Posts Tagged ‘Lord Kelvin’

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William Thomson, later Lord Kelvin (left), James Joule and the famous hand-operated pump. The Joule-Thomson effect is named after them, as are the SI units of thermodynamic temperature (kelvin) and energy (joule).

Historical background

In early May 1852, in the cellar of a house in Acton Square, Salford, Manchester (England), two men began working a mechanical apparatus which consisted of the above hand-operated forcing pump attached to a coiled length of lead piping equipped with a stopcock at its far end to act as a throttle.

The two men were the owner of the house, 33-year-old James Joule, a Manchester brewer who was rapidly making a name for himself as a first-rate experimental scientist, and 27-year-old William Thomson (later Lord Kelvin), a maverick theoretician who was already a professor of natural sciences at Glasgow University. Over a period of 10 days, they were to conduct a series of experiments with this highly original apparatus which would serve to crank experimental research into the modern era and herald the birth of what we would now call big science.

What Joule and Thomson were looking for was a slight cooling of the expanded gas as it emerged from the throttle – and they found it. But the results were unsatisfactory due to the modest size of the apparatus; fluctuations in the ambient conditions exerted too much influence on the measurements for the data to be considered reliable.

The remedy was clear to them. As they wrote in their first joint paper, read to the British Association for the Advancement of Science on Friday 3 September 1852: “… the authors are convinced that, without apparatus on a much larger scale, and a much more ample source of mechanical work than has hitherto been available to them, they could not get as complete and accurate results as are to be desired…”

It was easy enough to read between the lines. Joule and Thomson were fishing for money from sponsors to fund the scaling up of their apparatus. And they got it. In fact, a repeating pattern of funding and upscaling over the following years would become a key characteristic of Joule and Thomson’s collaboration.

From modest beginnings in the cellar at Acton Square, the experiments conducted in Manchester by Joule and Thomson were expanded in size and scope on an unprecedented scale by these two increasingly influential scientists. By the time they ended their work a decade later, they were using massive, highly pressurised equipment driven by steam engines and financed by substantial government grants.

The first round of scaling up. Joule and Thomson's experimental equipment was longer and taller than a London Bus.

The first round of scaling up. Joule and Thomson’s experimental equipment was longer and taller than a London Bus.

Scaling-up continues. By 1854, the Joule-Thomson equipment stretched the length of 3 London buses.

Scaling-up continues. By 1854, the Joule-Thomson equipment stretched the length of 3 London buses.

This was light years beyond what published experimental science in Britain had been up to that point – a desultory activity for individual gentleman-devotees of an enquiring disposition, undertaken at their own expense and largely for their own amusement.

Another paradigm shift was that Joule and Thomson published all their work jointly, in a total of eight papers. It should be borne in mind that in the mid-19th century, a joint paper was a rarity. A whole series of joint papers was unheard of; even in the scientific centres of Europe, there had never been anything like it.

While Europe’s laboratories were mainly occupied with the accurate determination of physical constants, the work going on in Manchester represented something radically new. It was the systematic and continued exploration of the unknown by talented individuals of complementary ability. Not surprisingly it led to discoveries, which turned out to have commercial as well as purely scientific value, since the Joule-Thomson effect made possible the liquefaction of gases and opened the way to important applications of throttling such as refrigeration.

Refrigerators, liquefied gases for industrial and domestic use, and air conditioning systems. All these technological advances resulted directly from the discovery of the Joule-Thomson effect.

Refrigerators, liquefied gases for industrial and domestic use, and air conditioning systems. All these technological advances resulted directly from the discovery of the Joule-Thomson effect.

Joule and Thomson’s sustained and extraordinary work provided a new model of collaborative scientific enquiry that would help the scientific establishment (and governments) to recognize the need for research institutions with both the physical and financial resources to undertake advanced and ambitious scientific programmes in order to gain valuable knowledge, scientific pre-eminence and commercial advantage.

All this took time, and of course there were other factors involved, but the original driving force that led to the establishment in 1874 of the Cavendish Laboratory in Cambridge can be traced back directly to the handle of the forcing pump that William Thomson cranked in a Manchester cellar in the spring of 1852.

The birthplace of big science. It was in the cellar of this house in Acton Square, Manchester, that Joule and Thomson began the work that would propel experimental research into the modern era. The cellar layout is practically unaltered to this day, and the house is now owned and occupied by the University of Salford. Photo credit: Charlie Hulme, johncassidy.org.uk

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The Joule-Thomson Experiment explained

Ok, so now let’s turn our attention to the thermodynamic characteristics of the Joule-Thomson experiment. The elegantly simple steady-state experimental set-up is easy enough to describe, but not so easy to understand.

Briefly stated, Joule and Thomson’s apparatus allowed a pressurised gas to flow along a tube which narrowed at a certain point, after which the gas expanded into a region of lower (atmospheric) pressure. The pressurised gas upstream of the throttle was kept at a constant temperature, and precautions were taken to ensure that the gas did not gain heat from, or lose heat to, the throttling section of the apparatus before it emerged on the other side and the temperature of the expanded gas was measured.

When the first experiments were conducted using air, a slight cooling on expansion was detected. This result was interpreted by a number of contemporary scientific observers as the familiar cooling observed when a gas does external work under adiabatic conditions. But this is not what happens in the apparatus; the cooling has a different explanation.

The Joule-Thomson effect can be understood by looking at a diagrammatic representation of the experiment, in which the flow of a given mass of gas from the high pressure region to the low pressure region is equated to work done by, and on, conceptual pistons:

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Upstream of the throttle in the high pressure region, the flow of the gas can be equated to work done on the gas by the conceptual piston at left against the resistance of the throttle. The force-distance work done by the conceptual piston is equivalent to the pressure-volume product P1V1 of the gas.

Downstream of the throttle in the low pressure region, the flow of the gas can be equated to work done by the gas against the resistance of the conceptual piston at right, which is under lower pressure (atmospheric pressure in the original Joule-Thomson experiment). The force-distance work on the conceptual piston is equivalent to the pressure-volume product P2V2 of the gas.

The net work W done on the given mass of gas is therefore

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In the Joule-Thomson experiment, no heat is gained or lost by the gas (Q = 0) as it flows from the higher to the lower pressure region. Applying the first law of thermodynamics to this transition:

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[the + sign shows that W represents work done on the gas]

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U + PV happens to be a thermodynamic state function, called enthalpy. The Joule-Thomson experiment therefore involves a constant-enthalpy, or isenthalpic, expansion. Cooling observed under these conditions has a fundamentally different thermodynamic aetiology to the cooling observed when a gas does external work under (reversible) adiabatic conditions, which is a constant-entropy, or isentropic, expansion.

When Joule and Thomson began their work “on the thermal effects of fluid in motion” in 1852, they were not aware that their cleverly-designed experiment was subject to isenthalpic conditions. The recognition of enthalpy as a thermodynamic state function did not come until 1875 when J. Willard Gibbs in America introduced it as “the heat function for constant pressure”, although the Scottish engineer and theoretician William Rankine – who was well aware of Joule and Thomson’s work – showed in his 1854 paper “On the geometrical representation of the of the expansive action of heat” that the equation of the curve of free expansion in their experiment was d(U+PV) = 0. Similarly, James Clerk Maxwell in his 1871 book Theory of Heat recognised that in the Joule-Thomson experiment “the sum of the intrinsic energy and the product of the volume and the pressure remains the same after passing through the plug [throttle], provided no heat is lost or gained from external sources”.

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The Joule-Thomson Coefficient

In Joule and Thomson’s first experiments with their apparatus, they varied the upstream pressure and temperature, while the downstream pressure was always atmospheric since the end of the pipe was open to the air. These were pathfinding experiments – they were exploring the unknown.

It was later realised that more useful results are obtained if the upstream pressure and temperature are held constant, and the downstream  pressure is held at several decreasing values at each of which the downstream temperature is measured. The data is then recorded on a temperature-pressure plot. Each point on the plot represents a state for which the enthalpy is equal to the initial (upstream) enthalpy. By joining up the points, a constant-enthalpy line, or isenthalpic curve, is obtained.

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The slope at any point on an isenthalpic curve is known as the Joule-Thomson coefficient μJT. The maximum point of the curve, at which the coefficient is zero, is called the inversion point for the isenthalpic curve in question. By joining up the inversion points on each isenthalpic curve, an inversion curve is obtained. In the region within the inversion curve where μJT is positive, cooling will occur. In the region outside the inversion curve where μJT is negative, heating will occur.

The upper intersection of the inversion curve with the line of no pressure denotes the maximum inversion temperature for the given gas. Above this temperature the Joule-Thomson effect cannot produce cooling at any pressure.

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The Joule-Thomson coefficient is defined:

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Since the initial pressure is always greater than the final pressure in the Joule-Thomson experiment, ∂P is always negative. So a positive slope (μJT >0) on the isenthalpic curve means that ∂T is also negative i.e. cooling will occur. Conversely a negative slope (μJT <0) on the isenthalpic curve means that ∂T is positive i.e. heating will occur. 

Joule-Thomson cooling vs. Adiabatic cooling

The Joule-Thomson coefficient also provides a convenient mathematical means of showing the fundamental difference between Joule-Thomson cooling and adiabatic cooling.

In the Joule-Thomson experiment, the thermodynamic relationship between the independent state variables P and T, and the state function enthalpy (H), is such that we may write the implicit function:

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Making use of the triple product rule, one of the useful relationships among first partial derivatives that follows directly is:

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The second term on the right has particular significance for a perfect gas, since just as the internal energy is independent of volume at constant temperature, so by parallel reasoning the enthalpy is independent of pressure at constant temperature:

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For a perfect gas therefore, μJT is zero. Which means that unlike a real gas, a perfect gas cannot exhibit Joule-Thomson cooling. This is in direct contrast to the familiar adiabatic expansion of a gas doing external work, where a perfect gas would indeed exhibit cooling, just like a real gas.

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Related blog posts (click on title, opens in separate window)

Joule, Thomson, and trouble with the neighbours
The story of how Joule and Thomson came to form their historic partnership, their increasingly ambitious research in Manchester, and the unfortunate circumstance that derailed it.

The Liquefaction of Gases – Part I
The story of how the scientific community came to realise that the term ‘non condensable’ gases was a misnomer, and the role that the Joule-Thomson effect had in enabling the commercial liquefaction of air.

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Acknowledgements
I am indebted to Charlie Hulme, Kenneth Letherman President of the Manchester Literary and Philosophical Society, Professor Keith Ross of the University of Salford, Professor Nigel Mellors of the University of Salford, and John Beckerson, Senior Curator of the Museum of Science and Industry, Manchester, for their engagement and input during the preparation of this article.

Header photo credits
(left) William Thomson / Smithsonian Libraries (centre) The forcing-pump used by Joule and Thomson in their first experiments of May 1852, now preserved by the Museum of Science and Industry, Manchester / MOSI (right) James Joule / Manchester Libraries

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The house in Manchster where neighbour trouble broke out. Photo credit: Charlie Hulme

The house in Manchester where neighbour trouble broke out. Photo credit: Charlie Hulme

We all have our problems. And those engaged in the business of scientific discovery are no strangers to it. Budget cuts, lack of resources, experiments that fail, theories that fall apart, and so on. Rarely though does trouble with the neighbours derail one’s research programme.

Yet curiously, this is exactly what happened to the research conducted in the 1850s by James Joule and William Thomson [later Lord Kelvin] into the expansion of gases – pioneering work that led to the discovery of the Joule-Thomson effect before their endeavours were brought to an abrupt end.

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In the late 1840s, Henri Regnault in France published the most accurate data so far attained of the pressure volume relationship of air maintained at constant temperature. Although the data substantially confirmed Boyle’s law, or Mariotte’s law as Regnault would have called it, the results nevertheless revealed a small discrepancy, in that the density of air increased slightly more than expected in relation to pressure.

Hardly a big deal you might think, but to those involved in the newly-forming, cutting-edge science of Thermo-dynamics as it was spelled then, the discrepancy suggested that there should be a similarly small cooling effect when air expands through a throttle into a region of lower pressure. Here was an opportunity to study the behaviour of real gases in motion and explore their differences, however slight, from ideal behaviour. At Glasgow University in Scotland, the maverick Professor William Thomson designed an innovative steady state experimental method, for which he had a collaborator of proven experimental skill in mind – Mr James Joule of Manchester.

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James Joule, the son of a brewery owner, had a passion for experimentation and from an early age had been conducting scientific experiments at home which had convinced him that heat could be created by mechanical means, and that there was a precise quantitative relationship between the two. This was in stark opposition to the tenets of the caloric theory, which at the time was the prevailing belief of the scientific establishment. But Joule was not a member of the scientific establishment, and this freed him from peer pressure and allowed him to pursue his own ideas and increasingly refined experimentation.

There was a downside to Joule’s non-membership of Britain’s scientific club, however. None of its members took any notice of him, or what he had to say. To them he was an uneducated commoner, an amateur, an outsider.

Joule’s collected papers, which can be read online at archive.org, chart his tireless yet fruitless efforts to get either the Royal Society or the British Association for the Advancement of Science to take notice of his discovery. He kept at it, without luck, for four years. And then one day, in 1847, his luck changed. As Joule himself wrote in a subsequent note:

“It was in the year 1843 that I read a paper “On the Calorific Effects of Magneto-Electricity and the Mechanical Value of Heat” to the Chemical Section of the British Association assembled at Cork … the subject did not excite much general attention, so that when I brought it forward again at the meeting [in Oxford] in 1847, the chairman suggested that I should not read my paper but confine myself to a short verbal description of my experiments. This I endeavoured to do, and discussion not being invited, the communication would have passed without comment if a young man had not risen in the section, and by his intelligent observations created lively interest in the new theory. The young man was William Thomson, who had two years previously passed the University of Cambridge with the highest honour, and is now [1855] probably the foremost scientific authority of the age.”

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Foremost scientific authority he may later have been, but the fact is that William Thomson was at the time of the Oxford meeting a staunch supporter of the yet-to-be-discredited caloric theory, and history shows that his conversion to the dynamical theory that James Joule espoused was somewhat slow – some would even say reticent. But by 1852, Thomson was sufficiently convinced that heat and work were interconvertible, in the quantitative ratio that Joule had discovered.

Now, with Regnault’s discoveries waiting to be tested,  the two men were ready to embark on their first collaborative work (Joule having been admitted to the Royal Society in the meantime, thus making him eligible for research grants). Some accounts suggest that their collaboration was conducted by correspondence, with Thomson in Glasgow devising experiments and analysing results while Joule did the experimental work in Manchester. But an account of Joule’s life by Osborne Reynolds (he of the Reynolds number) shows that Thomson made several trips to Manchester and seems to have enjoyed his visits. In one recollection, Thomson writes of Mr and Mrs Joule that “both she and he showed me the greatest kindness during my visits to them in Manchester for our experiments on the thermal effects of fluid in motion”.

The experiments involved forcing a gas under constant pressure through a tube, narrowed at one point along its length to act as a throttle, and open to the atmosphere at the distal end. Thermometers were positioned in the flow to measure the temperature of the gas on entering and exiting the throttle. The first experiments, using air,  were conducted in one of the cellars of the Joule’s family home at 1 Acton Square, Manchester, opposite what is now the campus of the University of Salford.

Although some cooling was detected, the effect was very small and it became quickly clear that the apparatus needed to be scaled up, and the pressures increased. So with a forcing pump furnished by a grant from the Royal Society, the experiments were moved to the family’s brewery in New Bailey Street Manchester. This was later followed by yet another round of upscaling, this time with the installation of a full size steam engine to drive the pressure pump, again financed by the Royal Society. The design of the throttle was refined with the use of a porous plug rather than a single small orifice, and the gases used in the experiments now included hydrogen and what was referred to as carbonic acid, which we now call carbon dioxide.

It must have been a sight to see Joule and Kelvin, who would ultimately have their names commemorated in the units of energy and absolute temperature respectively, up to their elbows in engine oil and slaving away in the dank cellars of a Manchester brewery to keep their hugely pressurised apparatus in a steady state and obtain meaningful measurements. If someone had taken a photograph of them, it would be worth gold now.

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The next few years brought personal tragedy to Joule, with the death of his newborn second son, closely followed by the death of his wife. During this painful time he sold the brewery and moved back to his father’s house with his young son and daughter, and his steam engine. His elder brother Benjamin writes of how Joule threw himself into continued experimental work at this time:

“My brother was very busy with experiments, many of which were decidedly dangerous owing to the pressure he made use of. During this period, for some months he could not find time to take his meals properly – just ran in and out again. The experiments were so delicate that many were carried out in the night, because a [horse-drawn] cab or cart passing along the road disturbed them, though the laboratory was at the back of the stables.”

Then tragedy struck again with the death of Joule’s father. The house was sold, and Joule moved on yet again, this time buying a house in Old Trafford (the district where Manchester United’s stadium is today). He took with him all the Joule-Thomson experimental apparatus, including the steam engine.

And it was at this point that the neighbour trouble appeared.

There was an obscure item in the house purchase deed that prohibited any steam engine being used at the property. This fact was known to the occupant of the neighbouring property, who insisted upon its strict observance despite it being an obsolete clause, and despite protests from other more lenient and understanding local residents.

Joule’s experiments juddered to a sudden halt, and although he reacted by putting his newly acquired home up for sale, it was an empty gesture and the incident seemed to deflate him. His brother Benjamin wrote of Joule suffering  “a great and lasting disappointment”, and noting that “what really affected him was the refusal to be allowed the use of his one-horse power steam engine … My brother was anticipating a series of important experiments in conjunction with W. Thomson, for which a grant had been obtained.”

In his collected papers, Joule himself couches his disappointment in more detached language:

“[William Thomson and I] pursued the discussion of the thermal effects of fluids in motion until the experiments were interrupted by the action of the owners of the adjacent property, who on the strength of an obsolete clause in the deeds of conveyance, threatened legal proceedings, the cost of which I did not feel disposed to incur”.

Joule and Thomson, the latter having lately suffered a debilitating fall,  experimented no more after this setback. The threat of legal action by a perverse individual ended an historically important piece of research.

But the work performed by the dynamic duo, and the series of joint papers they published, established the Joule-Thomson effect and the knowledge that throttled (real) gases can cool or heat on expansion depending on whether they are below or above their inversion point. This knowledge, and the equations that attach to it, are of great practical importance to today’s chemical engineers in the liquefaction of gases, refrigeration and many other fields of application.

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Related blog posts

Joule, Thomson, and the birth of big science
The story of how Joule and Thomson’s extraordinary collaboration in the 1850s propelled experimental research into the modern era. The second part of this post also explains the thermodynamics of the Joule-Thomson effect.

The Liquefaction of Gases – Part I
The story of how the scientific community came to realise that the term ‘non condensable’ gases was a misnomer, and the role that the Joule-Thomson effect had in enabling the commercial liquefaction of air.

In textbooks dealing with thermodynamics, the story is often recounted that Carnot’s groundbreaking memoir Réflexions sur la Puissance Motrice du Feu (Reflections on the Motive Power of Fire) went unnoticed by the scientific world when it was published, and lay forgotten for 24 years until Lord Kelvin seized on its significance and brought Carnot’s seminal work – in which lay the seeds of the second law of thermodynamics – into the spotlight of publicity.

This popular account, although broadly accurate, is incomplete in one important respect. It neglects the vital role played by Clapeyron.

Benoît Émile Clapeyron (1799-1864)

Benoît Émile Clapeyron (1799-1864)

Sadi Carnot (1796-1832) and Émile Clapeyron (1799-1864) were contemporaries. Both were engineers by training, and both had studied at the École Polytechnique in Paris. When Carnot published his memoir (at his own expense) in 1824, Clapeyron had already left Paris and was teaching at an engineering school in St. Petersburg, Russia. He returned to Paris just two years before Carnot’s untimely death during a cholera epidemic in 1832. By that time, Sadi Carnot’s little book had long since disappeared from the booksellers’ shelves. But Clapeyron had evidently obtained a copy, and had clearly recognised the importance of his compatriot’s work. Clapeyron’s own Mémoire sur la Puissance Motrice de la Chaleur (Memoir on the Motive Power of Heat), published in Journal de l’École Polytechnique in 1834, contains a full restatement of Carnot’s theoretical principles – albeit in a more analytical form.

While Carnot’s privately published booklet quickly faded into obscurity, Clapeyron’s memoir published in an academic journal did not. It was read in scientific circles and remained available in scientific libraries, and so kept Carnot’s powerful ideas alive. In 1837, Clapeyron’s memoir was translated into English and formed one of the papers presented in Volume I of Taylor’s Scientific Memoirs. This was how Lord Kelvin became aware of Carnot’s work – we know this because the following footnote appears in the historic paper On an Absolute Thermometric Scale which Lord Kelvin published in Philosophical Magazine in October 1848:

“Carnot’s Theory of the Motive Power of Heat – Published in 1824 in a work entitled Réflexions sur la Puissance Motrice du Feu, by M. S. Carnot. Having never met with the original work, it is only through a paper by M. Clapeyron, on the same subject, published in the Journal de l’École Polytechnique, Vol. XIV, 1834, and translated in the first volume of Taylor’s Scientific Memoirs, that the Author has become acquainted with Carnot’s Theory.”

William Thomson, later Lord Kelvin (1824-1907)

William Thomson, later Lord Kelvin (1824-1907)

At the end of 1848, Lord Kelvin succeeded in obtaining a copy of Carnot’s original work, and the following year published a lengthy paper entitled An account of Carnot’s Theory of the Motive Power of Heat in the Transactions of the Edinburgh Royal Society, XVI, 1849.

Curiously, just as Lord Kelvin came to discover Carnot’s masterwork through the agency of Émile Clapeyron’s memoir, so did another key figure in the development of thermodynamics – Rudolf Clausius.

In his first and most famous paper On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat published in Annalen der Physik  in 1850, Clausius cites Carnot’s memoir on the opening page and adds this footnote:

Réflexions sur la Puissance Motrice du Feu, par S. Carnot. Paris, 1824. I have not been able to obtain a copy of this work, and am acquainted with it only through the work of Clapeyron and Thomson [Lord Kelvin]”

Rudolf Clausius (1822-1888)

Rudolf Clausius (1822-1888)

Clapeyron’s memoir had been translated into German in 1843 and published in the same journal in which Clausius’ 1850 paper appeared – Annalen der Physik – so it likely to be this translation to which Clausius refers. It is doubtful whether Carnot had much inkling of how crucially important his ideas would be to the development of thermodynamics. But there is no doubt that Clapeyron immediately saw value in them. In the introduction to his memoir, Clapeyron describes Carnot’s ideas as ‘both fertile and beyond question‘ and ‘worthy of the attention of theoreticians‘.

He was right. The two foremost theoreticians of the day certainly found Carnot’s fertile ideas worthy of attention. And we have Émile Clapeyron to thank for enabling Lord Kelvin and Rudolf Clausius to discover them.