarmingly) that although the total amount of energy in the universe remains constant, its total usefulness is always decreasing.

There is an easy calculation which keeps track of this "energy usefulness". To see how it works and appreciate why it makes sense, imagine two metal containers side by side, one holding hot water and the other cold. If they are touching, heat will gradually flow from the hot container into the cold one. After a long time, the water in the two containers will be at almost equal temperatures. The hot water has become cooler, while the cold water has warmed up. (Obviously, both containers must be shielded from outside air currents and other effects).

Suppose now that we wish to get our water samples back to their original temperatures. That is not nearly so simple. Heat flows easily and naturally from hot objects to cold ones, but not the other way round. To heat up the first container, it is necessary to supply energy (from electricity or by burning some fuel). Cooling down the second container also requires effort or interference on our part (e.g. using a refrigerator, which itself requires energy of some sort).

When heat passed from our hot container to our cold one, the total energy in them did not change. However, after that energy becomes shared, it is no longer as useful as it was before. (Its only possible role might be to heat up something even colder than itself).

Here then is a scheme by which physicists measure how energy becomes "less useful": they simply divide heat amount by temperature. The result is called "Entropy". That temperature, incidentally, must be measured in degrees above absolute zero* (which is equal to minus 273 degrees Celsius): those degrees are called "kelvins" (denoted "K").

Of course, other formulae might have been considered - for example, heat squared divided by temperature - but the simpler calculation is supported by thermodynamic theory.

Referring to our two containers again, suppose that 7000 joules of energy flowed out of the hot one whilst it cooled from 78 to 76 degrees Celsius. Its average absolute temperature during that time was about 273 + 77 = 350 K. So its loss of entropy during those minutes was

At the same time, suppose that the cool container warmed up from 6 to 8 degrees C when it received the 7000 joules. Average absolute temperature then was about 273 + 7 = 280 K, so its gain in entropy was

Taking both containers together, the total amount of entropy therefore increased by 5 joules per kelvin

That one-way heat flow between those two containers is similar to what happens when a stone flies through the air, because heat energy produced by air friction and by impact quickly spreads away into surrounding air or ground, where the temperature is lower. In the same way, heat wastage occurs from friction between moving parts in all engines, and it is even worse when something is dragged along the ground

Electricity consumption results in a similar loss. A wire carrying an electric current always heats up - particularly if that wire has high resistance. Inevitably, its heat flows away into something cooler and cannot easily be recovered

Almost every activity on the Earth (and indeed throughout the universe) results in entropy increasing, i.e. in a reduction of energy usefulness or availability. This reflects the fact that our energy resources are running out, converted to energy forms which are becoming ever more difficult to harness

As far as we are concerned, there is no reason to panic, because the Sun (our main source of energy, at an extremely hot temperature) should continue shining for thousands of millions of years more. However, it does lead to an interesting conclusion – that the universe must have been created with very low entropy, i.e. with an enormous quantity of available energy. It is almost like a clock which was once wound up, but is now relentlessly running down.
 
 

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* "Absolute zero" is the coldest temperature possible, occurring at minus 273.16 degrees Celsius. At this temperature, all atoms and molecules stop migrating and vibrating - so it is a much more meaningful zero than the freezing point of water. The absolute (or Kelvin) temperature scale therefore adopts absolute zero as its starting-value. However, its degree step-sizes are exactly the same as in the Celsius system.

Physics formulae are often neater if they use Kelvin temperature values rather than Celsius ones. For example, if the Kelvin temperature of gas in a container is halved, its pressure is also halved. The speed of sound in air is also more easily related to Kelvin than it is to Celsius temperatures.
 
 

David L. McNaughton

E-mail: DLMcN@yahoo.com

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