Joseph Black

How to use this course

Joseph Black published one major paper in his life. It showed that a gas could be weighed, fixed into a solid, and released again, and it set a new standard for quantitative chemistry. His second great body of work, on heat, he never published at all. He taught it, year after year, to students who carried it across Europe and into the steam engines of James Watt.

This course follows both strands. Part I covers his upbringing and medical training. Part II reconstructs his experiments and puts them in modern language: mass balances and stoichiometry for fixed air, then calorimetry, specific heat and latent heat. Part III covers his long teaching career and his influence.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Black worked in Fahrenheit degrees; the lessons convert to modern units where that helps, and keep his scale where his own numbers are discussed.

Timeline

Bordeaux and Belfast, 1728–1744

Joseph Black was born on 16 April 1728 in Bordeaux, on the Garonne, where his father John Black worked as a factor in the wine trade. John Black came from Belfast, of Scottish descent; Joseph’s mother, Margaret Gordon, was the daughter of an Aberdeen man in the same trade. Joseph was one of twelve children.

His mother taught him at home, in English, until he was about twelve. He was then sent to Belfast to learn Latin and Greek at a grammar school, the usual preparation for a Scottish university. The family’s network linked Bordeaux, Belfast and Scotland, and that network decided where he would study.

Little else is recorded of his childhood. Later accounts describe a calm, reserved and orderly character, traits that show in his laboratory notebooks and in his lifelong reluctance to publish anything he had not checked repeatedly.

Glasgow and Cullen, 1744–1752

Around 1744 Black entered the University of Glasgow. He took the general arts curriculum for several years, including natural philosophy, and then chose medicine, partly to satisfy his father’s wish that he have a profession. The decisive encounter was with William Cullen, who had begun lecturing on chemistry at Glasgow in 1747.

Cullen taught chemistry as a science in its own right, not only as a servant of pharmacy. He was interested in heat: in 1748 he showed that ether evaporating under reduced pressure cools sharply. Black became his laboratory assistant for about three years, and the two remained close for life. The style Black absorbed from Cullen was experimental and sceptical of grand systems.

Black was also skilful with instruments. Around 1750, while still a student, he designed a light, sensitive balance with a thin beam resting on a wedge-shaped fulcrum. Careful weighing would become the backbone of his chemistry.

Edinburgh and the thesis, 1752–1756

In 1752 Black moved to Edinburgh, whose medical school was then the most prestigious in Britain, to finish his degree. A live medical controversy gave him his thesis topic. Physicians hoped that alkaline substances might dissolve kidney and bladder stones. Lime water was one candidate, but quicklime was caustic. Black looked at a milder alkaline earth, magnesia alba, a white powder then sold as a purgative.

Early in 1754 he wrote to Cullen that the air released from chalk by acid extinguished a candle and a burning paper. His MD thesis, De humore acido a cibis orto et magnesia alba (On the acid humour arising from food, and on magnesia alba), was accepted in 1754. Its medical aim was modest. Its chemistry was not: he had found that magnesia alba loses a large fraction of its weight when heated, and that the loss is a kind of air.

In 1755 he read an expanded account to the Philosophical Society of Edinburgh, and in 1756 it appeared in the Society’s Essays and Observations, Physical and Literary. The same year Cullen moved to Edinburgh, and Black returned to Glasgow to take his place.

Magnesia alba and the weight of air

For the general reader. When limestone is burned it becomes quicklime, which is lighter and burns the skin. Chemists before Black thought fire added something caustic to the stone. Black showed the opposite. Something is driven out, and that something is an air with weight. Put the air back and the mild stone returns.

The experiments

Black prepared magnesia alba from Epsom salt and pearl ash (potassium carbonate). It effervesced with acids, like chalk. Strongly heated, it became magnesia usta, which no longer effervesced and weighed much less. Distilling a sample of three ounces in a retort, he collected only a little water, far less than the loss in weight. Following Stephen Hales, who had shown that many solids yield “air”, he concluded that most of the loss was air.

The decisive step closed the cycle. He dissolved magnesia usta in acid and precipitated it with a mild alkali. The powder that came down effervesced again and had recovered almost all the original weight. The air had gone into the mild alkali’s product and come back out of it.

Black then applied the same logic to lime. Mild alkali becomes caustic when it is treated with quicklime, because the quicklime takes the fixed air from it. Causticity is a property of the substance deprived of its air, not of any “fire matter” absorbed in the kiln.

Black’s magnesia alba was in fact a basic magnesium carbonate containing hydroxide and water, so its loss on heating is larger than the idealized formula gives. His reasoning does not depend on that. What mattered was that the weights balanced around a closed cycle, the first time a gas had been tracked quantitatively through a chain of reactions.

Fixed air as a distinct gas

For the general reader. Before Black, chemists spoke of “air” as a single element, sometimes dirty or damp. Black showed that the air locked in chalk is a different substance. It is heavier than ordinary air, puts out flames, kills small animals, and turns lime water milky. He found the same gas in our breath, in fermenting beer and in burning charcoal.

A chemical identity test

Black kept the name “fixed air”, already used by Hales, for air fixed in solid bodies. He noticed that lime water, a solution of quicklime, is clouded by this air, because the dissolved lime takes it up and becomes insoluble chalk again:

This gave chemistry its first specific test for a gas. Black used it to show that fixed air is present in exhaled breath, is produced by fermentation, and arises when charcoal burns. He also reported that it does not support combustion or animal life, that it is denser than common air, and that it behaves like a weak acid toward alkalis.

With \(M(\mathrm{CO_2})=44.0\) g/mol and an effective molar mass of dry air of \(29.0\) g/mol, carbon dioxide is about 1.52 times as dense as air. It pools in cellars, wells and brewing vats, a hazard that brewers knew empirically.

Where fixed air comes from

Jan Baptist van Helmont had described a “gas sylvestre” from burning charcoal and fermentation a century earlier. Black’s contribution was to tie it to a definite weight in definite compounds and to give a reproducible chemical test. His student Daniel Rutherford, working on air in which animals had breathed and from which the fixed air had been removed with alkali, isolated the gas later called nitrogen in 1772.

Temperature is not heat

For the general reader. A thermometer tells how hot something is. It does not tell how much heat it holds. A bathtub of warm water and a cup of boiling water show that the two ideas differ. Black was the first to make the distinction sharp and to build measurements on it.

The equilibrium of heat

The mercury thermometer of Daniel Gabriel Fahrenheit, reliable and reproducible from the 1710s onward, made temperature a measured number. Black taught that when bodies of any kind are left together, heat passes among them until a thermometer applied to each reads the same. A piece of iron and a piece of wood in a cold room both reach the room’s temperature, although the iron feels colder to the hand. The hand, he argued, judges the rate at which heat flows out of it, not the temperature of the object.

Temperature is intensive: it does not depend on how much material there is. Quantity of heat is extensive: twice the water warmed through the same range needs twice the heat. This simple distinction was not standard before Black. Many writers had treated the reading of the thermometer as a measure of the amount of heat present.

Why iron feels colder

When two semi-infinite bodies at temperatures \(T_1,T_2\) are brought into contact, the heat equation predicts that the contact surface jumps at once to

where \(k\) is conductivity, \(\rho\) density and \(c\) specific heat. The quantity \(e\) is the thermal effusivity. Skin has a value near that of water; iron’s is roughly ten times larger, wood’s several times smaller. So skin touching iron is pulled almost to the iron’s temperature, while skin touching wood stays close to its own.

Capacity for heat

For the general reader. Pour hot mercury into an equal volume of cold water and the mixture ends up much closer to the water’s original temperature than the mercury’s. Mercury is far denser than water, yet it carries less heat. Black concluded that each substance has its own capacity for heat. Today we call it specific heat.

Mixing experiments

Black built on experiments by Fahrenheit, reported in Herman Boerhaave’s Elementa chemiae (1732), in which mercury and water at different temperatures were mixed. He connected them with the observation of the Scottish physician George Martine that mercury heats and cools faster than water over a fire. Around 1760 he drew the general conclusion: the same quantity of heat changes the temperature of different substances by different amounts, and the difference does not follow bulk or density.

Derivation. The heat lost by the first body is \(m_1c_1(T_1-T)\) and the heat gained by the second is \(m_2c_2(T-T_2)\). Setting them equal and solving for \(T\) gives the formula. The final temperature is a weighted mean, with weights equal to the heat capacities \(C_i=m_ic_i\). Conversely, if \(c_2\) is known (water, by convention \(c=1\) in old units), a measured \(T\) gives \(c_1\):

Black worked the method with his assistant William Irvine, who made many such measurements in the 1760s and 1770s; Irvine’s results were not published in his lifetime. The modern specific heat of water is \(4.18\) J g\(^{-1}\) K\(^{-1}\), that of mercury \(0.140\).

Later regularity

Specific heats per gram vary widely, but in 1819 Pierre Louis Dulong and Alexis Thérèse Petit found that for many solid elements the heat capacity per mole is nearly the same, about \(3R\approx25\) J mol\(^{-1}\) K\(^{-1}\). The explanation, and its failure at low temperatures, came only with statistical mechanics and quantum theory.

The latent heat of fusion

For the general reader. Snow lying on the ground does not melt the moment the air rises above freezing. It takes hours or days. If melting needed only a tiny push of heat, Black reasoned, every thaw would be a sudden flood. Instead ice soaks up a large amount of heat while its temperature stays at the melting point. Black called this heat latent, meaning hidden from the thermometer.

From observation to theory

Black’s starting point was an observation by Fahrenheit, recorded by Boerhaave: water can be cooled below its freezing point without freezing, and when it is disturbed it partly freezes and its temperature jumps up to the freezing point. Heat must be released by freezing. Black was teaching the idea in Glasgow before he had measured it, perhaps as early as 1757–58.

The ice and water experiment (December 1761)

He needed cold weather. In December 1761, in a large hall beside his college rooms, he set equal masses of ice and of water just above freezing in identical vessels, in air at a steady temperature, and timed them. In the version reported in later accounts, the room was at 47 °F and the water rose from 33 °F to 40 °F, a gain of 7 degrees. The ice took about 21 times as long to melt and reach 40 °F. Assuming the two vessels drew heat from the air at the same rate, the ice received \(21\times7=147\) degrees’ worth of heat. Only 8 of these showed on the thermometer (32 to 40 °F); about 139 had vanished into melting.

The mixing experiment

A cleaner method used the law of mixtures. Black mixed ice at 32 °F with an equal mass of hot water and found the temperature of water needed to melt the ice exactly, leaving everything at 32 °F. The water had to start at about 176 °F, so it gave up 144 Fahrenheit degrees of heat to melt its own mass of ice.

Modelling the timing method

Newton’s law of heating states that a body gains heat from surroundings at \(T_a\) at a rate proportional to the difference, \(\dot Q=h(T_a-T)\). For water of heat capacity \(C\) this gives \(T(t)=T_a-(T_a-T_0)e^{-ht/C}\). While ice melts its temperature is fixed at \(T_m\), so the heat inflow is constant, \(h(T_a-T_m)\), and the melting time is \(t_m=mL_f/[h(T_a-T_m)]\). Black’s simple rule, “equal times, equal heats”, treats the rate as constant for both vessels. Because the water vessel’s temperature difference shrinks as it warms, the rule is approximate, and the exercises explore how much it matters.

Steam, vaporization and Watt’s engine

For the general reader. A kettle comes to the boil quickly, but it takes far longer to boil dry. Black timed the two and concluded that turning water into steam swallows several times more heat than heating it from cold to boiling. That heat comes back when the steam condenses, which is why steam scalds and why early steam engines burned so much coal.

The experiment (late 1762)

Black sealed measured amounts of water in tin vessels and set them on a red-hot iron plate. He timed how long the water took to go from 50 °F to boiling, and then how long it took to boil away. The difficulty was a steady source of heat. A practical distiller assured him that a furnace in good order delivered a predictable yield per hour, and Black checked this on his own laboratory furnace. Averaging three trials, he found that boiling off the water absorbed as much heat as would raise the liquid by a little over 800 Fahrenheit degrees, if that were possible. In 1764, with Irvine, he measured the latent heat of steam again by condensing it.

Black’s value was about 15% low, a good result for a timing method with an open fire. The ratio \(L_v/L_f\approx6.8\) for water explains the order of the effects: a pot boils dry slowly, and steam carries far more heat than hot water.

James Watt and the model engine

James Watt became instrument maker to the University of Glasgow in 1757, and Black soon became his friend, adviser and, for a time, lender. In 1763–64 Watt repaired the university’s model of a Thomas Newcomen engine. In that engine steam fills a cylinder, cold water is sprayed in to condense it, and the atmosphere drives the piston down. Watt found the model consumed far more steam than the cylinder’s volume could account for. The cylinder walls were cooled at every stroke, and each fresh charge of steam was largely spent reheating them.

Watt measured the heat of steam himself, and when he took his results to Black, Black explained the theory of latent heat to him. In 1765 Watt conceived the separate condenser: condense the steam in a vessel kept cold, and keep the cylinder hot. Watt later insisted that the condenser was his own idea and was not suggested by Black’s doctrine, while crediting Black with teaching him how to reason and experiment.

After Black: calorimetry to thermodynamics

For the general reader. Black gave chemistry and physics two measurable quantities, specific heat and latent heat, and a method, calorimetry. Others built on them: to measure the heat of chemical reactions and of breathing animals, to speculate about an absolute zero, and finally, with the steam engine as a model, to found thermodynamics.

Heat as a substance

Black told his students that some philosophers thought heat a motion of particles and others an elastic, imponderable fluid. He leaned toward the fluid, because a conserved quantity that flows and can be “absorbed” fitted his experiments. In the 1780s Lavoisier named this fluid caloric. Black’s caution was characteristic: his laws of calorimetry hold whatever heat is, as long as no work is done.

The ice calorimeter

Around 1782–83 Antoine Lavoisier and Pierre-Simon Laplace turned Black’s latent heat into an instrument. A sample sits inside a shell of ice at 0 °C, itself shielded by an outer jacket of ice. Every bit of heat the sample gives off melts ice, and the meltwater is weighed: \(Q=m_{\text{melt}}L_f\). They used it to measure specific heats, heats of combustion, and the heat produced by a guinea pig, and argued that respiration is a slow combustion.

Irvine’s hypothesis

William Irvine proposed that a body’s total heat is proportional to its capacity times its temperature above an absolute zero \(T_0\). Latent heat would then be just the change in capacity on melting: \(L_f=(c_{\text{w}}-c_{\text{i}})(T_m-T_0)\). This gave a way to compute \(T_0\) from measured quantities. Applied to different substances it gave inconsistent answers, which counted against the hypothesis.

Latent heat in thermodynamics

Derivation sketch. On the coexistence curve the two phases have equal specific Gibbs energy, \(g_1(T,p)=g_2(T,p)\). Differentiating along the curve with \(dg=-s\,dT+v\,dp\) gives \((s_2-s_1)\,dT=(v_2-v_1)\,dp\). Since the transition is reversible at fixed \(T\), \(s_2-s_1=L/T\). For the vapour case, \(\Delta v\approx v_{\text{gas}}=RT/(Mp)\). Émile Clapeyron derived the relation in 1834 from Sadi Carnot’s analysis of heat engines; Rudolf Clausius put it on its modern footing in 1850. Black’s hidden heat had become an entropy change.

The Glasgow professor, 1756–1766

When Cullen left for Edinburgh in 1756, Black succeeded him as lecturer in chemistry at Glasgow. He was also appointed professor of anatomy, a subject he did not care for, and in 1757 he exchanged it for the chair of medicine. He ran a large medical practice in the city as well. His chemistry course began in the 1757–58 session.

These ten years were his most productive in research. The work on heat began soon after his arrival and peaked in 1761–62. In April 1762 he described his theory of latent heat to a society of Glasgow professors. He then taught it every year but never wrote it up for print. Others, including the Genevan natural philosopher Jean-André Deluc, later published similar results and claimed priority, and Johan Carl Wilcke in Sweden reached the latent heat of melting independently in the 1770s.

Glasgow also gave him Watt. Black lent him money, introduced him to men of business, and remained a lifelong correspondent as Watt’s engine became an industry.

Edinburgh teacher, 1766–1799

In 1766 Cullen moved to another chair, and Black succeeded him as professor of chemistry at Edinburgh, at the age of 38. He held the post until his death and did little further research. He gave over a hundred lectures a year, from October to May, illustrated with simple and elegant demonstrations. He was paid not by salary but by student fees, three guineas each. Attendance grew for three decades and exceeded two hundred a year in the 1790s; he is estimated to have taught about five thousand students. Manuscript notes of his course circulated widely.

His students included John Robison, William Irvine, Daniel Rutherford, Thomas Charles Hope, Benjamin Rush, Thomas Thomson and, briefly, Thomas Young. Former pupils held chairs at Edinburgh, Glasgow, Cambridge and Oxford.

Black was a central figure of the Scottish Enlightenment. With Adam Smith and the geologist James Hutton he met weekly at the Oyster Club, a dining society, and he was a close friend of Hutton and David Hume. He was a member of the Poker Club, a founding member of the Royal Society of Edinburgh in 1783, president of the Royal College of Physicians of Edinburgh from 1788 to 1790, and principal physician to George III in Scotland. He helped revise the Pharmacopoeia Edinburgensis in 1774, 1783 and 1794. He never married.

He was a cautious convert to the new chemistry of Antoine Lavoisier, who admired his work on fixed air. In October 1790 Black wrote to Lavoisier that he had begun recommending the new system to his students. From 1795 Thomas Charles Hope shared the teaching, and Black gave his last lectures in the 1796–97 session. He died at his house at 12 Nicolson Street on 6 December 1799, aged 71, and was buried in Greyfriars Kirkyard. In 1803 Robison published his Lectures on the Elements of Chemistry from Black’s notes.

Legacy

• Chemistry: the first rigorous use of the balance to follow a gas through a cycle of reactions, and the identification of carbon dioxide as a distinct substance. Pneumatic chemistry, from Henry Cavendish and Joseph Priestley to Lavoisier, grew from this.
• Physics: the distinction between temperature and heat, specific heat, latent heat and calorimetry, the experimental foundation on which thermodynamics was built.
• Technology: the theory of latent heat as the language in which Watt understood and improved the steam engine.
• Honours: the chemistry buildings at Edinburgh and Glasgow bear his name, and a lunar crater was named after him in 1976.

Connections

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

Teachers and advisors

• William Cullen 1747-1752

Students

• Ernest Rutherford
• Thomas Young
• Benjamin Rush
• John Robison
• Thomas Charles Hope
• Thomas Thomson

Influenced by

• Daniel Gabriel Fahrenheit
• Herman Boerhaave
• Stephen Hales

Influenced

• Antoine Lavoisier 1789-1790
• Count Rumford
• Henry Cavendish
• Joseph Priestley

Colleagues and collaborators

• Henry Cavendish
• William Irvine 1764-1770

Rivals

• Jean-André Deluc

Friends

• James Watt 1757-1799
• Adam Smith
• David Hume
• James Hutton

Family

• Adam Ferguson

Also mentioned in this life

• Rudolf Clausius
• Josiah Willard Gibbs
• Pierre-Simon Laplace
• Isaac Newton
• Sadi Carnot

Fields

• chemistry 21 lives
• medicine 8 lives

Sources and further reading

Biography

1. Joseph Black, Wikipedia.
2. “Black, Joseph”, Complete Dictionary of Scientific Biography, via Encyclopedia.com.
3. School of Chemistry, University of Edinburgh, Joseph Black.
4. Royal College of Physicians of Edinburgh, Joseph Black.
5. Black, Joseph, Encyclopaedia Britannica, 11th edition (1911).
6. APS News, This Month in Physics History: April 1762.
7. R. G. W. Anderson and J. Jones (eds.), The Correspondence of Joseph Black, Ashgate, 2012.

Science

1. J. Black, Experiments upon Magnesia Alba, Quicklime, and Some Other Alcaline Substances, Essays and Observations, Physical and Literary 2 (1756). Reprinted as Alembic Club Reprint No. 1.
2. J. Black, Lectures on the Elements of Chemistry, ed. J. Robison, 2 vols., Edinburgh, 1803.
3. Latent heat, Wikipedia (history section).
4. D. McKie and N. H. de V. Heathcote, The Discovery of Specific and Latent Heats, Arnold, 1935.
5. A. Lavoisier and P.-S. Laplace, Mémoire sur la chaleur (1783).
6. H. Chang, Inventing Temperature, Oxford University Press, 2004.