Energy is an abstract concept and it can be hard to get a feel for the quantity of energy transferred in different events. The table below gives the orders of magnitudes of energy transferred by a range of events in the universe:

When comparing fuels, it can be more useful to consider the amount of energy stored per unit mass (the energy density) rather than the absolute magnitude of energy transfer. A comparison of the energy densities of different fuels highlights the potency of uranium:

Excluding nuclear blasts, perhaps the most energetic human-created explosion was a test carried out by American scientists in 1987, codenamed Misty Picture. In order to mimic the effect of a low yield nuclear weapon, the scientists detonated 4,685 tonnes of ammonium nitrate and fuel oil explosives at White Sands Missile Range in New Mexico. The explosion is estimated to have had a yield of 33.4 TJ (33.4 x 10¹² J).

A wonderfully detailed list of the energy expenditures of various activities has been produced:

Some diet regimes have suggested that dieters consume ‘negative calorie’ foods in order to lose weight. Theoretically, negative calorie foods require greater energy expenditure in digestion than is gained from their consumption, resulting in a net energy deficit. Celery is a commonly cited example of such a food. A recent study of celery consumption by bearded dragons suggests that the idea that celery is a negative calorie food is a myth, at least for these reptiles. It is reported that the lizards retained at least 24% of the energy in the celery they consumed.

Rather than simply comparing the absolute calorific value of foods, energy density can be a useful measure. Feeling hungry is one of the challenges of dieting, so foods which provide relatively few calories per unit mass – i.e. they have a low energy density - may provide a feeling of fullness with limited calorie consumption.

•  Low energy density foods are defined as those which contain less than 2.5 kJ/g or 0.6 kcal/g. They include non-starchy fruits and vegetables
•  High energy density foods contain 17-38 kJ/g or 4-9 kcal/g and include biscuits, crisps and peanut butter.
•  In general, fats have a higher energy density, at around 38 kJ/g or 9 kcal/g, than protein or carbohydrate, both around 17 kJ/g or 4 kcal/g.
•  The World Cancer Research Fund has recommended that the mean energy density of a person’s diet should be 5.23 kJ/g or 1.25 kcal/g. The diets of subsistence farmers in Gambia averaged 4.50 kJ/g or 1.08 kcal/g, excluding drinks. This compared to 6.70 kJ/g or 1.6 kcal/g for Western diets. A study of Scottish diets reported that individuals in the most deprived areas ate diets with higher energy densities than those in the least deprived areas.

Vegetarian diets have a significant environmental benefit in terms of the energy costs of production. Just 4% of the energy transferred from the fossil fuels used to produce animal-based food typically becomes protein, but this measure is 46% for grains.

The word ‘energy’ originates from the Greek energhéia, a concept Aristotle linked with the idea of hypothetical entities becoming real. It was applied by physicians until the 1600s to the notion of a supposed irritant substance conveyed by nerves that stimulated action.

Aspects of the concept of work done appear as early as 60AD in the writings of Hero of Alexandria. Hero reported that if a weight were raised with a pulley system by the exertion of a force less than the weight being lifted, the rope must be pulled with a speed greater than the speed with which the weight rises.

Galileo and Descartes get the ball rolling

Galileo, without explicitly discussing the concept of conservation of energy, hinted at an understanding that certain kinds of machines were impossible:

… as if with their machines they could cheat nature whose instinct — nay, whose most firm constitution — is that no resistance may be overcome by a force that is not more powerful than it.

Descartes’ writings also include a theologically inspired assertion that pre-empted conservation laws:

God… in the beginning created matter along with motion and rest, and now, through His ordinary concourse alone, conserves just as much motion and rest in the whole of it [i.e., the material world] as He put there at that time.

In his 1664 Principia Philosophiae, Descartes proposed a number of (flawed) laws of collisions that used the concept of quantity of motion, calculated as the product of mass and undirected speed. Building on Descartes work, in 1668, John Wallis, Christopher Wren and Christiaan Huygens presented work to the Royal Society in which they argued that the direction of velocity was a significant aspect of the quantity of motion.

Leibniz −  force dead or alive?

Leibniz disagreed with the Cartesian notion that the total ‘motion’ was conserved and distinguished two concepts: vis viva (the living force), defined as mass times velocity squared (twice the modern kinetic energy), and vis mortua (dead force) which is somewhat related to the modern notion of potential energy. Leibniz derived his definition of vis viva by considering the ‘force’ acquired by two falling bodies, one of mass m dropped a distance 4h and another mass 4m which falls a distance h.

Leibniz used the law of falling bodies to argue that the object with mass m reaches double the velocity of the 4m object, because it falls four times the distance. As the same ‘force’ is required to lift both bodies, the value of vis viva should be related to mv² not mv. Moreover, Leibniz argued that the quantity mass multiplied by velocity squared was conserved.

A disagreement between followers of Leibniz and Descartes over the nature of vis viva occupied philosophers for over 50 years. English and French thinkers tended to favour the notion that ‘living force’ was represented by mv, with Dutch, German and Italian philosophers preferring Leibniz’s mv² construction.

It is argued that Newton understood, and used mathematically, the concepts of the kinetic and potential energy in the context of objects in orbit, without having explicit terminology for the concepts.

Du Châtelet −  inferior to no one

A significant contribution to the debate about the nature of the concept of energy was made by Émilie du Châtelet, a French philosopher and scientist born in 1706. Du Châtelet had been brought up by a progressive father who encouraged his daughter’s training in horse-riding and fencing alongside an academic education in mathematics, literature and science.

After an arranged marriage to a member of the nobility, du Châtelet became a mother but resumed her mathematical studies with a series of eminent tutors. At the time, the Café Gradot in Paris was a favourite venue for thinkers to meet and debate but, when du Châtelet attempted to follow a tutor into the café to continue their discussion, she was ejected because she was a woman. Undeterred, du Châtelet had a man’s suit made and returned a week later, in disguise, to engage in the discussions.

One of du Châtelet’s most significant contributions to the energy debate was a critique of an argument proposed by James Jurin, who supported Descartes’ model of ‘force’ as mv. She proposed a thought experiment in which a spring projects a ball forwards on the deck of a boat. She pointed out that Jurin (and others) had neglected the recoiling motion of the boat. She asserted that the model of ‘force’ as mv, which had been supported from this mistaken assumption, should be replaced with the quantity 1/2mv² and proposed the conservation of total energy in addition to conservation of total momentum.

Du Châtelet became the first woman to have a paper published by the Paris Academy. She had developed a close personal and professional relationship with Voltaire with whom she collaborated on scientific research. However, when he entered a paper on the nature of fire to the Academy’s essay competition in 1738, she disagreed with his thesis and submitted her own rival paper. Neither won.

In addition to her scientific pursuits, du Châtelet enjoyed gambling at cards, losing 84,000 livres (just over a million pounds in today’s money) in one evening. She encountered significant prejudice throughout her life due to her gender. The German philosopher Kant wrote:

A woman who… carries on fundamental controversies about mechanics, like the Marquise du Châtelet, might as well even have a beard, for perhaps that would express more obviously the mien of profundity for which she strives.

She was unbowed and refused to be seen simply as a footnote to men’s lives, writing:

Judge me for my own merits, or lack of them, but do not look upon me as a mere appendage to this great general or that renowned scholar, this star that shines at the court of France or that famed author. I am in my own right a whole person, responsible to myself alone for all that I am, all that I say, all that I do… I confess that I am inferior to no one.

Her final project was translating Newton’s Principia into French. Aged 43, du Châtelet discovered she was pregnant and feared she would die before she completed the translation. She increased her work schedule reporting:

I get up at nine, sometimes at eight; I work till three; then I take my coffee; I resume work at four; at ten I stop to eat a morsel alone; I talk till midnight with M. de Voltaire, who comes to supper with me, and at midnight I go to work again and keep on till five in the morning… I must do this… or lose the fruit of my labours if I should die in child-bed.

Sadly, her fears turned out to be justified. Du Châtelet died six days after giving birth.

Newtonian treason

Around 1720, the Dutch physicist Willem Gravesande set out to experimentally resolve the controversy over whether vis viva was best represented as mv or mv². Gravesande dropped balls of different weight into a layer of clay and measured the depth of the impressions they made. This led him to conclude that Leibniz’s construction of mv² was correct; a difficult conclusion as Newton, his idol and mentor, had championed the quantity of motion as mv. When it was argued that his conclusions were ‘treason’ to the Newtonian cause, Gravesande replied: “Real Newtonians don’t follow a person but a method.”

Gravesande is also notable for devising the common classroom experiment in which a brass sphere can be passed through a brass ring at room temperature but fails to fit after the sphere has been heated.

Resolution

Some historians of science argue that the vis viva debate was finally resolved by Jean Le Rond d’Alembert in 1743. He pointed out that the controversy was “un dispute de mots”, a dispute over words, rather than a disagreement of physical models. He showed that it was possible to use both conservation of mv and mv² in the same system.

In 1807, Thomas Young was the first person to use the modern sense of the word ‘energy’ for the quantity of mass multiplied by velocity squared. William Thompson, who later became Lord Kelvin, is credited with introducing the concept of kinetic energy in 1849. We now associate the concept of an object’s kinetic energy with the quantity of one half of its mass multiplied by its velocity squared.

An important factor in the failure of Robert Falcon Scott’s expedition to the South Pole was an error in estimating the energy expenditure of his men. Scott provided rations of 4,400 calories a day when his men were expending on average 7,000 calories hauling their equipment. The calculations Scott had based his rationing on were derived from men working at sea level and he made no correction for the increased rates of respiration his men would experience at altitude. It is thought his team experienced a calorie deficit and lost around 1.5 kg of body mass per week. At the time of his death, it is estimated that Scott had lost 40% of his body mass. Scott’s team had packed rations with a high proportion of protein (29%), for example pemmican (a food made from dried meat, fat and berries) and biscuits, but it is now argued that the slow plodding motion of sledge hauling is better supported by high-fat rations. A typical contemporary Antarctic ration contains 57% fat and only 8% protein.

When engaged in a difficult task, you may have justified the consumption of a sweet treat based on the belief that the sugar will help you concentrate. A body of research has examined whether the consumption of carbohydrates, such as glucose, can boost mental function. A review of the literature concluded that there is a consensus that for people with poorly regulated blood sugar who are undertaking cognitively challenging tasks, the consumption of glucose may indeed boost performance. Sadly, the evidence is inconclusive as to whether consuming additional glucose boosts mental function in all cases.

James Joule, born in 1818, came from a long-established brewing family and the Joule family brewery is still in operation today in Market Drayton.

Firearms and eyebrows

Joule had a laid-back approach to safety in his experimentation. To investigate an echo from Scafell, a mountain in the Lake District, he loaded his father’s pistol with a triple charge of powder. On firing, the recoil blew the weapon into a lake.

The experience did not instil a cautious approach to experimentation in the young scientist — in further experiments with firearms, Joule is reported to have blown his eyebrows off. It was not only his own safety that was threatened by his experimentation. He tested the effects of a Leyden jar on a servant girl, asking her to report the sensations she experienced whilst increasing the intensity of the shocks until she lost consciousness. Though it is often reported that Joule took a thermometer with him on his honeymoon, and made measurements of the temperature of a waterfall, Joule’s biographer reports that the story only appeared 35 years after the alleged event and is likely a fable.

The paddle-wheel experiment

William Thompson (later, Lord Kelvin) remarked to his brother that Joule’s ideas “have a slight tendency to unsettle one’s mind”. A good example is Joule’s well-known paddle-wheel experiment. Although intuitive today, it was the first method which demonstrated work done mechanically is equivalent to work done by heating.

The paddle-wheel experiment seems to be straightforward, but attempts to replicate it from Joule’s methodological description highlight his prowess as an experimental scientist. Joule’s instructions require an experimenter to use pulleys to raise and then drop two 13 kg masses 20 times within a 35-minute period — a feat which requires considerable muscle strength. To add to the challenge, between each winding, the experimenter must pause to take temperature readings from behind a wooden shield to prevent heating by their body affecting the experiment.

A present-day replicator of the experiment concluded with exasperation: “Having worked to replicate Joule’s experiments with his apparatus, I find it more than a little irritating that he states, without elaborating, that ‘the method of experimenting was simply as follows’.”

Later years

In 1858, Joule was returning home from London on the Scotch Express when, near Nuneaton, the train hit a cow that had wandered onto the rails. The carriages toward the front of the train were derailed in the collision and three passengers were killed. Though Joule was unharmed, he reported his shock at seeing the locomotive crew calmly eating sandwiches in the aftermath of the crash. The accident made him anxious about train travel and it is claimed that he turned down the opportunity to be renominated to the Council of the Royal Society to avoid further trips to London.

Despite his many scientific achievements Joule was a modest man. He commented to his brother: “I believe I have done two or three little things, but nothing to make a fuss about.” His gravestone, in Sale, Greater Manchester, has the number 772.55 engraved on it, the magnitude of work required to heat a pound of water by one degree in foot-pounds (an imperial unit of work whereby 1 foot pound is equivalent to 1.4 J).

Another proposer of the principle of conservation of energy, Benjamin Thompson (later, Count Rumford), was born in Woburn, Massachusetts in 1753. Rumford left school at 13 and moved between a number of jobs, being apprenticed first to a merchant, then a shopkeeper and finally a doctor. During this time, Rumford began to carry out experiments on heat transfer but his unstable employment situation prevented focused work.

His luck changed when he met and married Sarah Rolfe, a wealthy and socially well-connected heiress. Through his wife’s connections, Rumford was appointed as a major in the New Hampshire Militia. His new status led him to support the loyalist colonists in the American Revolutionary War and he was twice charged with spying for the British against the revolutionary Americans. Faced with these charges, Rumford fled from America, first to London and then to Bavaria, leaving his wife and daughter, whom he would never see again. Rumford’s charm allowed him to secure the position of aide-de-camp to the prince-elector of Bavaria and he was able to resume his experiments on energy.

Boring cannons

Whilst in Munich, he oversaw the manufacture of cannons and observed that a blunted borer made the cannon’s brass casing hot enough to boil water. The contemporary theory of heat transfer suggested that the process of boring released a fluid, called ‘caloric’, from the metal which entered the water, heating it up. Rumford disagreed with this interpretation and argued that the metal did not contain a fluid form of heat, but that the motion of drilling generated heat. We would now say that the drilling motion caused heating of the metal — energy is transferred to a thermal store by mechanical working.

Rumford’s inventions and underwear

Whilst living in Paris, Rumford gained a reputation for eccentricity. During the winter he wore a white hat and coat to better reflect hypothetical rays of cold known at the time as frigorific rays.

Amongst other inventions, Rumford designed: a drip coffee maker, the first enclosed kitchen range, and Rumford soup, a broth which was intended to improve the diet of the masses. Due to his investigation of the thermal properties of various materials, Rumford is credited with the invention of thermal underwear.

Remarriage and legacy

In addition to his scientific works, Rumford established workhouses for the poor, created the Englischer Garten in Munich and instigated the cultivation of the potato to Bavaria. For these services, in 1791, he was made a count of the Holy Roman Empire. In the final years of his life, together with Joseph Banks, Rumford founded the Royal Institution in 1799 and appointed Humphry Davy as its first lecturer.

Rumford’s story has a curious twist. When he moved to Paris, he began an affair, and later married, Marie-Anne Paulze Lavoisier. A French chemist herself, she had been married to the executed scientist Lavoisier who had proposed the caloric theory which Rumford had rejected.

Joseph Black, who became professor of medicine and chemistry at Glasgow University, was born in Bordeaux in 1728 to a family of wine merchants. Black was interested in changes of state and introduced the term latent heat to refer to energy that appeared hidden in the process of melting but would reappear in freezing. He contrasted latent heat with sensible heat, the energy that, when transferred, results in the changes in temperature of materials between changes of state. In a collection of lectures published in 1807, after his death, Black noted a curious effect that occurred when an equal of amount of ice and 80°C water were mixed together (the units have been converted from Fahrenheit in the original text):

…the result was that the fluid was no hotter than water just ready to freeze. Nay, if a little sea salt be added to the water and it be heated only to 74 or 77°C, we shall produce a fluid sensibly colder than the ice was in the beginning, which has appeared a curious and puzzling thing to those unacquainted with the general fact.

Black observed that different quantities of substances needed differing amounts of energy transferred to them to raise their temperatures by the same amount and coined the term specific heat. His research was instrumental in the separation of the concepts of ‘heat’ and ‘temperature’.

Black is also credited with discovering that, when heated, magnesium carbonate releases a gas, which he labelled ‘fixed air’ but was later renamed ‘carbon dioxide’ by Lavoisier.

It seems intuitive that, when energy is added to a system, its temperature will rise. Hence, the notion of negative heat capacities seems an impossibility. However, astrophysicists have argued that a star, or cluster of stars, can cool down when energy is added. Virial theorem describes the mean total kinetic energy of a system of particles bound by a potential over time. When applied to the cores of main sequence stars, as hydrogen is converted to helium by fusion, the mean molecular mass of particles increases and the core collapses. This contraction, according to virial theorem, results in a decrease in potential energy and an increase in thermal energy. Hence the core’s temperature increases as its energy falls, suggesting a negative heat capacity. A similar argument holds for clusters of atoms with negative heat capacities observed in clusters of sodium atoms.

The Greek historian Herodotus reported that, once the site had been prepared, it took 100,000 men twenty years to build the Great Pyramid. A professor of physics has analysed whether this claim is realistic and estimates that the total work required to construct the Great Pyramid is around 1.3 x 10¹³ J. Assuming that one person could do 150 kcal (628 kJ) of work on the pyramid per day, the academic argued that the work could be completed by only 5,700 people over 10 years.

The horsepower unit derives from a marketing gimmick devised by James Watt. When attempting to sell his newly invented steam engine in the 1770s, Watt realised that many of his customers would use the machine to replace horses, so he set out to measure the power delivered by a horse.

He set two heavy dray horses to pull a 100 lb (45kg) mass from the bottom of a well and found they could achieve the task by walking comfortably at 2.5 miles an hour. Watt then added an extra 50% to the calculation to account for work done in overcoming friction and defined 1 horsepower as the power needed to lift 150 pounds (68 kg) out of a 220 foot (67 m) deep well in one minute.

It has been claimed that Watt deliberately overestimated the power output of a horse to ensure that his steam engines performed better than the horses they replaced. Whilst the peak mechanical power of a single horse can reach up to 15 horsepower, it is estimated that a typical horse can only sustain an output of 1 horsepower (746 W) for three hours and, if working for an eight-hour day, a horse might output only three quarters of one horsepower. Researchers have calculated the average power output of various animals (as a rough guide, a healthy animal can pull 10-15% of its weight for a period of four hours):

Despite his financial success, Watt was not a natural businessman and he wrote in a letter:

I would rather face a loaded cannon than settle an account or make a bargain. In short I find myself out of my sphere when I have anything to do with mankind; it is enough for an engineer to force Nature, and to bear the vexation of her getting the better of him.

These business difficulties inspired one of his lesser-known inventions. With his commercial partner, Watt had built a thriving company that supplied steam-driven pumps to mines. However, with the company’s success, the volume of paperwork he was faced with increased and Watt struggled to find suitable clerks to copy documents. With Joseph Black (see above), Watt invented a novel system to copy documents. The pair developed a gelatinous ink which was used to write the first version of a document. The document was dampened and pressed against another thin sheet by passing the two documents between two rollers. The copy was only legible if read through the back of the copied sheet to overcome the mirroring produced by the copying process. Watt patented the device and, in the first year after in went on sale, sold 200 of the copiers, including a number to Thomas Jefferson. Later in his career, Watt worked on a device for copying sculptures using a system of parallel, hinged arms. He never completed the design but, 20 years after Watt’s attempt, the sculptor Benjamin Cheverton patented a working device based on Watt’s idea.

A paper by a team of forensic pathologists calculated the energy required to break beer bottles in order to determine whether they were capable of fracturing a human skull. They determined that full bottles were broken by 30 J of work done whereas empty bottles shattered by a transfer of around 40 J (based on sample of six bottles). The breaking energies were calculated by dropping a 1 kg steel ball onto the bottles in a materials’ testing drop tower. The authors report that electrohydraulic experiments with human cadavers had found that skull fractures occurred in different regions of the skull at energies between 14.1 J and 68.5 J. They conclude that beer bottles may act as formidable weapons.

• During a marathon, a typical runner transfers around 100 J during each foot strike with the ground, of which around 35 J is transferred to the elastic store of the Achilles tendon. A good running track can return an additional 12 J per step and increase running speeds by approximately 2%. Running tracks are designed to have a natural frequency of around 2 Hz to maximise energy transfer.
• Much of the energetic benefit of swimming for losing weight may be due to thermal transfer from the body rather than the work done in moving the body forward. An estimate of the energy transferred by a 65 kg swimmer in a pool at 27°C concluded that around 2 kJ/min of work is done propelling the swimmer forwards but ten times that amount, about 20 kJ/min, will be thermally conducted from the body. The author of the paper concludes, “This fact can be utilised by overweight persons to burn their extra fats [sic] even by just sitting in the water with their head above the surface.”
• By modelling the human body as a series of segments, a group of students calculated that the energy transferred by the upward motion of a press-up is around 342 J for the average male.

A paper has estimated the power output of a single Norman water mill as around 1.3 kW and, using the number of mills listed in the Doomsday Book of 1086, calculated the total power output of Norman millers to be around 7.8 MW.

A researcher at the University of Leeds has produced a series of estimates for the energies involved in fights between pre-historic creatures. It is estimated that a tail blow by a Doedicurus, a heavily armoured relative of the armadillo, could transfer around 2.5 kJ.

The world’s largest solar furnace, in Odeillo in the French Pyrenees, was built in 1968. The furnace could, when newly constructed, concentrate solar power by a factor of 16,000, but this has decreased to a multiplier of around 9,500 as temperature variation has moved the mirrors out of alignment. It can reach temperatures of 3,500°C and is used for testing materials, including heat shields for spacecraft.

Concerns have been raised about a solar thermal power plant in the Mohave Desert because the plant had been igniting birds that flew over the facility. Federal biologists estimated that as many as 6,000 birds may have been incinerated by the Ivanpah Solar Plant every year. The plant consists of a 14 km² array of mirrors which follow the Sun, focussing light onto three 40-storey tall towers. Located on a migratory route, the Pacific Flyway, birds approach the towers to eat insects attracted by the focused beams of light. In response to concerns about the bird deaths, a number of operational adjustments were suggested including clearing land and covering ponds around the plant to make it a less attractive roosting site. Since changes were introduced, the avian mortality rate at the facility has been significantly reduced.

That hot water freezes quicker than cool water had been noted by many observers including Aristotle, Bacon and Descartes. However, the effect has come to be named after the schoolboy who brought the phenomenon back to the attention of scientists. In the 1960s, Erasto Mpemba, then a secondary school student in Tanzania, was making ice cream and noted that boiled milk placed in the freezer froze faster than milk at room temperature. He approached his science teacher who said he must have been confused and mocked his answers in class, describing his ideas as ‘Mpemba physics’. When a professor from a local university visited his school, Mpemba raised the issue. The scientist asked a technician to confirm the result and the academic and Mpemba published a co-authored paper on the effect.

This counter-intuitive result has led to the publication of several papers on the phenomenon. There is an on-going debate about the causes of the Mpemba effect. Some researchers argue that the properties of hydrogen bonds explain the phenomenon, whilst others claim that the effect is merely an artefact of experimental technique.

For hundreds of years, legends spoke of a boiling river in the Amazonian jungle. In 2011, geoscientist Andrés Ruzo rediscovered and began studying the river. It is more than 650 km from the nearest active volcano yet the average temperature of the water is 86°C. At 25 m wide and 6 m deep in places, it runs at high temperatures for a distance of over 6 km. Although its ancient name is “Shanay-Timpishka”, roughly translating to “boiled with the heat of the Sun”, it is heated by hot springs powered by geological fault lines.

Before becoming a professor of physics, Albert Einstein worked as a patent clerk. Familiar with the process, he submitted a number of his own patents including a camera that self-adjusts to the ambient light level and an electromagnetic sound reproduction device. A number of his patents were related to refrigeration, a project on which he collaborated with nuclear physicist Leo Szilard. In the 1920s, Szilard was a frequent visitor to Einstein’s home. One day, after he had read a report of a family who had been killed by the toxic gases leaking from their refrigerator, Einstein commented to Szilard that, “There must be a better way.” The two physicists devised and patented multiple designs for new refrigerators based on principles including absorption, diffusion and electromagnetism. The Swedish company AB Electrolux bought the patent for the absorption refrigerator for $750 and subsequently the diffusion design, though never developed either appliance. Einstein and Szilard also collaborated on the design of an electromagnetic pump, which they assumed would be silent. Instead, due to cavitation (the formation of bubbles) in the fluid, contemporaries reported the pump “howled like a jackal”.

William Thomson, who would later become Lord Kelvin, was a precocious student. At the age of 16, he published his first paper, a development of ideas in a paper by Fourier. He holds the record for being both the youngest and oldest member of Glasgow University - when he was 10 years old, Kelvin participated in a programme for able primary school students at the university and was a member of faculty there until he was 75. Kelvin studied at Cambridge University, founded the Cambridge Musical Society and spent two hours a day rowing. Though he finished second in his year in his final exams, a story reports that one of his examiners remarked to another, “You and I are just about fit to mend his pens.”

After graduating, Thompson spent a year in Paris, before being appointed a full professor at the University of Glasgow at the age of 22. One of Kelvin’s most significant projects was his contribution to the laying of Atlantic telegraph cables, for which he received a knighthood. He invented the mirror galvanometer, the electrostatic syphon recorder, a device for recording telegraphic Morse code messages that pre-empted the invention of the inkjet printer, and a machine for predicting tides (now housed in London’s Science Museum).

In 1867, Peter Guthrie Tate gave a demonstration of the strange behaviour of smoke rings in his Edinburgh laboratory. He showed how, if two rings travelled along the same axis, the leading ring slowed, expanded and the pursuing ring accelerated and contracted, passing through the other. Kelvin was greatly influenced by this demonstration and developed a vortex model of the atom, going on to argue that the Sun gained energy from the action of a vortex of comets circling it.

Kelvin made use of an innovative questioning technique in his lectures. He wrote the names of his students onto cards and sorted them into a box divided into three sections:

1.  purgatory (for those who had yet to be questioned)
2.  heaven (for those who had answered correctly)
3.  hell (reserved for students who had answered a question incorrectly and needed to be retested)

Kelvin’s question box now forms part of the collection of the Hunterian Museum.

Many teachers will empathise with another of Kelvin’s quirks. After two successive lectures in which he could not find a single suitable piece of chalk, Kelvin ordered his assistant to have a hundred pieces ready for his next lecture. His assistant dutifully set out a hundred pieces of chalk along a 5 m window ledge. At the start of his next lecture, Kelvin counted the pieces of chalk and congratulated his assistant to the applause of his audience.

Kelvin’s scientific thinking sometimes spilled over into his personal life. Over lunch one day, his wife suggested a walk and Kelvin is said to have replied: “At what time does the dissipation of energy begin?”

In his lifetime, Kelvin published 661 scientific papers and filed 75 patents. Despite his great successes, he made a number of assertions that proved to be incorrect. He is said to have remarked that, “X-rays will prove to be a hoax” and famously underestimated the age of the Earth to be only somewhere between 20 and 400 million years. Rutherford reported being troubled by the prospect of giving a speech at the Royal Institution when Lord Kelvin was part of the audience because of their disagreement over the age of the Earth. Fortunately, a conflict was avoided:

To my relief; Kelvin fell fast asleep, but as I came to the important point, I saw the old bird sit up, open an eye and cock a baleful glance at me! Then a sudden inspiration came, and I said Lord Kelvin had limited the age of the earth, provided no new source was discovered. That prophetic utterance refers to what we are now considering tonight, radium! Behold! The old boy beamed upon me.

Kelvin received 21 honorary degrees from universities around the world, was awarded the Legion of Honour, Grand Officer by France, the Order of the First Class of the Sacred Treasure of Japan and was made a Knight of the Prussian Order Pour le Mérite.

An unusual piece of thermodynamics research is presented in a paper: Impact of wet underwear on thermoregulatory responses and thermal comfort in the cold. Academics recruited eight male volunteers who were willing to wear wet underwear in a climate-controlled space whilst having their skin and rectal temperatures monitored for an hour. Every ten minutes, the volunteers completed a questionnaire reporting how much they were shivering and sweating. The researchers, unsurprisingly, concluded that men with wet underwear felt colder and less comfortable than men with dry underwear. They report that the construction of underwear has an effect on the rate of evaporation and hence cooling and that the thickness of the underwear has a more significant effect on thermal comfort than the material it is made from.

Flanders and Swan wrote a song about the first and second laws of thermodynamics that contains the verses:

You can’t pass heat from a cooler to a hotter.

Try if you like, you far better notter,

‘cause the cold in the cooler will get hotter as a ruler,

‘cause the hotter body’s heat will pass to the cooler.

Heat is work and work’s a curse

And all the heat in the universe

Is gonna cool down

Because it can’t increase.

The differential heating of the sides of an asteroid by sunlight can lead to the exertion of a small thrust force, a phenomenon known as the Yarkovsky effect. In September 2016, NASA launched a spacecraft, OSIRIS-REx, to intercept and collect samples from the asteroid Bennu. It successfully landed on the asteroid in October 2020. In addition to collecting a sample of the asteroid and returning it to Earth, OSIRIS-REx will investigate the Yarkovsky effect on Bennu in order to develop potential techniques to deflect asteroids that are on a collision course with the Earth.

It is recorded that both Philo of Byzantium and Hero of Alexandria carried out experiments using thermoscopes, tubes filled with liquids without scales marked on them, as a crude temperature probes. For example, Philo constructed a device consisting of a hollow lead sphere, to which a curved U-shaped tube was connected. The free end of the tube was placed under water and bubbles were detected when the sphere was placed in the Sun.

 The Venetian physician Santorio Santorre is credited with the first mention in print of the liquid-in-glass thermometer in 1612, even though Galileo’s experiments preceded it.

Though it didn’t catch on, Newton developed his own temperature scale. He constructed a thermometer using linseed oil and set the zero of his scale to be ‘the heat of air in winter at which water begins to freeze’ and defined 12 as ‘the greatest heat which a thermometer takes up when in contact with the human body’. On this scale, Newton reported that the “heat of iron… which is shining as much as it can” registered a value of 192.

The Swedish professor, Anders Celsius, developed his eponymous scale in 1742 but, though the scale was divided into the familiar 100 units, it was initially inverted so the boiling point of water was at 0°C and freezing at 100°C. The direction of the scale was switched by the taxonomist Carl Linnaeus.

During the 17th and 18th centuries, temperature measurement was complicated by the existence of at least 35 different temperature scales. Robert Boyle complained that instruments could only provide relative measurements and that “we cannot communicate the idea of any such degree to another person”. Boyle entered into a discussion of the nature of the primum frigidum, a superlatively cold body that was supposed to exist by some philosophers and Boyle described as “…some body or other, that is of its own nature supremely cold, and, by participation of which all other bodies obtain that quality”. Early thinkers had associated the primum frigidum with different elements. Boyle found none of their arguments satisfactory. For example, he critiqued Plutarch for associating the primum frigidum with earth because, he argued, it is the cold air that causes the ground to freeze, and he rejected the notion that water was the ideally cold element, because the ocean depths do not freeze. Ultimately, Boyle rejected the concept of a primum frigidum as an ‘unwarrantable conceit’.

Dalton described a ‘natural zero of temperature’ which exhibited an ‘absolute privation of heat’ and proposed it occurred at 6,000° below the freezing point of water. Both Laplace and Lavoisier calculated numerical estimates for absolute zero in the range of -600°C to -14,000°C. In an 1848 paper, Kelvin’s initially proposed temperature scale had no zero point. He argued the scale should go down to ‘infinite cold’ and, though he was aware of the zero volume of gases at -273°C, assumed that the result was not physically meaningful.

After writing his 1848 paper, Kelvin read Reflections on the Motive Power of Fire, the seminal work by Sadi Carnot, the French military engineer and physicist. By contrast with its eventual importance, Carnot’s writing had been ignored by scientists for 25 years, but caused Kelvin to realise that an ideal heat engine’s efficiency would approach a hundred percent as the temperature approached -273°C. To avoid a violation of the principle of conservation of energy, in 1852, he revised his temperature scale to include a zero of temperature.

The principle of conservation of energy seems to have been developed by a number of scientists working independently around the same time. One of the earliest statements was proposed by a German doctor, Julius Robert Mayer, who served as a ship’s physician in the tropics.

Mayer noted that venous (deoxygenated) blood in the tropics appeared to be unusually red and he hypothesised that someone living in a hot region required less oxygen than a person in a cooler climate. This train of thought led the doctor to consider the relationship between the consumption of food and bodily exertion. Using the term ‘force’ as an explanatory principle for phenomena such as growth and motion in humans, in 1841 Mayer formulated a conservation statement:

Forces, like matter, are quantitatively invariable… motion, heat and… electricity are phenomena which can be explained by a single force… and can be transformed into one another in accordance with definite laws. Motion is transformed into heat by being neutralised by an opposite motion.

However, his idea received little attention at the time, perhaps because he was forced to self-publish some of his work.

Tragically for Mayer, at the same time as the scientific community showed indifference to his work, he lost three of his children and he attempted suicide by jumping from a window, leaving him permanently lame. He was admitted to a mental asylum for a time, but after leaving, Mayer found that his scientific reputation had flourished and he continued to work as a physician till his death in 1878.

A cat has appeared as the co-author of a paper on low temperature physics (Two-, three-, and four-atom exchange effects in bcc He 3 in the journal, Physical Review Letters). The paper’s first author, Jack Hetherington, reports that though he was the only author of the paper, he had accidently written the article using the pronouns ‘we’ and ‘our’. Rather than rewriting the paper, he added the name of his cat, Chester, used the initials of its species name, Felis domesticus, and the name of the cat’s father, Willard, as its surname to give the co-author: FDC Willard.

It is challenging to toast bread to the perfect colour because of thermal runaway: as the surface of the bread darkens it absorbs more thermal radiation so its temperature rises faster and the blackening process accelerates. A more serious but related effect occurs as highly reflective white ice sheets melt, decreasing the net reflectivity of the Earth’s surface and accelerating global warming. In reverse, this phenomenon can be used to make urban environments more comfortable. As part of the city’s urban cooling agenda, a pilot programme in Los Angeles has painted some normally dark-coloured pavements with a white, reflective paint. The paint led to a decrease in pavement surface temperatures by up to 6°C.

There is evidence that, in the Egyptian Old Kingdom around 2500 BC, and as early as 3000 BC in India, evaporative cooling technology was used to cool liquids. To achieve the cooling effect, a porous earthenware pot with a narrow neck was filled with water. Water seeped through the porous earthenware walls of the container and evaporated, cooling the water remaining inside. An evaporative cooler’s efficiency is dependent on the humidity of the air — the theoretical maximum change in temperature possible is equal to the difference in reading between a wet and dry bulb thermometer.

Before the development of electric refrigerators, Australians made use of ‘Coolgardie safes’. The devices, invented in the Coolgardie gold mines in Western Australia, consist of a cupboard made from metal mesh with the walls lined with hessian. A container on top of the device kept the hessian damp via a link pipe. As water evaporates from the hessian, it cools the contents of the ‘safe’ and draws water down from the tank via the pipe. An evaporative cooler can extend the shell-life of tomatoes from 2 to 20 days.

Recognised as one of Junior Chamber International’s Ten Outstanding Young Persons of the World in 2010, Emily Cummins is an inventor and entrepreneur from Leeds. Emily reports that since her grandfather first handed her a hammer at the age of four, she was inspired to create. During her degree she invented a sustainable fridge that uses dirty water to cool food by evaporation. Her cylindrical fridges are now used across southern Africa.

A story reported to John Aubery by Thomas Hobbes claims that Francis Bacon died whilst carrying out research on the preservation of food. According to the story, Bacon, on seeing some snow on the ground, got the idea that it could be used to preserve meat, in a similar way to salt. He bought a hen, removed its viscera and stuffed it with snow. It is reported that the exposure caused him to fall ill and he died a few days later.

Georges-Louis Leclerc, Comte de Buffon, a naturalist and mathematician, provided an early estimate of the age of the Earth by observing cooling cannon balls. In a 1775 work, the Frenchman describes making a number of iron spheres of various diameters and heating them till they were white hot. He recorded the time taken to reach two points: a temperature when they could be held comfortably and room temperature. Buffon argued that the time taken to reach the two temperatures was proportional to the balls’ diameter and estimated that it would have taken the Earth “ninety-six thousand and six hundred seventy years and one hundred and thirty-two days” to reach room temperature. Buffon’s estimate preceded Kelvin’s famous erroneous estimate of the age of the Earth (see end of Kelvin’s achievements on page 28) via a similar method.

The stack effect is a phenomenon that occurs in tall buildings. In hot weather, lower density warm air rises and escapes through windows or cracks at the top of the building, creating an area of relatively low pressure at the bottom of the building in comparison to the outside. The pressure differential causes air to be drawn into the base of the building through cracks and holes. The stack effect can lead to the exertion of strong forces on conventional doors, hence, most high-rise buildings have revolving or double doors to mitigate against the effect. The stack effect can be observed on buildings that are being renovated and covered in sheeting. In hot weather, tarpaulins tend to be drawn in at the bottom of the building and pushed out at the top. The direction of the effect is reversed in cold weather.

British Standards (BS), the national standards body which produces a range of different technical specifications for products and services, has produced a standard for making a cup of tea. Published in 1980, BS 6008:1980 refers to the “Method for preparation of a liquor of tea for use in sensory tests”. The standard recommends the use of a pot of “…white porcelain or glazed earthenware, with its edge partly serrated… and provided with a lid”. The pot should be filled with freshly boiled water to within 4-6 mm of the rim and the tea should be brewed for six minutes. When preparing tea with milk, the guidance suggests tea is added to the serving vessel after the milk, to avoid scalding the milk. Though the writers avoid controversy by adding the caveat: “unless this procedure is contrary to the normal practice in the organisation concerned”. The writers counsel that, “If the milk is added afterwards, experience has shown that the best results are obtained when the temperature of the liquor is in the range 65 to 80°C when the milk is added.”

Passengers who use the deep lines on the London Underground in hot weather will have experienced how uncomfortable the trains can become. When London’s underground railway was first constructed in the 1800s, it was marketed as one of the coolest places to be in hot weather. Since then, however, temperatures have been rising.

In recent years, passengers on the Underground system have experienced a mean temperature of 11°C above the ambient temperature, with some areas considerably hotter still. In 2019, The Independent newspaper reported that the Central Line had reached temperatures of over 36°C.

 When the Underground’s tunnels were originally dug, the surrounding clay was relatively cool and acted as a heat sink – in the 1900s the temperature of the clay was around 14°C. Since then, energy transferred by trains (mainly from braking) has been absorbed by the clay and currently the ground surrounding the tunnels is at an average temperature of 20 – 25°C. The Underground’s designers had not anticipated this problem and the system currently has inadequate ventilation to dissipate heat. Whilst making changes to the deep and narrow existing tunnels is challenging, engineers have begun to consider creative solutions, including increasing train coasting time and developing a system to recapture energy during deceleration. The new Crossrail network’s engineers have addressed the problem by using a system in which cold air is blown over a train’s traction and braking systems whilst the train is in a station and the hot air is vented along the underside of the platform.

Marc-Auguste Pictet was a Swiss editor of the Bibliothèque Britannique, a publication that shared scientific knowledge developed in Great Britain with a continental audience. In addition to his journalism, Pictet carried out his own scientific studies. In one experiment, the report of which was published in 1790, he arranged two tin mirrors 3 m apart and placed a thermometer and a ‘matrass full of snow’ at their respective foci. He reported that as soon as the ‘matrass’ was in place, the temperature recorded on the thermometer began to fall. Pictet found that he could cause a greater fall in temperature by pouring nitric acid on the snow. He reported that, “The act was notorious, and amazed me at first; this phenomenon offered nothing more than a final proof; if it had been necessary, of the reflection of heat...”. The phenomenon would be now be described as the result of the reflection (or lack of reflection) of infra-red radiation.

Concorde’s designers were aware of potential heating of the airframe due to supersonic travel and set a maximum safe limit for the temperature of the aluminium body over the life of the aircraft at 127°C, limiting the top speed of the aircraft. The aircraft was painted with a highly reflective white paint to prevent overheating.

In 1996, an Air France Concorde was given a blue livery as part of an advertising promotion with Pepsi. The pilots were warned to limit Mach 2 flight to no more than 20 minutes due to the additional aerodynamic heating of the new paintwork.

 Concorde would expand by as much as 300 mm when travelling at supersonic speeds and a gap would open between the flight engineer’s console and a bulkhead. On the plane’s final flight, an engineer placed a hat in the gap, where it became permanently lodged as the plane cooled down for the last time.

Typically, for everyday objects, a single point on the object might be expected to be at a single temperature. However, research by physicists at the University of Exeter suggests that, for small objects, the situation might be more complicated.

In the 1930s, Heisenberg and Bohr applied the uncertainty principle to the relationship between heat transfer and temperature. In order to precisely measure the temperature of an object, it has to be isolated from its surroundings. But measurement of temperature involves some contact with a measuring device which will cause uncertainty in the temperature reading.

Whilst a typical thermometer will display some uncertainty in its readings, one of the authors of the Exeter research, Henry Miller, argues that when measuring on the very small scale, a quantum thermometer has a different issue: “What we find is that because the thermometer no longer has a well-defined energy and is actually in a combination of different states at once, that this actually contributes to the uncertainty in the temperature that we can measure.” One interpretation of this claim is that an object might be considered to be at two temperatures at once.

Energy generating companies need to predict the load on their network to ensure that demand can be met. A commonly plotted graph is that of the net load on the network against the time of day which displays the difference between the demand and the supply from renewable energy sources. A graph was developed by the California Independent System Operator to show the power demands that would remain after the power supplied from solar power had been removed. When the graph was plotted it was noted that the curve resembles a duck.

In many contexts, after sunrise, demand for power falls just as the power output of photovoltaic systems rises creating the concave back of the duck. Peak demand for power occurs just after sunset when no solar power is being generated, creating the peak that forms the head of the duck. The duck curve highlights the importance of power storage technologies such as batteries and pump storage, to ensure grids with a high percentage of photovoltaic power generation can meet consumer demand. 

As discussed above, the use of solar panel technology requires systems that can store energy and release it when solar power output falls. A potential solution to this problem is to use a body of water, such as a lake, to store solar energy. However, convection currents set up in the water result in efficient energy loss from the water and, during a day, the temperature of a pond may vary by only a few degrees. If convection currents could be inhibited, the transfer of energy from the pond would be reduced leading to a significant water temperature rise and more effective solar energy storage. One way to do this is to dissolve salt into a pond. Due to the difference in densities of high and low salinity water, saltwater will form a natural concertation gradient, a halocline, with concentration increasing with depth. In a solar pond, a halocline is created. When solar radiation warms the dense highsalinity water near the pond’s floor, convection is limited as the high-salinity water does not mix readily with the low salinity water in the layer above. Using this technique, researchers have managed to create ponds that can reach up to 90°C simply from solar heating. From the 1950s, researchers in Beit Ha’aravah in Israel have used a 210,000 m² solar pond to generate a maximum of 5 MW of power at an efficiency of around 1%.

The Independent newspaper reported that residents of Woodland, North Carolina rejected plans for the construction of solar power plant near their town. The paper claims that, at a town council meeting, a local man expressed concerns that the solar panels would “suck up all the energy from the sun”, harming local business. It is reported that a local retired science teacher, Jane Mann, worried that the construction of the farm would prevent plants in the area photosynthesising. Mann had noted that plants located close to solar panels turned brown and died.

Perhaps the first quantitative measurement of solar radiation reaching the Earth was carried out by the French physicist Claude Pouillet. In the 1830s, Pouillet constructed a double-walled cylinder 61 cm long and of 10 cm radius. He filled the space between the walls with ice. At one end, he placed a piece of opaque material, with a pinhole drilled into it, that allowed a beam of sunlight to enter the interior of the double cylinder and to fall on the blackened bulb of a thermometer inserted through the opposite end of the tube. Using a calculated value of the heat capacity of the instrument, he could estimate the solar radiation falling on the device. Pouillet observed that, at noon on the summer solstice, solar radiation caused the thermometer reading to increase by 7.5°C. From his data, he calculated that the annual solar radiation would be sufficient to melt a layer of ice surrounding the globe 14 m thick.

Whilst on a tour of Europe, John Herschel, the son of the German British astronomer Frederick William Herschel, travelled over an Alpine pass and recorded in his journal the effects of solar radiation: “Vision quite scorched with the € [the Sun] & found sensation dreadful.” He noted that this experience sparked a curiosity to investigate the power output of the star:

…the scorching effect of the Sun’s rays upon every exposed part of the skin proved so severe as to excite in my mind a lively desire to subject to some precise means of measurement the cause of so disagreeable an effect.

Herschel invented a new instrument, the actinometer, to study solar radiation. The device consisted of a thermometer-like device but the thermometer tube, rather than terminating in the usual bulb, was attached to a cylinder with a moveable metal cap that could be adjusted by turning a screw. The cylinder was filled with copper sulphate solution (a dark colour to absorb radiation) and placed in a box shielded on three sides and with a glass wall on the fourth. A comparison of the average heating in direct sunlight with the mean cooling in the shade gave a measure of the effect of solar radiation. Whilst the device did not allow Herschel to make quantitative estimates of solar radiation, he concluded that the Sun’s surface must be hotter than a furnace.

In 1838, Herschel was working at the Cape of Good Hope, carrying out astronomical observations, including the production of a catalogue of nebulae. He returned to his interest in solar radiation by conducting an experiment using a tin cylinder, filled with inky water, within a larger iron container with a circular hole drilled in it that allowed light to fall on the tin vessel. From data collected using the instrument, Herschel proposed a unit of solar radiation, the actine, which was defined as the intensity of vertically incident radiation that will melt a layer of ice one micrometre thick in one minute. He calculated the yearly solar radiation intensity would be sufficient to melt a layer of ice 26.652 m deep across the surface of the planet.

Whilst it has been erroneously used by climate deniers to argue against anthropogenic climate change, the eccentricity of the Earth’s orbit does cause minor changes to the radiation incident on the Earth. However, orbital variation cannot account for the rapid and large-magnitude changes in global temperature linked to human activity.

In the 1920s, the Serbian geophysicist Milutin Milanković hypothesised that small changes in the eccentricity of the Earth’s orbit, its axial tilt and precession would cause cyclical changes to the intensity of solar radiation reaching the surface of the Earth.

First, Milanković noted that the eccentricity of the Earth’s orbit varies between 0.005 and 0.058 (it is currently 0.017) with the major component of the variation having a period of 404,000 years. This change in the shape of the Earth’s orbit arises because of the gravitational forces exerted by other bodies in the solar system, primarily Jupiter and Saturn. The changing eccentricity of the Earth’s orbit changes the lengths of the seasons and consequently the radiation incident of the surface of the planet. Currently, the Earth’s orbit is becoming less eccentric and so season length is equalising.

Second, the Earth precesses on its axis due to the torque exerted by the Sun and the Moon. The Earth’s axis of rotation currently aligns with the star Polaris. But around 3000 BC, the Egyptians observed that the night sky seemed to revolve around Alpha Draconis. The major component of the axial precession has a period of 25,700 years and currently we are roughly in the middle of a cycle of change between 21.8° and 24.4°. Changes to axial tilt alter the amount of solar radiation incident on the poles.

Third, the Earth’s elliptical orbit itself precesses in space relative to fixed stars with a period of 112,000 years. This precession changes the relative length of the seasons on Earth.

One of the many challenges of launching and safely returning astronauts to space is the problem of re-entry into the Earth’s atmosphere. The competitors in the early space race, the Soviet Union and the United States, took different approaches to solving the re-entry problem, leading to differently shaped spacecraft. The designers of the Vostok missions, a series of Soviet spaceflights in the early 1960s, chose a spherical shape to give stability during flight through the atmosphere. By contrast, HJ Allen of NASA’s Ames Aeronautical Laboratory proposed the blunt body principle which suggests that the shock wave formed by a blunt spacecraft travelling through the atmosphere will dissipate up to 90% of the heating due to friction caused by re-entry. Allen’s principle led to the truncated cone shape of the Mercury spacecraft, the first series of American spacecraft designed to carry humans into space.