Posts Tagged ‘heat’

A couple of blocks down from the Metro station Jussieu in Paris’s 5th arrondisement lies Rue Cuvier, which runs along the north-western edge of the botanic gardens which houses the Natural History Museum. The other side of the road is bordered by various institutes of the Sorbonne, notably UPMC (formerly Pierre and Marie Curie University).

The Curies have historical associations with a number of streets in the Latin Quarter, and Rue Cuvier in particular. Pierre Curie was born at No.16 and it was in a science faculty building in this street that the Curies conducted their fundamental research on radium between 1903 and 1914. The building still exists, shielded from public curiosity by a set of prison-style metal gates, and it was in this laboratory that the first pioneering research into what would later be recognized as nuclear energy was conducted in 1903.

Yet it was not the renowned husband-and-wife team which carried out this experiment. It was in fact Pierre Curie and his young graduate assistent Albert Laborde who did the work and reported it in Comptes Rendus in a note entitled Sur la chaleur dégagée spontanément par les sels de radium (On the spontaneous production of heat by radium salts). The note, which barely covers two pages, was published in March 1903.

The laboratory in Rue Cuvier where the Curies and Laborde worked was at No.12. Just across the street is No.57, which once housed the Appled Physics laboratory of the Natural History Museum. It was here in 1896 that Henri Becquerel serendipitously discovered the strange phenomenon of radioactivity.

Between that moment of discovery on one side of Rue Cuvier and Curie and Laborde’s remarkable experiment on the other, lay the years of backbreaking work in a shed in nearby Rue Vauquelin where the Curies, together with chemist Gustave Bémont, processed tons of waste from an Austrian uranium mine in order to extract a fraction of a gram* of the mysterious new element radium.

*the maximum amount of radium coexisting with uranium is in the ratio of their half-lives. This means that uranium ores can contain no more than 1 atom of radium for every 2.8 million atoms of uranium.

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The Curie – Laborde experiment

Albert Laborde (left) and Pierre Curie, in 1901 and 1903 respectively

Pierre Curie and Albert Laborde were the first to make an experimental determination of the heat produced by radium because they were the first to have enough radium-enriched material to make the experiment practicable. It was a close-run thing though. Ernest Rutherford and Frederick Soddy had been busy working on radioactivity at McGill University in Canada since 1900, but they were hampered by lack of access to radium and were using much weaker thorium preparations. This situation would quickly change however when concentrated radium samples became available from Friedrich Giesel in Germany. By the summer of 1903, Soddy (now at University College London) and Rutherford would have their hands on Giesel’s supply. But Curie and Laborde had a head start, and they turned their narrow time advantage to good account.


To determine the heat produced by their radium preparation, they used two different approaches – a thermoelectric method, and an ice calorimeter method.

This diagram of their thermoelectric device, taken from Mme Curie’s Traité de Radioactivité (1910), Tome II, p272, unfortunately lacks an explanation of the key, but the set-up essentially comprises a test ampoule containing the chloride salt of radium-enriched barium and a control ampoule of pure barium chloride. These are marked A and A’. The ampoules are placed in the cavities of brass blocks enclosed in inverted Dewar flasks D, D’ with some unstated packing material to keep the ampoules from falling down. The flasks are enclosed in containers immersed in a further medium-filled container E supported in a space enclosed by a medium F, all of which was presumably designed to ensure a constant temperature environment. The key feature is C and C’ which are iron-constantan thermocouples, embedded in the brass cavities, with their associated circuitry.

The current produced by the Seebeck effect resulting from the temperature difference between C and C’ was measured by a galvanometer. The radium ampoule was then replaced by an ampoule containing a platinum filament through which was passed a current whose heating effect was sufficient to obtain the same temperature difference. The equivalent rate of heat production by the radium ampoule could then be calulated using Joule’s law.

The second method used was a Bunsen calorimeter, which was known to be capable of very exact measurements using only a small quantity of the test substance. For details of the operational principleof this calorimeter, the reader is referred to this link:

The above diagram of the Bunsen calorimeter is taken from Mme Curie’s Traité de Radioactivité (1910), Tome II, p273.


For most of their experiments, Curie and Laborde used 1 gram of a radium-enriched barium chloride preparation, which liberated approximately 14 calories (59 joules) of heat per hour. It was estimated from radioactivity measurements – no doubt using the quartz electrometer instrumentation invented by Curie – that the gram of test substance contained about one sixth of a gram of radium.

Measurements were also made on a 0.08 gram sample of pure radium chloride. These yielded results of the same order of magnitude without being absolutely in agreement. Curie and Laborde made it clear in their note that these were pathfinding experiments and that their aim was solely to demonstrate the fact of continuous, spontaneous emission of heat by radium and to give an approximate magnitude for the phenomenon. They stated:

» 1 g of radium emits a quantity of heat of approximately 100 calories (420 joules) per hour.

In other words, a gram of radium emitted enough heat in an hour to raise the temperature of an equal weight of water from freezing point to boiling point. And it was continuous emission, hour after hour for year after year, without any detectable change in the source material.

Curie and Laborde had quantified the capacity of radium to generate heat on a scale which was far beyond that known for any chemical reaction. And this heat was continuously produced at a constant rate, unaffected by temperature, pressure, light, magnetism, electricity or any other agency under human control.

The scientific world was astonished. This phenomenon seemed to defy the laws of thermodynamics and the question was immediately raised: Where was all this energy coming from?

Speculation and insight

In 1903, little was known about the radiation emitted by radioactive substances and even less about the atoms emitting them. The air-ionizing emissions had been grouped into three categories according to their penetrating abililities and deflection by a magnetic field, but the nature of the atom – with its nucleus and orbiting electrons – was a mystery yet to be unveiled.

Illustration from Marie Curie’s 1903 doctoral thesis of the deflection of rays by a magnetic field. Note the variable velocities shown for the β particle, whose charge-mass ratio Becquerel had demonstrated to be identical to that of the electron.

Radioactivity had been discovered by Henri Becquerel as an accidental by-product of his main area of interest, optical luminescence – which is the emission of light of certain wavelengths following the absorption of light of other wavelengths. By association luminescence was seen as a possible explanation of radioactivity, that radioactive substances might be absorbing invisible cosmic energy and re-emitting it as ionizing radiation. But no progress was made on identifying a cosmic source.

Meanwhile, from her detailed analytical work that she began in 1898, Marie Curie had discovered that uranium’s radioactivity was independent of its physical state or its chemical combinations. She reasoned that radioactivity must be an atomic property. This was a crucial insight, which directed thinking towards the idea of conversion of mass into energy as an explanation of the continuous and prodigious production of heat by radium that Pierre Curie and Albert Laborde had observed.

One of the major theories in physics at this time was electromagnetic theory. Maxwell’s equations predicted that mass and energy should be mathematically related to each other, and it was by following this line of thought that Frederick Soddy, previously Ernest Rutherford’s collaborator in Canada, came to the conclusion that radium’s energy was obtained at the expense of its mass.

Writing in the very first Annual Report on the Progress of Chemistry, published by the Royal Society of Chemistry in 1904, Soddy said this:

” … the products of the disintegration of radium must possess a total mass less than that originally possessed by the radium, and a part of the energy evolved must be considered as being derived from the change of a part of the mass into energy.”

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A different starting point

While Pierre Curie and Albert Laborde were conducting their radium experiment in Rue Cuvier, Paris, Albert Einstein – a naturalized Swiss citizen who had recently completed his technical high school studies in Zurich – was working as a clerk at the Patent Office in Bern. Much of his work related to questions about signal transmission and time synchronization, and this may have influenced his own thoughts, since both of these issues feature prominently in the conceptual thinking that led Einstein to his theory of special relativity submitted in a paper entitled Zur Elektrodynamik bewegter Körper (On the electrodynamics of moving bodies) to Annalen der Physik on Friday 30th June 1905.

On the basis of electromagnetic theory, supplemented by the principle of relativity (in the restricted sense) and the principle of the constancy of the velocity of light contained in Maxwell’s equations, Einstein proves Doppler’s principle by demonstrating the following:

Ist ein Beobachter relativ zu einer unendlich fernen Lichtquelle von der Frequenz ν mit der Geschwindigkeit v derart bewegt, daß die Verbindungslinie “Lichtquelle-Beobachter” mit der auf ein relativ zur Lichtquelle ruhendes Koordinatensystem bezogenen Geschwindigkeit des Beobachters den Winkel φ bildet, so ist die von dem Beobachter wahrgenommene Frequenz ν’ des Lichtes durch die Gleichung gegeben:

If an observer is moving with velocity v relatively to an infinitely distant light source of frequency ν, in such a way that the connecting “source-observer” line makes the angle φ with the velocity of the observer referred to a system of co-ordinates which is at rest relatively to the source of light, the frequency ν’ of the light perceived by the observer is given by:

where Einstein uses V (not c) to represent the velocity of light. He then finds that both the frequency and energy (E) of a light packet (cf. E=hν) vary with the velocity of the observer in accordance with the same law:

It was to this equation Einstein returned in a paper entitled Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? (Does the inertia of a Body depend on its Energy Content?) submitted to Annalen der Physik on Wednesday 27th September 1905.

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Mass-energy equivalence

Marie Curie and Albert Einstein, Geneva, Switzerland, 1925

Einstein’s paper of September 1905 – the last of the famous set published in Annalen der Physik in that memorable year – is less than three pages long and constitutes little more than a footnote to the preceding 30-page relativity paper. Yet despite its brevity, it is a difficult and troublesome work over which Einstein brooded for some years.

The paper describes a thought experiment in which a body sends out a light packet in one direction, and simultaneously another light packet of equal energy in the opposite direction. The energy of the body before and after the light emission is determined in relation to two systems of co-ordinates, one at rest relative to the body (where the before-and-after energies are E0 and E1) and one in uniform parallel translation at velocity v (where the before-and-after energies are H0 and H1).

Einstein applies the law of conservation of energy, the principle of relativity and the above-mentioned energy equation to arrive at the following result for the rest frame and the frame in motion relative to the body, the light energy being represented by a capital L:

At this point, things start getting a little tricky. Einstein subtracts the rest frame energies from the moving frame energies for both the before-emission and after-emission cases, and then subtracts these differences:

These differences represent the before-emission kinetic energy (K0) and after-emission kinetic energy (K1) with respect to the moving frame

Since the right hand side is a positive quantity, the kinetic energy of the body diminishes as a result of the emission of light, even though its velocity v remains constant. To elucidate, Einstein performs a binomial expansion on the first term in the braces, although he makes no mention of the procedure; nor does he show the math. So this next bit is my own contribution:

Let (v/V)2 = x

The appropriate form of the binomial expansion is

Setting x = v2/V2 and n = ½

The contents of the braces in the kinetic energy expression thus become

Now back to Einstein. At this point he introduces a new condition into the scheme of things, namely that the velocity v of the system of co-ordinates moving with respect to the body is much less than the velocity of light V. We are in the classical world of v<<V, and so Einstein allows himself to neglect magnitudes of fourth and higher orders in the above expansion. Hence he arrives at

This equation gives the amount of kinetic energy lost by the body after emitting a quantity L of light energy. In the classical world of v<<V the kinetic energy of the body is also given by ½mv2, and since the velocity v is the same before and after the light emission, Einstein is led to identify the loss of kinetic energy in his thought experiment with a loss of mass:

Gibt ein Körper die Energie L in Form von Strahlung ab, so verkleinert sich seine Masse um L/V2. Hierbei ist es offenbar unwesentlich, daß die dem Körper entzogene Energie gerade in Energie der Strahlung übergeht, so daß wir zu der allgemeineren Folgerung geführt werden: Die Masse eines Körpers ist ein Maß für dessen Energie-inhalt.

If a body gives off the energy L in the form of radiation, its mass diminishes by L/V2. The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that: The mass of a body is a measure of its energy content.

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Testing the theory

The pavilion where Curie and Laborde did their famous work

When Einstein wrote Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? in 1905, he was certainly aware of the phenomenon of continuous heat emission by radium salts as measured by Curie and Laborde, and confirmed by several others in 1903 and 1904. In fact he saw in this a possible means of putting relativity theory to the test:

Es ist nicht ausgeschlossen, daß bie Körpern, deren Energieinhalt in hohem Maße veränderlich ist (z. B. bei den Radiumsaltzen) eine Prüfung der Theorie gelingen wird.

It is not impossible that with bodies whose energy content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test.

In hindsight, it was unlikely that Einstein could have made this test work and he soon abandoned the idea. Not only would the mass difference have been extremely small, but also the process of nuclear decay was conceptually different to Einstein’s thought experiment. In Curie and Laborde’s calorimeter, the energy emitted by the body (radium nucleus) was not initially in the form of radiant energy; it was in the form of kinetic energy carried by an ejected alpha particle (helium nucleus) and a recoiling radon nucleus.

But Einstein had a knack of getting ahead of himself and ending up in the right place. The mass-energy equivalence relation he obtained from his imagined light-emitting body turned out to be valid also in relation to the kinetic energy of radioactive decay particles.

To see this in relation to Curie and Laborde’s experiment, consider the nuclear reaction equation

Here Q is the mass difference in atomic mass units (u) required to balance the equation:
Mass of Ra = 226.02536 u
Mass of Rn (222.01753) + He (4.00260) = 226.02013 u
Mass difference = Q = 0.00523 u
The kinetic energy equivalent of 1 u is 931.5 MeV
So Q = 4.87 MeV

The kinetic energy is shared by the ejected alpha particle and recoiling radon nucleus. Since the velocities are non-relativistic, this can be calculated on the basis of the momentum conservation law and the classical expression for kinetic energy. Given the masses of the Rn and He nuclei, their respective velocities must be in the ratio 4.00260 to 222.01753. Writing the kinetic energy expression as ½mv.v and recognizing that ½mv has the same magnitude for both nuclei, the kinetic energies of the Rn and He nuclei must also be in the ratio 4.00260 to 222.01753. The kinetic energy carried by the alpha particle is therefore

4.87 x 222.01753/226.02013 = 4.78 MeV

This result has been confirmed by experiment.

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Links to original papers mentioned in this post

Sur la chaleur dégagée spontanément par les sels de radium ; par MM. P. Curie et A. Laborde
Comptes Rendus, Tome 136, janvier – juin 1903

Zur Elektrodynamik bewegter Körper; von A. Einstein
Annalen der Physik 17 (1905) 891-921

Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? von A. Einstein
Annalen der Physik 18 (1905) 639-641

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In Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? Einstein arrived at a general statement on the dependence of inertia on energy (Δm = ΔE/V2, in today’s language E = mc2) from the consideration of a special case. He was deeply uncertain about this result, and returned to it in two further papers in 1906 and 1907, concluding that a general solution was not possible at that time. He had to wait a few years to discover he was right. I include links to these papers for the sake of completeness.

Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie; von A. Einstein
Annalen der Physik 20 (1906) 627-633

Über die vom Relativitätsprinzip geforderte Trägheit der Energie; von A. Einstein
Annalen der Physik 23 (1907) 371-384

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P Mander June 2017


Reversible change is a key concept in classical thermodynamics. It is important to understand what is meant by the term as it is closely allied to other important concepts such as equilibrium and entropy. But reversible change is not an easy idea to grasp – it helps to be able to visualize it.

Reversibility and mechanical systems

The simple mechanical system pictured above provides a useful starting point. The aim of the experiment is to see how much weight can be lifted by the fixed weight M1. Experience tells us that if a small weight M2 is attached – as shown on the left – then M1 will fall fast while M2 is pulled upwards at the same speed.

Experience also tells us that as the weight of M2 is increased, the lifting speed will decrease until a limit is reached when the weight difference between M2 and M1 becomes vanishingly small and the pulley moves infinitely slowly, as shown on the right.

We now ask the question – Under what circumstances does M1 do the maximum lifting work? Clearly the answer is visualized on the right, where the lifted weight M2 is as close as we can imagine to the weight of M1. In this situation the pulley moves infinitely slowly (like a nanometer in a zillion years!) and is indistinguishable from being at rest.

This state of being as close to equilibrium as we can possibly imagine is the condition of reversible change, where the infinitely slow lifting motion could be reversed by an infinitely small nudge in the opposite direction.

From this simple mechanical experiment we can draw an important conclusion: the work done under reversible conditions is the maximum work that the system can do.

Any other conditions i.e. when the pulley moves with finite, observable speed, are irreversible and the work done is less than the maximum work.

The irreversibility is explained by the fact that observable change inevitably involves some dissipation of energy, making it impossible to reverse the change and exactly restore the initial state of the system and surroundings.

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Reversibility and thermodynamic systems

The work-producing system so far considered has been purely mechanical – a pulley and weights. Thermodynamic systems produce work through different means such as temperature and pressure differences, but however the work is produced, the work done under reversible conditions is always the maximum work that a system can do.

In thermodynamic systems, heat q and work w are connected by the first law relationship

What this equation tells us is that for a given change in internal energy (ΔU), both the heat absorbed and the work done in a reversible change are the maximum possible. The corresponding irreversible process absorbs less heat and does less work.

It helps to think of this in simple numbers. U is a state function and therefore ΔU is a fixed amount regardless of the way the change is carried out. Say ΔU = 2 units and the reversible work w = 4 units. The heat q absorbed in this reversible change is therefore 6 units. These must be the maximum values of w and q, because ΔU is fixed at 2; for any other change than reversible change, w is less than 4 and so q is less than 6.

For an infinitesimal change, the inequality in relation to q can be written

and so for a change at temperature T

The term on the left defines the change in the state function entropy

Since reversible conditions equate to equilibrium and irreversible conditions equate to observable change, it follows that

These criteria are fundamental. They are true for all thermodynamic processes, subject only to the restriction that the system is a closed one i.e. there is no mass transfer between system and surroundings. It is from these expressions that the conclusion can be drawn – as famously stated by Clausius – that entropy increases towards a maximum in isolated systems.

Rudolf Clausius (1822-1888)

Rudolf Clausius (1822-1888)

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Die Entropie der Welt strebt einem Maximum zu

Consider an adiabatic change in a closed system: dq = 0 so the above criteria for equilibrium and observable change become dS = 0 and dS > 0 respectively. If the volume is also kept constant during the change, it follows from the first law that dU = 0. In other words the volume and internal energy of the system are constant and so the system is isolated, with no energy or mass transfer between system and surroundings.

Under these circumstances the direction of observable change is such that entropy increases towards a maximum; when there is equilibrium, the entropy is constant. The criteria for these conditions may be expressed as follows

The assertion that entropy increases towards a maximum is true only under the restricted conditions of constant U and V. Such statements as “the entropy of the universe tends to a maximum” therefore depend on assumptions, such as a non-expanding universe, that are not known to be fulfilled.

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P Mander March 2015


St. Peter’s Parish Church, Bradford

The year is 1845. The location is the vicarage of St. Peter’s Parish Church, Bradford in Northern England. Inside the vicarage two men, one a 55 year-old retired sea captain and the other a 26 year-old brewery manager, have been conducting a series of experiments using a powerful magneto-electric apparatus. The results that they would publish the following year in Philosophical Magazine would prove beyond doubt that the electric motor was not the perpetual motion miracle that many believed, and put an end to the ‘electrical euphoria’ that had swept through Europe and the United States for a decade.

The retired sea captain, now the vicar of the parish and the owner of the massive magneto, was William Scoresby Jnr, a renowned Arctic explorer and an authority on whale fishery and compass navigation.

The young brewery manager, who had already published a number of scientific articles in the Annals of Electricity and who represented the ‘brains’ behind the experiments at the vicarage, was James Joule.

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It was Michael Faraday’s discovery of electromagnetic induction in 1831 that started it all. The magneto was invented that same year, and with the additional invention of the commutator by William Sturgeon and others, the electric motor became a reality in 1832. Inventors in Europe and America , sensing its possibilities, flocked to develop it.

William Sturgeon 1783-1850, inventor of the electromagnet and commutator

William Sturgeon 1783-1850, inventor of the electromagnet and commutator

In 1835, the euphoria began in earnest when Professor Moritz von Jacobi, a German professor of engineering at the Imperial University of Dorpat in Russia, published a paper on the physics of the electric motor in which he pointed out that if frictional forces and the counter-electromotive force (back emf) could be reduced to small proportions by ingenious design, a near-infinite velocity of rotation could be achieved and with it, virtually limitless power.

Moritz von Jacobi 1801-1874, whose 1835 paper triggered electrical euphoria

Moritz von Jacobi 1801-1874, whose 1835 paper triggered electrical euphoria

Jacobi’s paper was translated into English and appeared in 1836 in the Annals of Electricity, a British journal newly founded and edited by William Sturgeon, who besides independently inventing the commutator had also invented the electromagnet (in 1824). Among those who read Jacobi’s paper in the Annals was James Joule, an 18 year old lad from Manchester who had a fascination with magnetism and electricity.

Born into a wealthy family whose business was beer brewing, young James had plenty of free time to follow his favourite pursuit – electrical experiments. In Jacobi’s paper he saw the opportunity to turn his practical skills and ingenuity to good effect by designing and building an electric motor that would realise the promise of unbounded power. He worked for three solid years on this task, and got absolutely nowhere. But it was not a total waste of time, because along the way the teenager from Manchester made a significant discovery.

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The 1830s were important years for the emerging science of electricity. The magneto, the electric motor and the tangent galvanometer were all invented in this decade. And in 1834, the man who influenced the direction of scientific enquiry in Britain more than any other – Michael Faraday – discovered the laws of electrolysis. Unusually for Faraday, whose genius otherwise expressed itself in conceptual, qualitative relationships between things, his laws of electrolysis were quantitatively exact.

The effect of this on Joule cannot be understated. Although he had no training and little interest in mathematics, the young experimenter from Manchester was a natural hunter for numerical relationships between measurable quantities. With Faraday’s quantitative discoveries to spur him on, and with a home laboratory full of accurate (and expensive) devices for measuring temperature and electric current, Joule was well-equipped for discovery. And it was not long in coming.

In December 1840, at the age of 21, Joule sent to the Royal Society a paper entitled “On the production of heat by Voltaic electricity”. In it, he stated that the heat generated by the passage of an electric current through a wire is proportional to the square of the current and the resistance of the wire. He further claimed that the law held irrespective of the shape, size or form of the circuit or the type of wire used. In other words, he was enunciating a general law. The Royal Society rejected the paper for the prestigious Transactions, but allowed a short abstract of it to appear in the more lowly Proceedings for that month. What we now know as Joule’s first law (ohmic heating) made a modest entry into this world.

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William Scoresby (1789-1857), owner of the great magneto-electric machine

William Scoresby (1789-1857), owner of the great magneto-electric machine

James Joule first met Captain the Reverend William Scoresby at a scientific meeting in Manchester in 1842. Scoresby was a colourful character by all accounts; having attended Edinburgh University he decided to follow his father’s calling and go to sea, becoming the master of a whaling ship in true pre-mechanised, Moby Dick fashion. Following the death of his wife, Scoresby gave up the sea to take Holy Orders and was now installed as the Vicar of Bradford.

Unlike most whalers of his era, he had the benefit of a scientific education, and his time at sea had given him a strong interest in terrestrial magnetism and its application in compass navigation. It was a common interest in magnetism that brought Scoresby and Joule together, and it was at this meeting that Joule learned of Scoresby’s ‘great magneto-electric machine’ now housed in the vicarage at Bradford. It was a mighty machine with enormous magnets, capable of producing a hefty current. Joule now had an acquaintance who owned the mother of all magnetos.

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Joule’s discovery of ohmic heating during his futile attempts to build an ingeniously designed electric motor introduced the first seeds of doubt in his mind about the validity of Professor Jacobi’s bold assertion. The unavoidable heating of the circuit during power production clearly implied a waste of zinc in the Daniell cell which Joule had used a source of voltaic electricity. And since zinc cost 60-70 times the same weight of coal, things didn’t look quite so promising, at least from an economic perspective.

From a purely scientific perspective the heating effect also set Joule wondering, like Count Rumford before him: Where does the heat come from? If heat were a substance, as the scientific establishment insisted it was, the heating effect could only be explained by transference, i.e. the magneto acting as a heat pump to move heat from the armature to the outside circuit and being necessarily cooled in the process. This was something that could be ascertained by careful experiment, and Joule appointed himself to the task.

The summer of 1842 was a hectic time for Joule. Besides visiting Scoresby in Bradford to experiment with the massive magneto in the vicarage, he was also slaving away at home in Manchester on those careful experiments which would eventually bring him to prominence as a great man of science. But years of struggle lay ahead of him before he achieved that goal.

Suffice to say that in his 1843 paper “On the calorific effects of magneto-electricity and on the mechanical value of heat”, read before the British Association for the advancement of science, Joule demonstrated that heat was not a substance; it was generated by the chemical action of the battery when the magneto-electric machine was operated as a motor, and by mechanical work when operated as a magneto. And he went on to propound the thesis that not only were work and heat interconvertible, but that a precise numerical relationship existed between them – what he called the mechanical value of heat.

In 1843, no-one listened. The scientific establishment dismissed Joule’s youthful paper – he was only 24 – as the work of a misguided and uneducated amateur.

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While the British Association was busy ignoring Joule, Joule was busy thinking about zinc, the anode metal that was consumed in the Daniell cell which he had used in his experiments. The idea was forming in Joule’s mind that the work obtained from an electric motor must arise from the conversion of heat due to the chemical reaction by which zinc was consumed in the cell. Since a precise numerical relation existed between work and heat, there must be a limit to the work obtainable from the consumption of a given amount of zinc. In Joule’s mind, Professor Jacobi’s golden vision of the electric motor as a limitless source of power was fading fast.

Joule followed up on his new thinking with a truly inspired idea. He reasoned that since the heat released from the complete combustion of zinc in a calorimeter must represent the maximum heat attainable, he could calculate – by means of the mechanical equivalent – the maximum work attainable from the consumption of a given amount of zinc by any means whatsoever. Using this yardstick, he could rate the performance of any design of electric motor.

Joule wasted no time in doing the calorimetry and determining the maximum work using his best estimate of the mechanical equivalent of heat. He was now ready to test his idea on an actual magneto-electric machine, the biggest one he knew of, which sat in the home of Captain the Reverend William Scoresby.

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I mentioned at the start of this post that Joule represented the ‘brains’ behind the experiments conducted at the vicarage of St. Peter’s Church Bradford in 1845. Without any disrespect to Scoresby’s undoubted competences as a scientific thinker and writer, the work that was accomplished here and published under their joint names the following year was very much a synthesis of all that Joule had learned from his own efforts. Indeed, Joule notes in the introduction to their paper that he wrote it almost entirely himself.

Joule used three Daniell cells to power Scoresby ‘s machine as an electric motor, and his purpose in conducting the experiment was to determine the quantity of heat (arising from the consumption of zinc) that was converted into useful work. His method was simple, but brilliantly conceived.

Joule first connected the battery to the motor at rest (i.e. with the rotor prevented from turning), and with a carefully calibrated tangent galvanometer measured the standing current (a). He then allowed the rotor to turn, and when the motor was running steadily, he measured the driving current (b). Joule knew from his own discovery that ohmic heating would be generated by the current in the circuit, and from Faraday’s law that the measured current was in direct proportion to the quantity of zinc consumed in the battery. The difference of the currents, a – b, “will therefore represent the quantity of heat converted by the engine into useful mechanical effect” as Joule put it.

It was now a simple matter to compute the mechanical effect of the motor. Joule had already determined by calorimetry that if all the heat from the combustion of a grain of zinc could be converted into work, it would be equal to raising 158 pounds through a distance of 1 foot.
Since (a – b) represented the heat actually available for conversion, and (a) the amount theoretically available, the work obtainable from the motor per grain of zinc was:

W = 158 x (a – b)/a.

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It was this formula, and the generalisation it implied, that provided the final refutation of Professor Jacobi’s heady suggestion of infinite power and put an end to electrical euphoria. For it showed that the work obtainable from a source of electrical power is finite, and limited by the heat (=energy) in the fuel.

Furthermore, it showed that the maximum amount of work can only be achieved when (b) becomes vanishingly small. But since (b) is the driving current, the power will then also tend to zero, and it would take an infinitely long time to accomplish the work (students of classical thermodynamics will no doubt detect a familiar principle here).

Besides electric motors, Joule and Scoresby also discussed the fuel economy of steam engines and horses in their paper, and came to a firm conclusion on which of them was the most efficient. But for now we must leave them, sipping their brandy by the fireside and contemplating what they had discovered.

For Joule, it would be a further two years before anyone paid any attention at all to the fact that he had discovered an important electrical heating law, laid the foundations for the first law of thermodynamics, revealed the limits imposed on power production by the second law, and saved gullible investors from wasting their life savings on electrical dream machines.

But he was only 26 years old. He had time on his side.

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8 years later…

William John Macquorn Rankine (1820-1872)

William John Macquorn Rankine (1820-1872)

One day in 1853, a letter arrived for the now famous James Joule. It was from William Rankine, a Scottish engineer and physicist, who was at the time playing a central role in laying the theoretical foundations of thermodynamics.

In the letter, Rankine drew attention to the fact that the efficiency of an electric motor, given by the fraction (a – b)/a in the Joule-Scoresby formula


was exactly analagous to the thermodynamic expression for the efficiency of a heat engine

(q1 – q2)/q1

where q1 is the heat received, q2 is the heat rejected, and the difference between them is the heat converted into useful work. This expression had been deduced from complex theoretical considerations by Rankine, Rudolf Clausius and William Thomson, all skilled mathematical physicists.

It is a testament to Joule’s abilities as an experimental physicist that, without the benefit of his contemporaries’  mathematical training, he nonetheless found his way to the same mathematical truth.

An engraving from the earliest known portrait of James Joule, painted 18 years after the experiments with William Scoresby in Bradford

An engraving from the earliest known portrait of James Joule, painted 18 years after the experiments with William Scoresby in Bradford

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Links to the original scientific papers cited in this post

Professor Jacobi’s paper, published in the Annals of Electricty in 1836:

James Joule’s first published work, a letter to the Annals of Electricity written in 1838 at the age of 19:

An abstract of Joule’s rejected 1840 paper “On the production of heat by Voltaic electricity”, in which he states the law of ohmic heating:

Joule’s 1843 paper “On the calorific effects of magneto-electricity and on the mechanical value of heat”, ignored by science until William Thomson (later Lord Kelvin) suddenly seized on its significance in 1847:

Joule & Scoresby’s joint paper, published in Philosophical Magazine in 1846:

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photo credits

Moritz von Jacobi / wikipedia
William Sturgeon /
William Scoresby /
William Rankine / Wikipedia

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P Mander October 2013