James Prescott Joule

How to use this course

James Prescott Joule held no university post and earned his living from a brewery. Between 1840 and 1850 he showed that an electric current heats a wire in proportion to the square of the current, that the heat produced by mechanical work is always in the same ratio to the work, and that this ratio is the same whether the work is done by electricity, by compressing a gas or by stirring water. His number, about 772 foot-pounds of work for each pound of water warmed one degree Fahrenheit, is within one percent of the modern value. The SI unit of energy carries his name.

Each technical lesson opens with a paragraph for the general reader, then gives statements, derivations and exercises with folded solutions. Several exercises use Joule’s own numbers, in his units. Converting them is part of the training: it shows how small the effects were and how carefully he had to work. The physics lessons follow his work in order: electrical heating (1840–41), motors and magnets (1838–1847), the equivalent of heat (1843–1850), kinetic theory (1851) and the experiments with William Thomson (from 1852).

Timeline

Salford and Dalton, 1818–1837

James Prescott Joule was born on 24 December 1818 in New Bailey Street, Salford, across the river Irwell from Manchester. His father, Benjamin Joule, owned a prosperous brewery; his mother was Alice Prescott. The family had money, and the boys were educated at home.

Manchester in the 1830s was the first industrial city in the world. Steam engines drove its mills, and engineers there cared about one number above all: the work an engine delivered for a given amount of coal, called its duty. Joule grew up among people who measured efficiency for a living, and his science kept that habit.

Lessons with Dalton

Around 1834, when James was fifteen, he and his elder brother Benjamin were sent for lessons to John Dalton, the founder of the chemical atomic theory, who taught private pupils at the rooms of the Manchester Literary and Philosophical Society. Dalton taught them arithmetic and geometry. The lessons lasted about two years, until Dalton’s health failed after a stroke. Dalton gave him an example: careful quantitative measurement, done privately, with home-made apparatus, could change a science.

Joule continued with other tutors, including the chemist John Davis. He began experimenting at home, in rooms of the family house fitted as a laboratory, and joined his father in managing the brewery.

Electricity in the brewery, 1838–1842

In the late 1830s the electric motor looked like the coming rival of the steam engine. Moritz Jacobi had driven a boat on the Neva with an electromagnetic engine, and William Sturgeon, who had built the first practical electromagnet, ran a journal, the Annals of Electricity, full of designs for such engines. Joule’s first papers, from 1838, appeared there. He wanted to know whether electric motors could replace the steam engines in the brewery.

Sturgeon moved to Manchester in 1840, and Joule joined the circle of scientific men around him. Joule’s approach to the motor was an engineer’s. He measured the work each engine did against the zinc it consumed in the battery. The answer was discouraging. Zinc cost far more than coal, and an engine fed by a battery could not compete with steam (Lesson 05). But the investigation raised a deeper question. If the battery’s chemical action can produce either heat in the wires or work at the motor, what is the exchange rate between them?

The heating law

To answer it Joule first had to know how much heat a current produces. In 1840 he communicated to the Royal Society a paper On the Production of Heat by Voltaic Electricity, which stated that the heat produced in a wire in a given time is proportional to its resistance and to the square of the current. The Society printed only an abstract. The full paper, On the Heat evolved by Metallic Conductors of Electricity, and in the Cells of a Battery during Electrolysis, appeared in the Philosophical Magazine in 1841. Lesson 04 treats it. To make it, Joule had to build his own galvanometers and fix a reproducible unit of current, since none existed.

Against the caloric, 1843–1847

Most physicists of 1840 held that heat is a weightless fluid, caloric, which can move from body to body but is neither created nor destroyed. Sadi Carnot’s theory of the steam engine rested on it. Joule’s electrical work convinced him that heat could be generated. In August 1843, at the British Association meeting in Cork, he read a paper On the Calorific Effects of Magneto-Electricity, and on the Mechanical Value of Heat. He had turned a small generator by falling weights and measured the heat produced in its coil. A pound of water warmed by one degree Fahrenheit, he concluded, needed the work of 838 pounds falling one foot. A postscript added a second result, from forcing water through narrow tubes: 770 foot-pounds. The audience responded with silence.

He tried again with gases. Compressing air in a vessel under water warmed the water; letting it expand cooled it. The Royal Society declined his paper, which appeared in the Philosophical Magazine in 1845. In June 1845, at the British Association meeting in Cambridge, he described a new method: a brass paddle wheel, driven by falling weights, stirring water in a can. Its first value was 890 foot-pounds. In a letter to the Philosophical Magazine he averaged his methods to 817, and suggested that water at the foot of Niagara should be about a fifth of a degree warmer than at the top.

Oxford, 1847

In June 1847 the British Association met in Oxford. Joule presented his paddle-wheel results. In the discussion a young Glasgow professor, William Thomson, later Lord Kelvin, raised objections. Thomson believed in Carnot’s theory and could not accept that heat is consumed when work is done. He was also struck by the experiments, and the two men began a long friendship (Lesson 11). George Gabriel Stokes and Michael Faraday were also present.

That spring Joule had set out his views for a lay audience in Manchester, in a lecture On Matter, Living Force, and Heat, printed in a local newspaper. Living force (vis viva) cannot be destroyed, he argued. When it seems to vanish, as when a moving body stops, it reappears as heat.

On 18 August 1847 he married Amelia Grimes. On the honeymoon in the Alps he met Thomson again near Chamonix. The two planned to measure the warming of water at the Cascade de Sallanches. The measurement proved impractical.

The heating law of currents

For the general reader. A wire carrying a current gets warm. Joule found the rule: double the current and the heat goes up four times; double the resistance at the same current and the heat doubles. The rule governs toasters, fuses and the power lost in transmission lines. It also told him that the heat comes from the chemical work of the battery, not from some fluid carried along the wire.

Derivation

When a charge \(dq\) moves through a potential difference \(V\), the field does work \(V\,dq\) on it. In a resistor the carriers do not speed up on average: they collide with the lattice and pass the work on as disordered motion, that is, heat. In time \(dt\) the charge \(I\,dt\) passes, so the heat is \(VI\,dt\). Ohm’s law \(V=IR\) gives \(P=I^2R\). Locally, the force on the carriers in a volume element is \(\rho_q\mathbf E\), and its power is \(\rho_q\mathbf v\cdot\mathbf E=\mathbf J\cdot\mathbf E\).

Joule did not have the potential concept in this form, nor a standard unit of resistance. He wound wires of different lengths and metals, placed each in a glass jar of water, passed currents measured by a tangent galvanometer, and timed the temperature rise. He measured resistance by comparison with a standard wire. The square law came out of the data.

The whole circuit

Joule went further. He measured the heat produced inside the battery cells and in electrolytic cells as well as in the wires, and found that the total heat in the circuit, per unit of zinc consumed, is fixed. It equals the heat that the same chemical reaction would give if carried out directly, without the current. In modern terms, a cell of electromotive force \(\mathcal E\) delivering charge \(q\) does work \(\mathcal E q\), and all of it appears as heat when the current does nothing else. If an electrolytic cell in the circuit decomposes water, the heat is reduced by the chemical energy stored. The current is a carrier of energy from the zinc to the wire, a view Joule held by 1841.

Engines, batteries and magnets

For the general reader. Joule began as an inventor of electric motors. He found that when a motor does work, the battery’s current drops and the wires warm less: the work is paid for out of heat that would otherwise have appeared. He also found that iron grows very slightly longer when it is magnetized. Both results came from measuring an engine as an engineer would.

The motor’s energy balance

A battery of electromotive force \(\mathcal E\) drives a motor through a total resistance \(R\). A turning motor generates a back electromotive force \(\varepsilon\), proportional to its speed. The current is \(I=(\mathcal E-\varepsilon)/R\). Multiply \(\mathcal E=IR+\varepsilon\) by \(I\):

The battery’s power splits into Joule heat and mechanical power \(\varepsilon I\). A stalled motor has \(\varepsilon=0\), maximum current, and turns everything into heat. As the motor speeds up, the current and the heat fall. This is what Joule observed: the heat in a circuit is reduced when the motor does work, in proportion to the work.

Higher efficiency requires the motor to run faster, close to \(\varepsilon=\mathcal E\), where it delivers little power. No adjustment of the motor can extract more from the battery than the chemical energy of the zinc consumed.

Zinc against coal

Joule measured the duty of his engines, in work per pound of zinc, and compared it with the duty of the best Cornish steam engines, in work per pound of coal. Zinc gave far less work per pound and cost far more. He concluded that battery motors could not compete with steam, a judgment that held until generators driven by steam replaced batteries as the source of current.

Magnetostriction

In the course of his work on electromagnets Joule discovered that an iron bar lengthens slightly when magnetized along its length, while its volume stays nearly constant. He described the effect in 1847 in the Philosophical Magazine. The fractional change \(\lambda=\Delta\ell/\ell\) is of order \(10^{-6}\) to \(10^{-5}\) in iron at saturation. The effect is the source of the hum of transformers: in an alternating field the core changes length twice per cycle.

The mechanical value of heat, 1843–1845

For the general reader. If heat is a substance, work cannot create it. Joule set out to show that work does create heat, always at the same rate of exchange. He used a generator, water forced through tubes, and air squeezed in a pump. Each method gave roughly the same number, and the agreement was the evidence.

The magneto-electric experiment

A coil wound on an iron core rotated between the poles of an electromagnet, inside a tube of water. Joule measured the heat produced in the coil by the induced current, with the circuit closed through a galvanometer. The key point was that the induced current carried no heat from anywhere: the coil was the only place it could come from, and the only input was the mechanical work of turning. Running the machine with and without a battery in the circuit, and in both directions, he showed that a current induced by motion heats exactly as a battery current does. Turning the coil by falling weights, he related the heat to the work: 838 foot-pounds per pound of water per degree Fahrenheit.

Compression and expansion of air

In 1844 and 1845 Joule pumped air into a strong copper vessel immersed in water, measured the work of the pump and the heat given to the water, and then did the reverse, letting compressed air escape and measuring the cooling. For an ideal gas compressed slowly at temperature \(T\) from volume \(V_1\) to \(V_2\), the work done on the gas is

If heat is a form of work, this work must appear as heat \(Q=W/J\) in the water. His results were close to 800 foot-pounds; the rarefaction experiments gave 795.

Free expansion

The decisive experiment of 1845 used two equal copper vessels joined by a stopcock, one filled with air at about 22 atmospheres, the other evacuated, both in one water bath. On opening the stopcock the air rushed into the empty vessel. The bath showed no measurable change of temperature. The expanding air did no external work, and it neither gained nor lost heat. When the vessels were placed in separate baths, the one losing gas cooled and the one gaining gas warmed, by equal amounts. On the caloric view the expansion of a gas ought to absorb heat in its own right. Joule concluded that a gas absorbs heat on expansion only to the extent that it does external work.

The paddle wheel, 1845–1850

For the general reader. The most famous experiment in the history of energy is also one of the simplest. Weights fall and turn a paddle wheel in a can of water; the water gets warmer. The difficulty is that the warming is about half a degree Fahrenheit. Joule built thermometers he could read to a two-hundredth of a degree, accounted for every loss, and obtained a number within one percent of today’s.

The apparatus

In the final form described in the 1850 paper, a brass paddle wheel with eight sets of revolving arms turned between four sets of fixed vanes inside a copper vessel of water. The vanes stopped the water from rotating as a whole, so the work went into turbulent friction. Two lead weights of about 29 pounds each hung from cords wound on a wooden drum on the paddle axle. They fell about 63 inches, slowly, at roughly 2.4 inches per second. The drum was then disconnected, the weights wound up, and the fall repeated, twenty times per experiment, taking about 35 minutes. Each run of the apparatus was paired with a run without stirring to measure heat exchange with the room.

Reduction of the data

The work done on the water in one experiment is

where \(n\) is the number of falls, \(M\) the total falling mass, \(h\) the height, \(v\) the landing speed and \(W_{\rm f}\) the work lost to friction in the pulleys and the stiffness of the cords, which Joule measured separately. The heat is

with \(C_{\rm app}\) the heat capacity of the vessel and paddles, measured by Joule, and \(\delta T_{\rm rad}\) the correction from the paired run. Then \(J=W/Q\). Joule also corrected for the buoyancy of the air on the weights, giving values “in vacuo”.

He repeated the experiment with mercury and with cast-iron discs rubbing in mercury, getting values between about 772 and 776. He judged the water result, 772.692, the most reliable, and thought even that slightly high because some work went into vibration and sound.

The speed of gas molecules

For the general reader. If heat is motion, the pressure of a gas could be the drumming of its particles on the walls. Joule took this idea from John Herapath and computed, from the pressure and density of hydrogen, how fast its particles must move. The answer, over six thousand feet per second, was the first numerical estimate of a molecular speed.

Pressure from impacts

Joule’s paper Some Remarks on Heat and the Constitution of Elastic Fluids, published in 1851, imagined a cube of gas whose particles move in three groups, one along each axis. A particle of mass \(m\) moving along \(x\) with speed \(v\) between walls a distance \(L\) apart strikes one wall every \(2L/v\) seconds, delivering momentum \(2mv\) each time. The force on the wall is \(mv^2/L\). With \(N\) particles, one third along each axis, the pressure on a wall of area \(L^2\) is

Joule took a cubic foot of hydrogen at 60 °F and 30 inches of mercury and found a speed of 6225 feet per second. At the freezing point he obtained 6055. Since \(p\propto\rho v^2\) and, for a fixed density, \(p\) is proportional to the absolute temperature, \(v^2\) must vanish at the absolute zero. From the expansion of gases he placed it 491 °F below the freezing point of water, that is, at \(-459\) °F.

The Joule–Thomson effect

For the general reader. Joule’s free-expansion test was too crude to detect small forces between gas molecules. With William Thomson he designed a better one: push gas steadily through a plug of cotton or silk from high pressure to low, and measure its temperature on both sides. Most gases come out slightly cooler. The effect, repeated in stages, later made it possible to liquefy air.

Throttling

Gas flows steadily through an insulated porous plug. Follow a fixed amount of gas that occupies volume \(V_1\) at pressure \(p_1\) before the plug and \(V_2\) at \(p_2\) after. The gas behind pushes it in, doing work \(p_1V_1\); it pushes the gas ahead, doing work \(p_2V_2\). No heat flows and the kinetic energy of the slow flow is negligible, so

Derivation. From \(dH=T\,dS+V\,dp\) and \(dS=\frac{C_p}{T}dT-\big(\frac{\partial V}{\partial T}\big)_p dp\) (a Maxwell relation), \(dH=C_p\,dT+\big[V-T\big(\frac{\partial V}{\partial T}\big)_p\big]dp\). Setting \(dH=0\) gives the formula.

Joule and Thomson began the experiments in 1852 and published them in a series of papers On the Thermal Effects of Fluids in Motion. Air and carbon dioxide cooled; hydrogen, at room temperature, warmed very slightly. The measurements also allowed them to compare the gas thermometer with Thomson’s absolute scale of temperature (see the Kelvin module).

Van der Waals estimate

For a dilute van der Waals gas, to first order in \(a\) and \(b\), \(V_m\approx RT/p+b-a/RT\). Then

Below \(T_{\rm inv}\) attraction dominates and the gas cools; above it, the finite size of the molecules dominates and it warms.

From the equivalent to the joule

For the general reader. Joule measured a conversion factor between two units, one for heat and one for work. Once his result was accepted, heat was understood as energy, and the factor could be absorbed into the definition of the units. Today the joule measures all energy, and the calorie survives only as a defined multiple of it.

Joule’s numbers in modern units

One British thermal unit, the heat that warms one pound of water by one degree Fahrenheit, corresponds today to about 778.2 ft·lbf. Joule’s determinations, in foot-pounds per pound-degree Fahrenheit, were:

The agreement among methods mattered more than any single figure. In 1879 the American physicist Henry Rowland repeated the stirring experiment on a larger scale, driving the paddles with an engine, and showed that the specific heat of water varies by a fraction of a percent over the ordinary range of temperatures. A calorie therefore depends on which degree of the thermometer it refers to.

William Siemens proposed the name joule for \(10^7\) erg at the British Association in 1882. The International Electrical Congress adopted it, with the watt, on 31 August 1889, six weeks before Joule’s death. In 1948 the General Conference on Weights and Measures chose the joule as the unit of heat and discouraged use of the calorie.

Recognition and partnership, 1848–1870

Within three years of the Oxford meeting the scientific world had changed its mind. In 1850 the Royal Society published Joule’s paddle-wheel paper in its Philosophical Transactions and elected him a Fellow. In the same year Rudolf Clausius in Berlin, and in 1851 William Thomson in Glasgow, combined Joule’s equivalence of heat and work with Carnot’s principle and founded thermodynamics on two laws. The Royal Society gave Joule a Royal Medal in 1852.

Joule and Thomson

The collaboration with Thomson began in 1852. Joule did the experiments in Manchester; Thomson supplied theory and much of the planning, by letter. Their porous-plug experiments (Lesson 09) were the most lasting result. They also compared the air thermometer with Thomson’s absolute scale and studied the heating of bodies moving rapidly through air. The partnership was one between equals of very different kinds: a private experimenter and a professor of mathematical physics.

Loss and change

Joule and Amelia had three children: Benjamin Arthur (1850–1922), Alice Amelia (1852–1899) and Joe, born in 1854, who lived only three weeks. Amelia died in 1854. The same year the family brewery was sold. Joule lived on private means and continued to experiment in a laboratory at home. He received honorary degrees from Trinity College Dublin (1857), Oxford (1860) and Edinburgh (1871). He served the Manchester Literary and Philosophical Society as secretary and, several times from 1860, as president.

Mayer and the priority question

In 1848 Joule learned that the German physician Julius Robert Mayer had stated the equivalence of heat and work in 1842 and computed a value from the properties of gases. A short exchange in the Paris Comptes rendus followed. Joule argued that a number deduced from gas data without experiment was a hypothesis; Mayer replied that the idea and its first numerical expression were his. In 1862 John Tyndall championed Mayer at the Royal Institution, and Thomson and Peter Guthrie Tait answered in Joule’s defence, which turned the matter into a dispute between British and German science. Joule himself was more measured. The Royal Society gave him the Copley Medal in 1870 and gave it to Mayer the next year.

Last years and legacy, 1870–1889

Joule kept experimenting into the 1870s, refining thermometers and returning to the equivalent of heat. In 1878 he published a final determination by the paddle-wheel method, 772.55 foot-pounds. That year the government granted him a civil list pension of £200 a year, his private income having fallen. The Royal Society of Arts gave him its Albert Medal in 1880. The Physical Society of London published his collected papers in two volumes, in 1884 and 1887.

His health declined through the 1880s. He died at his home in Sale, Cheshire, on 11 October 1889, aged 70, and was buried in Brooklands cemetery in Sale. His gravestone is inscribed with the number 772.55. A memorial stands in the north choir aisle of Westminster Abbey, and a marble statue by Alfred Gilbert in Manchester Town Hall.

Legacy

• Energy: the experimental basis of the first law of thermodynamics, and with it the end of the caloric theory.
• Electricity: Joule heating, \(I^2R\), in every circuit design and in the theory of power transmission.
• Gases: free expansion, the first molecular speed, and with Thomson the throttling effect behind refrigeration and gas liquefaction.
• Method: precision measurement as a route to principle. Joule showed that a fraction of a degree, measured reliably, could decide a question of natural philosophy.
• Units: the joule, the SI unit of energy, work and heat.

Connections

People linked to James Prescott Joule across this collection. A name without a link has no page here yet. See James Prescott Joule in the network of all 337 lives →

Teachers and advisors

• John Dalton 1834-1837

Influenced by

• Count Rumford
• John Herapath
• William Sturgeon 1838-1843

Influenced

• Hermann von Helmholtz
• Osborne Reynolds
• Rudolf Clausius
• Henry Rowland

Colleagues and collaborators

• George Gabriel Stokes
• John Tyndall
• Michael Faraday
• Osborne Reynolds
• Peter Guthrie Tait
• William Thomson, Lord Kelvin 1847-1862

Rivals

• Julius Robert Mayer 1848-1862

Also mentioned in this life

• Carl Gustav Jacob Jacobi
• James Clerk Maxwell
• Georg Simon Ohm
• Sadi Carnot
• Johannes Diderik van der Waals

Fields

• thermodynamics 12 lives
• kinetic theory of gases 3 lives
• experimental physics 16 lives

On CoursesHub

• Thermodynamics

Sources and further reading

Biography

1. James Prescott Joule, Wikipedia.
2. James Prescott Joule, New World Encyclopedia.
3. James Prescott Joule, Encyclopaedia Britannica.
4. D. S. L. Cardwell, James Joule: A Biography, Manchester University Press, 1989.
5. O. Reynolds, Memoir of James Prescott Joule, Manchester Literary and Philosophical Society, 1892.
6. H. O. Sibum, Reworking the mechanical value of heat: instruments of precision and gestures of accuracy in early Victorian England, Stud. Hist. Phil. Sci. 26 (1995) 73–106.

Physics

1. J. P. Joule, On the heat evolved by metallic conductors of electricity, and in the cells of a battery during electrolysis, Phil. Mag. 19 (1841) 260.
2. J. P. Joule, On the calorific effects of magneto-electricity, and on the mechanical value of heat, Phil. Mag. 23 (1843).
3. J. P. Joule, On the existence of an equivalent relation between heat and the ordinary forms of mechanical power, Phil. Mag. 27 (1845) 205. Text at ChemTeam.
4. J. P. Joule, On the mechanical equivalent of heat, Phil. Trans. R. Soc. 140 (1850) 61–82. OCR text.
5. J. P. Joule, Some remarks on heat and the constitution of elastic fluids (1851). Excerpt, Classic Chemistry, Le Moyne College.
6. J. P. Joule and W. Thomson, On the thermal effects of fluids in motion, Phil. Trans. R. Soc. (1853–1862).
7. The Scientific Papers of James Prescott Joule, 2 vols., Physical Society of London, 1884–1887.
8. T. S. Kuhn, Energy conservation as an example of simultaneous discovery, in M. Clagett (ed.), Critical Problems in the History of Science, University of Wisconsin Press, 1959.
9. Mechanical equivalent of heat and Joule (unit), Wikipedia.