The Second Law

Imagine the Earth as it would be if it were in the outer fringes of the solar system – say in the region of Pluto 5,000,000,000 miles from the sun, rather than just 93,000,000 miles away as it is. It would be frigid, silent and still. Far colder than the Antarctic all over. No wind, no waves, no clouds, no sound, no movement, apart perhaps from occasional earthquake tremors and volcanic eruptions. The sky pitch black and the sun a twinkling star barely brighter than the appearance of Venus in our evening sky.

All movement, all change, all life, everything that living things accomplish – the nests of the birds, the dams of the beavers, our skyscrapers, airliners and communication satellites – is made possible by the stream of radiation from the sun.

Every day 2,880,000 MWh of energy arrive on Earth, and the same amount is radiated away into interstellar space from the night-time side of the planet. If the earth were not losing energy at the same rate as receiving it, it would get hotter and hotter – and the oceans would have boiled long ago. That energy arriving from the sun every day is ten thousand times as much as the entire human race uses up. All of our factories, cars, steamships, airliners, appliances, heating and air-conditioning could be run from just 0.01% of that solar radiation.

So – if there is no net change in the amount of energy on the Earth, what is it that is so important about this constant stream? It is that the quality of the energy received from the Sun is higher than the quality of that which is lost into the night sky.  The difference between the two allows the local reversal of the universal tendency towards decay and disintegration, and for interesting things to happen on this planet.

The Second Law of Heat and Movement didn’t feature in any science classes when I was at school, and I expect the same is true today. So for many people it has an air of mystery about it – especially as it is expressed in a number of different ways. But actually, we all have an intuitive grasp of it – as this video will illustrate:

What is the most obvious thing that you noticed when you watched it? – Of course it is the fact that the film is being run backwards! We simply never see a sequence of events such as this in real life. But why should such a sequence be impossible, bearing in mind that – as asserted by the First Law – the total energy of the system is exactly the same at the end as it was at the beginning? The gravitational potential energy is progressively transformed into energy of movement as it falls. When it reaches the ground the directed movement of all the atoms in the object are abruptly shaken into increased agitation in random directions slightly raising its temperature. In other words, transforming the energy of motion into heat. Since this object was fragile, a portion of the energy was used in overcoming the binding energy which held the atoms in place to form a rigid structure. As the dispersing fragments slide across the floor, frictional forces bring them to a standstill – again transforming movement into heat. Finally the slight excess temperature of the pieces dissipates into the surrounding air.

Newton’s Laws of Motion are symmetrical in time.  The slowing down of a ball thrown into the air exactly mirrors its acceleration as it falls back to earth. So why could that sequence above never happen the other way round? Couldn’t random agitation of atoms in the fragments align to create bulk motions of the object so that they rush inwards to meet and fuse together in the form of a flowerpot, and then re-orientate the directions of their motions to propel the jar upwards and back onto the table, as shown in the video? The suggestion is clearly absurd and preposterous – but why?

To illuminate the reason, let’s consider a simpler example, as shown in this video:

Once again, that reel is obviously running backwards – we don’t see things like this happening. On the other hand, it doesn’t have quite the same aura of absolute impossibility as the previous example. It’s a matter of probabilities. Maybe if we shook the jar for long enough the beans could just drop into a pattern like that by chance? After all it is it highly unlikely to get say 28 reds in a row in roulette but clearly it could happen. And perhaps it has – maybe once in about 250 million spins the wheel.

So what are the odds of shaking the beans into the brown and white layers? In that video there are about 100 beans of each colour. How do we calculate the odds? I ran the numbers for a simpler case of 50 of each colour. The probability is given by the ratio between the number of micro-states corresponding to ‘colours in layers’ compared with the number of micro-states representing ‘colours jumbled up’. It turns out that there are about 10¹²⁹ micro-states for beans in layers (that means 1 followed by 129 zeros – a truly huge number; for comparison there are estimated to be about 10⁸⁰ atoms in the entire observable universe). This sounds quite encouraging! Surely we could stumble across one of those before too long? Unfortunately, it turns out that there are about 10¹⁵⁸ micro-states for beans jumbled up – so the odds against shaking them into a pattern are about 10²⁹. If you shook the jar once per second, how long would it take to get a passing chance of shaking the contents into an ordered pattern? The universe is estimated to be 13 .6 billion years old – that is about 10¹⁸ seconds. So you would have to shake it up for a period 100 billion times longer than the entire age of the universe!

That was just for a system with a mere 100 items in it. The odds become far more extreme still when we consider entities made up of trillions of atoms.

It is clear in these two examples that the later state is more disordered or disorganised than the earlier one. It is an everyday observation that (unless otherwise manipulated) that is the way events unfold: iron rusts; wood decays; machines wear out; bodies age and weaken; toys scatter all over the floor. In two areas we see an apparent violation of this principle. One is the growth and development of living organisms – the chick grows from the formless yolk and white of the egg. The other is in the purposeful activity of birds, beasts and humans.

There is a technical name for this disorder which tends to increase over time it’s called entropy. We have just seen a couple of examples of changes in entropy; let’s deepen our feeling for it with a few more illustrations:

• Low entropy                /                    High entropy
• beans ordered in layers / beans jumbled up
• glass whole / glass broken
• water at top of hill / water at bottom
• objects hotter or colder than surroundings / objects same temperature
• items filed neatly / items scattered randomly
• parts assembled into a machine / collection of loose components
• computer disk with data files / corrupted or erased computer disk

There are a couple of other important instances of entropy comparison which may not be so intuitive.

• One is that an object or substance is in a higher entropy state the hotter it is; at absolute zero the atoms are still and their position is defined exactly. As the temperature rises they move faster and faster so their positions are less clearly defined.
• The other instance is that a given amount energy in the form of electromagnetic radiation has more entropy if it is at long wavelengths than at short ones.

As I said earlier there are several different formulations of The Second Law. The original one was:

• Heat cannot of itself flow from a colder body to a hotter.

This form is a reflection of the focus of interest at the time the law was formulated – the drive to understand how to make steam engines more efficient. Hence also the name “thermodynamics”, although we now know that the principle applies not not just to the energy movement but to all forms – including electrical chemical and biological.

The most common formulation is

• Any change within a closed system results in a net increase of the total entropy of the system.

Thus, we have a physical statement of the directionality of time: the flow is from lower entropy to higher. There is of course also a psychological arrow of time: it flows from the past – which we remember – towards the future which is unknown. The correlation between the psychological arrow and the thermodynamic one was the source of the cognitive dissonance we experienced in watching the video clips

Is this correlation essential or merely contingent? Would a universe be possible in which these arrows were reversed – when we remembered the higher entropy state and awaited the lower one? No, this would not be possible. The two arrows have to align this way as we shall see later.

Note that both examples we gave for statements of The Second Law contained a qualifying phrase: “of itself” and “within a closed system“. Heat does flow from a cold body to a warm room in the case of a refrigerator, but only because you provide electricity to drive the pump. And more heat is put out into the room than is extracted from the inside of the fridge.

And the Earth is not a “closed system”: it is continually receiving energy from the sun in the form of light, ultraviolet and heat radiation. The difference in entropy between this radiation and the far infra-red radiating from the Earth into the night sky enables all the natural processes on this planet, and all purposeful activity of the human race. The incoming radiation is at frequencies around 100 times higher than that from the Earth into the cold vastness of interstellar space.

There are four main effects of the energy that arrives from the sun that have the potential to be harnessed to do useful work and thereby create wealth:

1. Direct heating of locations in strong sunlight
2. Rising air currents in regions warmed by the sun, causing winds to blow towards the lower-pressure regions that this creates.
3. Evaporation of water from the oceans, forming clouds which condense to fall as rain on higher ground, then collect into rivers which flow back to the sea.
4. The formation of glucose molecules from carbon dioxide and water within the cells of blue-green algae and in the leaves of plants.

Until the last 300 years almost all human activity and creation of wealth was empowered by energy made available through that fourth process. The building of cities, temples, roads and canals; the tilling of fields and the harvesting of crops; the working of wood, metal, glass and pottery: all of this was accomplished by the muscle-power of humans or of animals. And the energy to provide that muscular activity came from plant food consumed, which embodied the energy captured from sunlight in the leaves of the plants. A small proportion of the energy came from the second and third processes: via the use of windmills and water-wheels. And the heat to warm houses, to cook food, and to fire forges came from the burning of wood or charcoal, which again was released from sunlight captured by the leaves of the trees.

And the coal, oil and gas that have fuelled our industrial age have likewise originated in that same photosynthetic process, but in this case the sunlight was captured millions of years ago in ancient forests and oceans.

All wealth creation involves a reduction in entropy. Steel represents a lower entropic state than the iron ore that it was made from. The ability to play a critical role in the wealth-creation process is what gives value to concentrated forms of high-quality energy such as coal and gas. That is why wars are fought over oilfields, and it is why the global elites are ambivalent in their attitude towards solar and other forms of renewable energy, which would reduce our dependency on their monopolies.

BP and Shell both dallied with initiatives to diversify into renewable energy projects, and both abandoned the activity when they realised that they can make a higher return (at least in the short run) by focusing on selling oil products, rather than promoting alternatives to them.

Harnessing the abundant, free, non-polluting energy from the sun is the key to the transition to the forthcoming era of universal peace and prosperity – as long as we don’t destroy civilisation first. Later in this thread we will look in more detail at what it would take to provide a decent, fulfilling standard of living for every human being on this planet – and one that is sustainable for millions of years. The poverty-stricken  of this world will be able to make the transition to the solar age without having to struggle through the smokestack era.

This is an extract from my forthcoming book The World in 2100: What might be Possible for Humanity?

If you haven’t already done so, you can register to receive a free review copy just before it goes on general sale later this summer. Registering will also take you straight to Chapter 1 – The Foundations which will give you more idea of what the book will cover.

Section 1.5 – Energy

Outline of the Work, Energy, Wealth and Power thread:

In 1865, economist William Jevons remarked that in about 100 years the British coal reserves would be exhausted, and that this would mean the end of Britain’s dominance as a major world power. This must have seemed inconceivable to his readers at that time – at the height of the wealth and confidence of the greatest global empire the world had ever seen, but – as we know now – it was uncannily accurate. By 1965 most of Britain’s coalfields were nearing exhaustion, and its time as a leading world power was indeed over.

In the previous section we touched on the fact that creating wealth involves work. Energy is what it takes to get work done. The energy to do the work of getting your car from one place to another comes from the gasoline that you put in the tank. The energy to run your sewing machine comes from the electric current flowing from the wall socket.  The energy to dig your vegetable patch comes from the sugar in your muscle cells causing them to change shape (the actual biochemistry is more complicated than this, but this is accurate as a summary).

Let’s trace this further back: the energy in the sugar came from the food ate you ate for dinner. The energy in the vegetables came from sugars that were manufactured in the leaves of the plant from energy in the sunlight. The energy in the sunlight came from the fusion of hydrogen into helium in the core of the sun (the same process that releases energy when a nuclear warhead is detonated). The energy in the meat came from plants that the animal ate.

The energy in gasoline is derived from sugars manufactured by marine plankton and other micro-organisms millions of years ago from sunlight that fell on the Earth at that time.

The energy that is delivered from your electric sockets came from the movement of spinning magnets within coils of wire in the generators in the power station. The magnets were spinning because they were connected to turbines driven by high-pressure steam. The energy in the steam came from coal burned in the boilers, and the energy in the coal came from sugars made in the leaves of trees in ancient forests, from sunlight which fell on the Earth between 300 and 360 million years ago.

But suppose the electricity was generated in a nuclear power station? In this case the heat for the steam to drive the turbines came from the breaking up of uranium nuclei into smaller lighter elements. This energy was originally stored in the Uranium by nuclear processes in the centre of stars that lived and died before our sun and solar system were formed.

From these reflections we can draw two conclusions: the first is that energy can take many forms and can be changed from one form to another myriad ways. Careful experiments carried out over the last few hundred years have established that in every conversion process the total amount of energy at the end is exactly the same as it was at the start. This is the First Law of Heat and Movement (it is usually called the First Law of Thermodynamics, but  as with other technical jargon elsewhere in the book, I’m going to substitute words in everyday language. ‘Thermodynamics’ sounds complicated, mysterious, difficult – but it’s just a fancy way of saying ‘heat and movement’, and if I use those words you will know what I’m talking about). Another name is the Law of Conservation of Energy.

When you are driving down the road, some of the energy consumed from the gasoline taken from your fuel tank has took been turned into the energy of the movement of your car, but not all of it. Some has been turned into heat energy making the engine hot; heat warming the air passing through the radiator; and heat in the gases emitted from the exhaust pipe. When you bring the car back to a standstill all that energy of movement is turned into heat energy in the hot brake discs and the air around them. – Unless you have an electric or hybrid car, in which case some of that would have been turned into electrical energy and stored in the battery, in the form of chemical energy.

The second conclusion is that although the total quantity of energy remains constant, the quality of it does not. You cannot use the heat that was dissipated into the environment from the radiator and the exhaust pipe  and the brakes to drive back home again! This observation is the basis for the Second Law of Heat and Movement, and it is the reason why it is impossible to build a perpetual motion machine.

In everyday usage the words energy and power are used more or less interchangeably, and many people are uncertain of the distinction between them. But to an engineer, the concepts are clear: energy, as we have said, is the capacity to do work, whereas power is the rate of doing work (or the rate of transforming one form of energy into another). It takes the same amount of energy to boil a litre of water whatever the power of your kettle, but a 3 kW kettle will do it in one third of the time that a 1 kW one would have. A 300 hp sports car will accelerate to 60 miles an hour about six times as quickly as a 50 hp family saloon of the same weight.

There is of course  another – somewhat related – meaning of the word power: the ability to control or exploit the actions of others, as in political or economic power. Political power depends on economic power, and – as human affairs are ordered currently – both are derived ultimately from military power. Hence the relevance of Britain’s  ability to operate a global empire being dependent on the energy supply from its coalfields. And hence the conflict today over control of the world’s oil supplies. The Work, Energy, Wealth and Power thread will explore these issues in greater depth, and examine their interactions with the other threads.

This is Section 1.5 of my forthcoming book The World in 2100: What might be Possible for Humanity?
When we return to the ‘Work, Energy, Wealth and Power’ thread, the next topic will be The Second Law – and Why You Cannot Build a Perpetual Motion Machine.

If you haven’t already done so, you can register to receive a free review copy just before it goes on general sale later this summer. Registering will also take you straight to Chapter 1 – The Foundations which will give you more idea of what the book will cover.