Posts Tagged ‘liquefaction of gases’

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Future Nobel Prize winners both. Kamerlingh Onnes and Johannes van der Waals in 1908.

On Friday 10 July 1908, at Leiden in the Netherlands, Kamerlingh Onnes succeeded in liquefying the one remaining gas previously thought to be non-condensable – helium – using a sequential Joule-Thomson cooling technique to drive the temperature down to just 4 degrees above absolute zero. The event brought to a conclusion the race to liquefy the so-called permanent gases, following the revelation that all gases have a critical temperature below which they must be cooled before liquefaction is possible.

This crucial fact was established by Dr. Thomas Andrews, professor of chemistry at Queen’s College Belfast, in his groundbreaking study of the liquefaction of carbon dioxide, “On the Continuity of the Gaseous and Liquid States of Matter”, published in the Philosophical Transactions of the Royal Society of London in 1869.

As described in Part I of this blog post, Andrews’ discovery of the critical temperature (aided and abetted by Joule and Thomson’s earlier discovery of isenthalpic cooling) opened the way to cryotechnological advances of great commercial importance, and gave birth to the industrial gases industry which played such a significant role in shaping the 20th century.

This fact alone was enough to ensure Dr. Andrews’ study a place in the history of physical science. But there was another aspect to his paper – a theoretical one – which had equally far-reaching effects and is the subject of the remainder of this post.

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Dr. Thomas Andrews FRS (1813-1885). Photograph taken in Paris 1875 when Andrews was 62.

Dr. Thomas Andrews FRS (1813-1885). Photograph taken in Paris 1875 when Andrews was 62.

Thomas Andrews was a scientist whose experimental skills were evidently comparable to those of the illustrious James Joule. Ten years of care and devotion went into Andrews’ study of the liquefaction of carbon dioxide (called carbonic acid in his day), the essential results of which are contained in this diagram taken from his 1869 paper.

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It is a pressure-volume diagram (with the line of no volume to the right) upon which are drawn isothermal carbon dioxide curves for temperatures ranging from 13.1°C to 48.1°C, pressures ranging from 50 to 100 atmospheres. Isothermal air curves are included in the upper left quadrant to illustrate the degree of deviation of the carbon dioxide curves from the rectangular hyperbola associated with ideal gas behavior.

The lowest isothermal curve (13.1°C) shows that at a pressure of around 47 atmospheres, condensation occurs. The compressed gas separates into two distinct coexistent portions – vapor and liquid – along a line of constant pressure, with further compression driving the conversion to the liquid form until finally the whole is converted to liquid, at which point compressibility becomes markedly reduced.

In the next isothermal curve (21.5°C), where condensation takes place at a pressure of about 60 atmospheres, gas and liquid are closer still in density, the liquid occupying nearly a third of the volume of the gas. As James Clerk Maxwell put it in Theory of Heat, written in 1871, “the exceedingly dense gas is approaching in its properties to the exceedingly light liquid”.

These properties eventually coincide at the isopycnic point* (the point of inflexion on the critical isotherm, marked X in the figure below) corresponding to a critical pressure of 72.8 atmospheres and a critical temperature of 31°C.

*isopycnic means ‘of equal density’. The isopycnic point (sometimes called the critical point) is where the densities of vapor and liquid coincide; this occurs under the conditions of critical temperature Tc and critical pressure pc.

Above the critical temperature, isothermals do not show any discontinuity; it is not possible to detect the point at which a liquid becomes a gas or vice versa. If liquid carbon dioxide, represented by point Z in the figure below, is heated at constant pressure until its temperature reaches 48°C, its condition at different temperatures will be represented by the line ZY. At Z the substance concerned is a liquid; at Y it is a gas. The change has taken place smoothly and continuously, representing continuity of state.

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It was this revelation provided by Andrews’ data that started theoreticians thinking about how to reconcile the idea of continuity of state with the discontinuous change observed experimentally within the confines of the dotted parabola shown in Fig.12.

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The history of science is full of coincidences – Belfast in Northern Ireland was the birthplace of not only Thomas Andrews, but also William Thomson (later Lord Kelvin) and his elder brother James. William frequently discussed thermodynamics with James, who just happened to be professor of civil engineering at Queen’s College Belfast exactly at the time when Thomas Andrews was conducting his famous experiments there.

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James Thomson (1822-1892), physicist and engineer, whose achievements were largely overshadowed by his equally hairy brother William Thomson, also known as Lord Kelvin. Photo credit: Wikipedia

Not surprisingly, James Thomson with his practised skills in thermodynamics took an active interest in Andrews’ remarkable results, and in 1871 proposed a highly original solution to the problem of reconciling the discontinuous isotherms below the isopycnic point with the continuous isotherms above it.

Thomson’s thesis was that the gaseous and liquid parts of a discontinuous isotherm (AB and CD in the above diagram) were only apparently discontinuous, and were actually parts of one smooth curve shown in dotted lines in the diagram below. Every isotherm, according to Thomson, was a continuous curve.

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Diagram from “Considerations on the Abrupt Change at Boiling or Condensing in reference to the Continuity of the Fluid State of Matter” by Professor James Thomson, LL.D., Queen’s College, Belfast. Communicated to The Royal Society of London by Dr. Andrews. Received July 4, 1871.

The task that now confronted theoreticians was to find a satisfactory mathematical equation for this curve. Thomson’s curve gave some useful clues, as Lewis and Randall subsequently observed in their classic textbook Thermodynamics and the Free Energy of Chemical Substances:

“It is evident that the equation for such a complete curve must be of odd degree in V, for V increases with diminishing P at both ends of the curve. Furthermore the equation must be of at least the third degree in V, since a certain pressure may correspond to more than one volume. At lower temperatures three roots of the equation are real, at the critical point the three coincide, and at higher temperatures two of them become imaginary.”

The first to provide a solution was a physics student in the Netherlands. His name was Johannes van der Waals.

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The title page of Johannes van der Waals’ doctoral thesis

At Leiden University on Saturday 14 June 1873, from 12 noon to 3 pm, Johannes van der Waals defended his doctoral thesis, which sought to explain Thomas Andrews experimental results on the basis of kinetic theory, and whose title “Over de Continuiteit van den Gas en Vloeistoftoestand (On the Continuity of the Gaseous and Liquid State)” was almost exactly the same as Andrews’ 1869 paper.

In his thesis, van der Waals introduced the concepts of molecular attraction and molecular volume, and derived the equation of state which bears his name:

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where a and b are gas-specific constants related to molecular attraction and molecular volume respectively; the term a/V2 identifies with the derivative (∂U/∂V)T while b turns out to be equal to a third of the critical volume.

Multiplying out the van der Waals equation gives

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Since this expression equals zero, it follows that

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Multiplying out and rearranging terms

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A cubic equation in V is thus obtained. For any given values of p and T, there will be three values of V, since a, b and R are constants for one mole of a given gas.

The cubic form of van der Waals’ equation produces curves like those shown below. They are very similar to the isothermal curves hypothesized by James Thomson (cf. above), and give three values of V along the line of first-order phase transition where all the roots A,B,C are real; on the critical isotherm the roots are coincident at the isopycnic point. At higher temperatures two of the roots become imaginary as the curves become increasingly hyperbolic.

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The van der Waals equation of state modifies the ideal gas equation, and is an improvement on it in accounting for the shape of pressure-volume curves above the critical isotherm. At lower temperatures it is also qualitatively reasonable for the liquid state and the low-pressure gaseous state.

During first-order phase transition (A↔C) however, the equation is clearly at variance with the empirically determined fact that the pressure remains constant. The reason why the van der Waals equation fails to describe the behavior of real substances within the dotted region in the above figure is precisely because it assumes continuity of state. It cannot therefore account for the fact that the substance, by separating into two coexistent phases – liquid and saturated vapor – is rendered more stable than in the homogeneous state.

It should be noted that under certain conditions, states corresponding to the portions AA’ and B’C are respectively realizable as superheated liquid and supersaturated vapor (both portions representing states stable with respect to infinitesimal variations but unstable relative to the coexistent liquid-vapor system). The portion of the curve A’B’, on the other hand, represents states that are absolutely unstable since

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and according to the energy test of stability in rational mechanics (not to mention common sense), such states where the volume and pressure increase and diminish together are never realizable.

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Thomas Andrews’ discovery of the critical temperature provided Johannes van der Waals with the starting point for yet further theoretical insight.

It is evident from the van der Waals equation that at the critical temperature, all three values of V are identical. At the isopycnic point (p=pc, V=Vc, T=Tc) the volume V can therefore be set equal to the critical volume Vc, so that

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or

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The cubic form of the van der Waals equation gives, on dividing terms by pc:

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Identifying like terms

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Divide the third term by the second term to get Vc:

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Substitute Vc in the third term to get pc:

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Substitute Vc and pc in the first term to get Tc:

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The term a/V2 in the van der Waals equation identifies with the derivative (∂U/∂V)T, since it follows from the fundamental relation of thermodynamics (dU =TdS – pdV) that

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Using the Maxwell relation

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Hence

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Taking the van der Waals equation

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and differentiating with respect to temperature at constant volume

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Substituting in (1)

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The derivative (∂U/∂V)T can be computed from the experimentally determined Joule-Thomson coefficient:

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Cp may be obtained calorimetrically or spectroscopically, while (∂V/∂P)T and (∂(PV)/∂P)T can be obtained from data on the compressibility of the gas at constant temperature.

Hence (∂U/∂V)T = a/V2 can be computed for any gas, enabling the constants a and b in the van der Waals equation to be determined. This in turn allows the three critical constants, Vc, pc, Tc, to be calculated.

These critical data – for which van der Waals provided further means of estimation in 1880 with his “principle of corresponding states” – were invaluable in helping Dewar’s determination of the method of liquefying hydrogen (Tc = 33K) in 1898, and Onnes’ determination of the method of liquefying helium (Tc = 5.2K) in 1908.

The van der Waals equation constants a and b also proved useful in the early days of the industrial gases industry. Taking the equation deduced in 1862 by Joule and Thomson for the temperature change ΔT when a gas is subjected to a pressure drop Δp under isenthalpic conditions:

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If we apply the van der Waals equation as the equation of state, the Joule-Thomson equation becomes

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If a and b become sufficiently small

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For most gases the expression in brackets is positive at not-too-high temperatures. A cooling effect is therefore obtained, since Δp is always negative. Carl von Linde, who in 1895 established the first large-scale air liquefaction plant, based the construction of his Joule-Thomson cooling machine on this fact.

It is only when the attractive forces between gas molecules are very small at ordinary temperatures, and thus the constant a becomes minuscule – as is the case for hydrogen and the inert gases helium and neon – that the expression in brackets becomes negative and ΔT becomes positive, i.e. heating occurs. For cooling to occur, the temperature must be lowered below the inversion point, which according to the above equation is

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JD van der Waals 1837 – 1923

The Nobel Prize in Physics 1910 was awarded to Johannes Diderik van der Waals “for his work on the equation of state for gases and liquids”.

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HK Onnes 1853 – 1926

The Nobel Prize in Physics 1913 was awarded to Heike Kamerlingh Onnes “for his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium”.

photo credits: nobelprize.org

Photo credit: Scientific American

Photo credit: Scientific American

On Monday 3 December 1877, the French Academy of Sciences received a letter from Louis Cailletet, a 45 year-old physicist from Châtillon-sur-Seine. The letter stated that Cailletet had succeeded in liquefying both carbon monoxide and oxygen.

Liquefaction as such was nothing new to 19th century science, it should be said. The real news value of Cailletet’s announcement was that he had liquefied two gases previously considered ‘non condensable’.

While a number of gases such as chlorine, carbon dioxide, sulfur dioxide, hydrogen sulfide, ethylene and ammonia had been liquefied by the simultaneous application of pressure and cooling, the principal gases comprising air – nitrogen and oxygen – together with carbon monoxide, nitric oxide, hydrogen and helium, had stubbornly refused to liquefy, despite the use of pressures up to 3000 atmospheres. By the mid-1800s, the general opinion was that these gases could not be converted into liquids under any circumstances.

But in 1869, a paper appeared in a British journal which caused the scientific community to rethink its view.

The paper, entitled “On the Continuity of the Gaseous and Liquid States of Matter” and published in the Philosophical Transactions of the Royal Society, was written by 55-year-old Thomas Andrews, the vice-president of Queen’s College Belfast in Northern Ireland.

Dr. Thomas Andrews FRS (1813-1885). Photograph taken in Paris 1875 when Andrews was 62.

Dr. Thomas Andrews FRS (1813-1885). Photograph taken in Paris 1875 when Andrews was 62.

In addition to his administrative role, Thomas Andrews was also professor of chemistry at Queen’s College Belfast. From the start of his long professorial career he took an interest in gases, beginning with a study of ozone conducted jointly with the Scottish mathematical physicist Peter Guthrie Tait. Then in the summer of 1860, Professor Andrews turned his attention to the liquefaction of gases, a subject that the influential Michael Faraday had brought into the scientific spotlight during the 1820s; Faraday had been the first to liquefy chlorine gas in 1823.

Not surprisingly perhaps, Thomas Andrews went for the big prize in his initial experiments, in which he attempted to liquefy the ‘non condensable’ gases. And not surprisingly, he got absolutely nowhere – none of these gases showed any willingness to liquefy. Andrews then refocused his research on the liquefaction of carbon dioxide [called carbonic acid in his day], and in 1863 made the observation that would set him on the path to fame.

He wrote: “On partially liquefying carbonic acid by pressure alone, and gradually raising at the same time the temperature to 88° Fahr. [31.1°C], the surface of demarcation between the liquid and gas became fainter, lost its curvature, and at last disappeared. The space was then occupied by a homogeneous fluid, which exhibited, when the pressure was suddenly diminished or the temperature slightly lowered, a peculiar appearance of moving or flickering striæ [stripes] throughout its entire mass. At temperatures above 88° no apparent liquefaction of carbonic acid, or separation into two distinct forms of matter, could be effected, even when a pressure of 300 or 400 atmospheres was applied.”

Andrews had discovered the existence of a fundamental property of gases, which he called the “critical temperature” – the temperature above which no gas could be liquefied by pressure alone. If all gases had a critical temperature, then all gases could be liquefied if cooled below that temperature. The gases deemed ‘non condensable’ were simply gases whose critical temperatures were lower than the lowest achievable temperature at that time, which was around –110°C. What was needed was a new cooling principle to enable lower temperatures to be reached.

The good news was that the new cooling principle was already known to science. It had been discovered by James Joule and William Thomson (later Lord Kelvin) in a Manchester cellar a decade earlier.

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

In May 1852, James Joule and William Thomson conducted a famous experiment in the basement of Joule’s home in Salford, Manchester, England, in which they pumped pressurised air at a steady rate through a coil of lead pipe which was narrowly constricted at a certain point along its length and open to the atmosphere at its far end.

The apparatus was equipped with thermometers to measure the temperature of the airflow on either side of the constriction, which was insulated to prevent heat exchange with the surroundings.

Joule and Thomson observed a lowering of temperature. The air was cooled as it flowed through the narrowed section of the pipe, from a region of higher pressure to a region of lower pressure.

The discovery of this cooling effect, called the Joule-Thomson effect in their honour, was a landmark moment in the history of physical science and opened the way to cryotechnological applications of great scientific and commercial importance.

The hand pump which formed part of the original apparatus used by Joule and Thomson in 1852 is now in the collection of the Museum of Science and Industry in Manchester.

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Good fortune has smiled on many along the path of scientific discovery, and Thomas Andrews was among the fortunate. In 1869 – the year he published his paper – the Royal Society chose his work as the Bakerian Lecture of that year and thereby brought Andrews and his singular study to prominence. Across the scientific world, important people took notice.

In Scotland, it made a deep impression on James Clerk Maxwell, who was busy writing his textbook Theory of Heat (1871) and devoted several pages to analysing Andrews’ findings.

In the United States, it made a deep impression on Josiah Willard Gibbs, who cited Andrews’ experiments on carbonic acid as supporting evidence for a free energy function in the 1873 paper “A method of geometrical representation of the thermodynamic properties of substances by means of surfaces”.

In the Netherlands it set a physicist thinking. His name was Johannes van der Waals.

And in the rest of Europe, it set off a race among enterprising engineers to liquefy the gases hitherto termed non condensable. As we have seen, that race was won by Louis Cailletet, although in fairness it should be stated that a Swiss physicist called Raoul Pictet also succeeded in liquefying oxygen within days of Cailletet.

The two men used different cooling principles: Pictet opted for enthalpic cooling using liquid SO2 and CO2 while Cailletet employed Joule-Thomson cooling. The advantage of the latter method, as Joule and Thomson had shown during their pioneering experimental work in the 1850s, was that it allowed recirculation of gas cooled by previous passage through the throttle.

Joule and Thomson's recirculation design from 1853. The red arrow shows the location of the throttle.

Joule and Thomson’s recirculation design from 1853. The red arrow shows the location of the throttle.

This self-intensifying cooling technique was the key to the first large-scale gas liquefaction method developed by William Hampson (1895) and by Carl von Linde (1895), in which the gas was recirculated through a heat exchanger in order to lower the temperature of incoming gas:

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In the early days of liquid oxygen production from air, the biggest use by far for the gas was the oxyacetylene torch, invented in France in 1904, which revolutionized metal cutting and welding in the construction of ships, skyscrapers, and other iron and steel structures.

Cylinders of oxygen being loaded on a tractor-trailer truck (1914) owned by the Linde Air Products Company. Courtesy Praxair, Inc.

Cylinders of oxygen being loaded on a tractor-trailer truck (1914) owned by the Linde Air Products Company. Courtesy Praxair, Inc.

Another method of commercial liquefaction of air, which employed adiabatic cooling as well as the Joule-Thomson effect, was developed by Georges Claude (1901) in France:

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A by-product of the air liquefaction process was neon, which spawned a lucrative new industry in the shape of neon lighting. The first public demonstration of neon lights was at the Paris Motor Show of 1910.

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Read Part II

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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.

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.

Links to original papers

Thomas Andrews, “On the Continuity of Gaseous and Liquid States of Matter”, Phil. Trans. R. Soc. Lond. 1869;159:545-590
The paper that challenged the prevailing notion of non condensable gases, and opened the way to a new era of cryogenic science. It also led to deeper understanding of the thermodynamics of real gases [to be explored in Part II of this blogpost]

Suggested further reading

“Liquefaction of gases – Cailletet’s Experiments” Scientific American, Vol. XXXVIII No.8, February 23, 1878
A detailed contemporaneous account of Cailletet’s experimental apparatus, method and results.

Andrea Sella, “Pictet’s liquefier”
Raoul Pictet deservedly had joint priority with Louis Cailletet for the first liquefaction of a ‘non condensable’ gas, namely oxygen. Here is his story, as told by Professor Andrea Sella of University College London. This is one of Professor Sella’s Classic Kit series on the Royal Society of Chemistry website.

T. O’Conor Sloane, “Liquid Air and the Liquefaction of Gases” (1899)
A wonderful period piece made available online at archive.org by the Omania University in Hyderabad, India. The picture reproduction is awful, but for pure historical interest it’s well worth delving into. Sloane’s writing style is a fascination in itself.