Wonders of the Universe

THE ORDER OF DISORDER

In 1712 the English inventor Sir Thomas Newcomen created the first commercially successful steam engine, paving the way for the Industrial Revolution. This accolade is more usually awarded to the Scottish inventor James Watt. In 1763 Watt was asked to repair a Newcomen engine by the University of Glasgow, and in doing so he developed a new steam engine which, it is appropriate to say without hyperbole, transformed the landscape of modern life. Watt’s steam engine was more efficient and more flexible than its predecessor; it used far less coal than the Newcomen for a given power output, and was therefore much cheaper to run. More importantly still, Watt’s engine could do more than pump water out of the wet mines, it could also generate the rotary motion that was needed to power the machines on the factory floor. No longer did a factory have to be situated by a river to turn its equipment; with the help of Watt’s engine a factory could be sited anywhere, catalysing the emergence of the modern industrial landscape. Steam-powered machines changed the course of history, and yet despite their importance, the nineteenth-century engineers who followed Watt struggled to improve them. There seemed to be fundamental principles that restricted their efficiency, but with profit margins to maximise, even a small increase in their effectiveness would be highly valuable. So understanding how hot the fire should be or what substance should be boiled in the engine were problems that were not only interesting from a scientific perspective but were also critical for businesses. It was out of these questions of engineering design that the science of thermodynamics arose, and with it the concepts of heat, temperature and energy entered the scientific vocabulary in a precise way for the first time.

In a series of simple experiments, Joule demonstrated that mechanical work could be converted into heat. Using a paddle wheel turned by falling weights, he stirred water in an insulated barrel and observed how the temperature of the water rose by the amount that depended on how far the weights fell.

One of the scientists working on these problems was the German mathematician Rudolf Clausius. Clausius was interested in heat, which until the first half of the nineteenth century was thought to be a fluid that flowed from hot things to cold things. Clausius and others realised that this description was not able to explain the cycle of a steam engine. The foundation for Clausius’s theoretical advances was laid by one of his contemporaries, the English physicist and brewer James Joule, who was working to improve the efficiency of the steam engines in his brewery. What finer motivation for the advance of fundamental physics? The quest for cheaper beer motivated him to investigate the relationship between the work his steam engines could do, and heat. In doing so he managed to reduce the costs of beer production and lay one of the cornerstones of the science of thermodynamics.

Using a series of beautifully simple experiments, Joule was able to demonstrate that mechanical work could be converted into heat. One such experiment used a falling weight to spin a paddle within an insulated barrel of water. Joule knew how much work was done by the falling weight and so could measure the temperature rise of the water. He conducted similar experiments on compressed gases and flowing water, and each time he found that it took the same amount of work to raise the temperature of a fixed amount of water by one degree Fahrenheit. Inscribed on his tombstone in Brooklands cemetery near Manchester is the number 772.55 – his measurement of the amount of work done in foot-pounds force that is required to raise the temperature of one pound of water by one degree Fahrenheit.

The reason that Joule’s work was important is that it demonstrated that heat is not a thing that can be created or destroyed. It doesn’t literally flow between things or move around, it is in fact a measure of something else. Even today, this is perhaps not obvious because we still speak of the flow of heat from hot to cold things. Heat, we now understand, is simply a form of energy. Just as a ball resting on a table has energy which can be released by dropping it (known as gravitational potential energy), so a hot thing has energy that can be released, at least in part, by putting it next to a cold thing. To heat something up, you simply have to transfer energy to it by doing work on it, as Joule found by using a falling weight, and it doesn’t matter how that work is done. It can be a falling weight, a shining light or an electric current, but as long as you do the same amount of work, the temperature increase will be the same. This was all quantified, as a result of Joule’s work, into the First Law of Thermodynamics, which is a statement of the fact that energy cannot be created or destroyed; it can only be changed from one form into another. Rudolf Clausius made the first explicit statement of the law, and laid down the foundations of the science of thermodynamics, in his landmark 1850 publication ‘On the mechanical theory of heat’.

Newcomen’s engine, created in 1712, was the first commercially successful steam engine and laid the foundations for the work of other inventors, such as James Watt, which would power forward the industrial revolution in Britain. the Newcomen atmospheric engine was used to pump water out of coal mines, using a pivoted arm (top) to transfer power between the piston and the rod. the piston was driven down by the pressure of a partial vacuum in the cylinder, which drew the rod upwards. as steam in the cylinder condensed, the piston was forced up, and the rod down.

SCIENCE, INDUSTRY & BUSINESS LIBRARY / NEW YORK PUBLIC LIBRARY / SCIENCE PHOTO LIBRARY

The first law can be written down mathematically as

which in words says that the increase in the internal energy of something (ΔU) is equal to the heat flow into it (Q) minus the work performed by it (W). If you performed work on it, the W would have a plus sign, and if you took heat out of it, the Q would have a minus sign.

Fifteen years after writing down the first law of thermodynamics, and far more importantly for our understanding of the arrow of time, Clausius introduced a new concept known as entropy, which lies at the heart of the Second Law of Thermodynamics. Clausius’s statement of the second law does not at first sight sound as if it has profound implications for the future of our universe. He simply stated that ‘No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature’. This simple proposition occupies such a profound position in modern science that Arthur Eddington said of the second law:

‘If someone points out to you that your pet theory of the Universe is in disagreement with Maxwell’s equations, then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation, well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.’

The concept of entropy enters when the second law is written down in quantitative form. The change in entropy of a system, such as a tank of water, is simply the amount of heat added to it at a fixed temperature. In symbols,

where ΔS is the change in the entropy as a result of adding a small amount of heat, ΔQ, at a fixed temperature T. It may still be unclear what this has to do with the Universe, but here is the profound point discovered by Clausius. In any physical process at all, you find that entropy either stays the same or increases. It never decreases. Here is the thermodynamic arrow of time. Clausius had discovered a physical quantity that can be measured and quantified which only ever increases in practice, and never decreases even in theory, no matter how cleverly you design your experiment or piece of machinery. This is extremely useful information if you are designing a steam engine, because it puts a fundamental limit on the efficiency. It also prevents the construction of the so-called ‘perpetual motion machines’ so beloved of crackpot inventors to this day. You could say that the second law tells you that you can’t get something for nothing, but the second law is more profound than this, because it introduces a difference between the past and the future. In the future, entropy will be higher than it is in the present because it always increases. In the past, entropy was lower than it is now because it always increases.

Clausius introduced the concept of entropy because he found it useful, but what exactly is entropy, and what is the deep reason that it always increases? And what was the meaning of Eddington’s cryptic quote about randomness and the arrow of time? He seemed to be equating entropy with the amount of randomness in the world, and indeed he was. Understanding this will make it clear why the Second Law of Thermodynamics mandates that our entire universe must, one day, die