## Joule, Thomson, and the birth of big science

Posted: January 1, 2013 in classical thermodynamics
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Photo credits: see below

In early May 1852, in the cellar of a house in Acton Square, Salford, Manchester, 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 – 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.

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.

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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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:

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 narrowing. 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

$W=P_{1}V_{1}-P_{2}V_{2}$

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:

$\Delta U=U_{final}-U_{initial}=Q+W$ [the + sign shows that W represents work done on the gas]

$U_{2}-U_{1}=0+P_{1}V_{1}-P_{2}V_{2}$

$U_{2}+P_{2}V_{2}=U_{1}+P_{1}V_{1}$

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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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.

The slope at any point on an isenthalpic curve is known as the Joule-Thomson coefficient μJT. When the coefficient is positive, cooling will occur (remember P2 is always less than P1), and when it is negative, heating will occur. The maximum point of the curve, at which the coefficient is zero, is called the inversion point for the isenthalpic curve in question.

The Joule-Thomson coefficient is defined:

$\mu_{JT}=\left ( \frac{\partial T}{\partial P} \right )_{H}$

This derivative 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:

$f(P,T,H)=0$

One of the useful relationships among first partial derivatives that follows directly is:

$\mu_{JT}=\left ( \frac{\partial T}{\partial P} \right )_{H}=-\left ( \frac{\partial T}{\partial H} \right )_{P}\left ( \frac{\partial H}{\partial P} \right )_{T}$

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:

$\left ( \frac{\partial H}{\partial P} \right )_{T}=0$

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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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.

(left) William Thomson / highfields-arc.co.uk (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 / Wikipedia

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