Figure 9.1. James Prescott Joule measured the increase in temperature of a vessel of water caused by the rotation of a paddle driven by a weight falling under gravity. The experiment demonstrated the conversion of mechanical work into heat. (Science History Images/Alamy Stock Photo)
Joule’s results illustrate what we now know to be correct: heat is a form of energy associated with the motion of atoms and molecules – the building blocks of matter. As the paddle rotates, it delivers kinetic energy to the water molecules by hitting them. The molecules move around faster, and this is what we measure as an increase in the temperature of the water. At the time, this idea was radical because there was no direct evidence that matter is composed of atoms, although Joule was taught by one of the leading proponents of the atomic hypothesis, John Dalton. In the words of Jacob Abbott, writing about Joule’s experiments in 1869:
‘It is inferred from this that heat consists in some kind of subtle motion – undulatory, vibratory or gyratory – of the elemental atoms or molecules of which all material substances are supposed to be composed. This, however, is a mere theoretical inference.’26
The link between work, temperature, and the motion of the proposed atomic constituents of matter is a clue that thermodynamics is related to the behaviour of the hidden building blocks of the world, whatever those building blocks may be. Incidentally, one of the papers that settled the atomic debate was Einstein’s 1905 paper on Brownian motion (and his follow-up in 1908), which explained the jiggling of pollen grains suspended in water under the assumption that they were being bombarded by water molecules. Einstein’s predictions were confirmed experimentally in 1908 by Jean Baptiste Perrin, who received the Nobel Prize in 1926 for his work on ‘the discontinuous structure of matter’.
The results of Joule’s experiments, as well as providing evidence for the existence of atoms, are captured in what we now call the First Law of Thermodynamics, which expresses the fundamental idea that energy is conserved: The total energy of a system can be altered either by supplying or extracting heat or by doing work. Moreover, a certain amount of work can be converted into an equivalent amount of heat and vice versa, so long as the total energy is conserved. This is the theoretical basis of the steam engine. Burn some coal and use the energy that’s released to spin a wheel. This isn’t all there is to a steam engine, however, because there is another essential component – the environment in which the engine sits. Crucially, the surroundings of the steam engine must be colder than the furnace, otherwise the steam engine won’t work. Why?
The answer is that energy is always transferred from hot objects to cold objects and never the other way round. This has nothing to do with the conservation of energy. Energy would still be conserved if it was removed from a cold cup of tea, making it colder, and transferred to a hot cup of tea, making it hotter. But this is not what happens in Nature. To account for this one-way transfer of energy, another law of Nature is required, and that is the Second Law of Thermodynamics. One way to state the Second Law is simply to say that heat always flows from hot to cold. Described in these terms, a steam engine is a device that sits between a hot furnace and the cold world outside. As energy flows naturally from hot to cold, the engine syphons off some of the flow and converts it into useful work. Hardly of profound significance at first sight, but it turns out that this almost self-evident statement of the Second Law captures the essence of a much deeper idea. In his book The Laws of Thermodynamics, Peter Atkins begins his chapter on the Second Law with this remarkable sentence: ‘When I gave lectures on thermodynamics to an undergraduate chemistry audience I often began by saying that no other scientific law has contributed more to the liberation of the human spirit than the second law of thermodynamics.’ ‘The second law,’ he continues, ‘is of central importance in the whole of science, and hence our rational understanding of the universe, because it provides a foundation for understanding why any change occurs. Thus, not only is it a basis for understanding why engines run and chemical reactions occur, but it is also a foundation for understanding those most exquisite consequences of chemical reactions, the acts of literary, artistic, and musical creativity that enhance our culture.’27
German physicist Rudolph Clausius introduced the idea of entropy in 1865. In his words: ‘The energy of the world is constant. The entropy of the world strives for a maximum.’* This is a beautifully succinct statement of the first two laws of thermodynamics. Let’s see how things work out in the case of Wheeler’s teacups. According to the First Law, energy is always conserved. This can be true whichever way the energy flows, as long as the amount of energy removed from one teacup is equal to the amount of energy deposited in the other. Clausius defined entropy such that the entropy increase caused by adding heat energy to cold tea is greater than the entropy decrease when the same amount of energy is removed from hot tea.† Thus, the combined entropy of the two cups will increase if heat flows from hot to cold, but not the other way round.
Energy can flow from a cooler object to a hotter object if, somewhere else, enough energy is dumped into another cooler object such that the overall entropy of everything increases. This is what happens in a fridge. Heat is removed from the inside, which lowers the entropy of the interior. The entropy of your kitchen must therefore increase by a larger amount to satisfy the Second Law. This is why the back of your fridge must be hotter than your kitchen. Here’s how it works.
A coolant circulates around the fridge from the interior to the exterior. On exiting the interior, the coolant is compressed and therefore heats up. It is then circulated around the element at the rear which, being hotter than your kitchen, transfer heat into the room. The coolant then goes back into the interior of the fridge. As it does so it expands and cools to below the temperature inside the fridge. Being cooler than the interior, it now absorbs heat from the interior. It then goes through the compressor again and the whole cycle repeats. The net effect is the transfer of energy from inside the fridge to outside – from cold to hot – but at the cost of the energy needed to power the compressor, which is why your fridge doesn’t work unless you plug it in.
The energy to power the compressor comes from a power station, which could be a steam engine; a hot furnace in a cold environment. The power station might run off coal or gas, which came from plants, which stored energy from the Sun, which is a hot spot in a cold sky. The stars are the furnaces of the Universe – the ultimate steam engines. At each stage in the flow of energy from the shining stars to the formation of the ice cubes for your (late) afternoon gin and tonic, the overall entropy of the Universe increases as energy flows from hot to cold, and perhaps the cool gin and tonic stimulates ‘acts of literary, artistic, and musical creativity that enhance our culture’.
The stars were formed by the gravitational collapse of primordial clouds of hydrogen and helium in the early Universe which, for reasons we do not understand, began in an extraordinarily low entropy configuration. The origin of this special initial state of the Universe – a reservoir of low entropy without which we would not exist – is one of the great mysteries in modern physics.