“A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is the scientific equivalent of: Have you read a work of Shakespeare’s?” Charles Percy Snow
Jon Osler is a chemistry graduate of the University of St Andrews. He gained his PhD in chemistry from the University of York for his work on the Cope rearrangement with Professor Richard Taylor. Jon’s research has been published in a number of leading international journals. He is currently living in Paris, teaching chemistry for the International Baccalaureate Diploma at the Ecole Jeannine Manuel.
If somebody applies perfume on a bus, the other passengers will soon smell it. If we add ice to our drink on a warm day, the ice will quickly melt. If we build a sandcastle on the dunes, the wind will eventually destroy the structure. We are all familiar with these everyday observations but many of us are ignorant of the scientific law that underpins them. The second law of thermodynamics is that law. It is a law of thermodynamics which Einstein described as “the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, will never be overthrown.” Einstein may yet be proved wrong but within the current model used by scientists to describe our universe, the second law of thermodynamics explains many phenomena. To name just a few, it explains why when we mix certain chemicals together they react vigorously yet when we mix others there is no reaction, why an entirely efficient engine is an impossible dream and why time only goes in one direction.
The second law of thermodynamics was cited by Charles Percy Snow, physical chemist and novelist, in his lecture on the Two Cultures at the University of Cambridge in 1959. Snow’s idea was that “the intellectual life of the whole of western society” was split into two cultures, the natural sciences and the “literary intellectuals”. Snow claimed that there was a gulf of ignorance between these two cultures. He highlighted this by pointing out how few non-scientists could describe the second law of thermodynamics, a law so fundamental to our understanding of science that Snow equated it to having read a work of Shakespeare’s in the arts. He concluded that in order for society to progress, the two cultures needed to do more to understand each other. My aim in this article is to explain the second law of thermodynamics in a clear and accessible way in order to help us achieve this goal!
What is Thermodynamics?
Thermodynamics is a branch of science concerned with transformations of energy and work.
In order to understand the laws of thermodynamics we need to understand some basic terminology used by scientists. We need definitions for energy, work and entropy.
Work is done when a body is moved a distance against an opposing force. For example, we do work on an object when we lift it a vertical distance against the force of gravity. This power lifter is doing work as he lifts the bar against the force of gravity.
A power lifter doing work (creative commons)
Energy is defined as the capacity to do work. A body may have energy because of its position (potential energy) or its motion (kinetic energy).
The first law of thermodynamics states that energy can be converted from one form to another but cannot be created or destroyed. For example, Newton’s famous apple possessed a certain amount of gravitational potential energy when it was on the tree and this energy was transformed into kinetic energy as it fell towards his head!
The second law of thermodynamics states that matter and energy tend to disperse. As time moves forward, matter and energy disperse and we say that the total entropy of the universe increases.
Let’s take as an example two rooms connected by a door and imagine that one room was filled with smoke. Smoke is made up of particles which possess kinetic energy (they are all moving about in random motion). If we were to open the connecting door, the smoke would diffuse over time until the particles of smoke were shared more or less equally between the two rooms. This is an example of the second law of thermodynamics in action. Matter and energy have dispersed over time and the entropy has increased. But what is entropy?
Copyright © 2017 Jonathan Osler, Smoke particles (represented by black dots) confined to the room on the left. When the door is opened the smoke diffuses over time until the smoke particles are shared more or less equally between the two rooms.
Entropy is a measure of the dispersal of energy and matter. To understand why entropy increases over time, let’s take the example of a cup of hot coffee. Over time, the cup of coffee will cool down and the air surrounding it will warm up. Imagine an idealised cup of coffee can hold four units of energy. Imagine also that the idealised surroundings can hold 12 units of energy. If we have 4 units of energy and they are all localised in the coffee cup, there is only one possible way of arranging this energy. We say this is a low entropy state. However, as soon as one unit of energy disperses into the surroundings (3 units of energy are in the coffee cup and 1 unit of energy is in the surroundings), there are now 48 different ways of arranging this energy. We say there are 48 possible microscopic arrangements for this macroscopic state. The greater the number of different microscopic states for a given macroscopic state, the greater the entropy.
Copyright © 2017 Jonathan Osler, The blue cells represent the cup of coffee and the yellow cells represent the surroundings. Q represents 1 unit of energy. When all 4 units of energy are contained in the coffee (left), there is only one way of arranging them (low entropy). In the cooler cup of coffee (right), 1 unit of energy has dispersed into the surroundings. There are now 4 x 12 = 48 ways of arranging the 4 units of energy (high entropy).
This leads us to an important conclusion. A coffee cup cools down and the surrounding air warms up, simply because it is statistically more probable that it will. As time moves forward, matter and energy disperse (entropy increases) simply because it is statistically more probable that it will. Our smoke particles diffused into the other room, simply because it was statistically probable that they would and sandcastles are destroyed by the winds over time for the same reason.
Ludwig Boltzmann was the first to connect entropy and probability. His famous formula is S = k ln W where S represents entropy, k is the Boltzmann constant and W the number of ways of arranging the particles and their energies.
Ludwig Boltzmann’s tombstone bears the inscription of his entropy formula (creative commons)
So what of Newton’s apple. When the branch connecting it to the tree snapped, why did it fall towards the ground? We are often taught at school that the apple falls spontaneously from a position of high gravitational potential energy to a position of low gravitational potential energy because it is more stable. Perhaps a more fundamental explanation would be to invoke the second law of thermodynamics.
The apple fell not because it was more energetically stable on the ground but because in falling friction with the air particles caused the apples potential energy to be dispersed as heat in the surrounding air molecules.
Imagine a skateboarder at the top of a half-pipe. We all accept that he will eventually come to rest at the bottom of the half pipe. This is not because he is inherently more stable at this position of low gravitational potential energy. In fact, in the absence of air resistance and friction he would continue to rise and fall continuously. He doesn’t in reality because friction and air resistance causes kinetic energy and potential energy to disperse from the skateboarder. Kinetic energy and potential energy that were concentrated in the skateboarder spread out as heat into the half-pipe and the surrounding air, thus increasing entropy.
Skateboarder on a half pipe (creative commons)
At school chemical reactions are also often explained using the same ideas of stability. Substances with strong chemical bonds have lower potential energy than those with weak chemical bonds. Reactions are often justified by explaining that the products of the reaction have stronger chemical bonds, have lower potential energy and are thus more stable. This reasoning is completely flawed. If it was true, then table salt wouldn’t dissolve in water. The bonding between the sodium ions and chloride ions in salt is very strong, stronger than the interaction between the sodium and chloride ions with water. This is clear from the fact that the temperature of water decreases as we dissolve salt in it (more energy is required to break the bonds in the sodium chloride than is released as a result of the ions interactions with water). The real underlying reason salt dissolves in water is because entropy increases as salt dissolves in water.
The potential energy of the NaCl (s) [left side of the diagram] is lower than that of NaCl (aq) [right side of diagram] but when we add NaCl (s) to water it dissolves to give NaCl (aq) due to the increase in entropy (creative commons)
The second law of thermodynamics also explains why it has proved impossible to construct an engine in which heat, from the combustion of a fuel, is converted completely into work, such as the work of moving a car. The withdrawal of energy as heat from the fuel reduces the entropy of the fuel (the temperature of the fuel has decreased so we have a new macroscopic state. In this new macroscopic state, the average kinetic energy of the fuel particles is lower and the range of speeds of the particles is lower. There are therefore fewer microscopic states in this new macroscopic state). The transfer of this energy into work has no effect on entropy and so given the decrease in entropy of the fuel, there would be an overall reduction in the entropy of the universe. Heat engines therefore lose some heat to a cold region called the sink. This raises the entropy of the sink and results in a net increase in entropy. The overall entropy increases even though some of the heat energy is converted into work because changes in entropy are temperature dependant. If a given quantity of energy is transferred to heat up a cold object (one in which the average kinetic energy is low and the range of speeds is low), the increase in entropy is more significant than if the same quantity of energy is transferred to heat up a hot object. The difference is a little like the effect of sneezing in a busy street (analogous to the hot object) and sneezing in a library (analogous to the cold object). The temperature dependance of entropy changes can be seen clearly in the equation ΔS = q / T where ΔS represents entropy change, q is the quantity of energy added and T is temperature.
Copyright © 2017 Jonathan Osler, The flow of energy in a heat engine. For the process to be possible, the decrease in the entropy of the heat source must be offset by the increase in entropy of the cold sink.
It was my goal to describe the second law of thermodynamics in a clear and accessible way for non-scientists. I hope I have succeeded and will now start my search for a “literary intellectual” who can explain to me the intricacies of the works of Shakespeare!
Jon Osler