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Many gases can be liquefied through refrigeration using other substances as coolants. However, hydrogen and helium have critical temperatures far below even the freezing points of other substances, so another method is needed to liquefy these gases. (The critical temperature of a substance is the temperature at which liquid and gas are indistinguishable.) Near the end of the nineteenth century, two physicists worked to liquefy these gases: Heike Kamerlingh Onnes, in Leiden, and James Dewar, in London. Dewar succeeded in liquefying hydrogen before Kamerlingh Onnes. By 1908, though, Kamerlingh Onnes had extended upon Dewar's methods to devise his own helium liquefaction system, which he called a "helium liquefactor."
In order to cool these gases, both Kamerlingh Onnes and Dewar used Joule-Thomson cooling. James Johnson and William Thomson (also known as Lord Kelvin) had shown in 1852 that certain gases would cool if allowed to expand adiabatically (occurring without loss or gain of heat) through a porous plug under constant enthalpy conditions. The most important condition that must be met is that the gas must start below a critical temperature, called the inversion temperature. Gases above their inversion temperature would warm if they expand under constant enthalpy, but gases below that temperature cool. For most gases, the inversion temperature is quite high, but for hydrogen it is 202 kelvins (-71 Celsius), and even lower, at 51 kelvins (-222 Celsius), for helium, so these gases must first be cooled by some other means below these temperatures before Joule-Thomson cooling can be used. The inversion temperature of helium is lower than the freezing points of nitrogen and oxygen, so Kamerlingh Onnes and Dewar both realized that liquid hydrogen must first be produced to precool the helium.
The helium liquefaction system that Kamerlingh Onnes built was in essence a series of liquefaction systems, with the helium liquefactor being simply the last step. The process started with a standard cascade refrigeration system to liquefy oxygen. The liquid oxygen was used to cool the hydrogen below its inversion temperature. Kamerlingh Onnes used Johannes Diderik van der Waals's principle of corresponding states to show that the critical point of helium was near 5 kelvins, thus a single-stage Joule-Thomson cooling, such as Dewar was using, would not suffice to liquefy helium. Thus, Kamerlingh Onnes built an iterative system. Helium was compressed, cooled with liquid hydrogen, and then allowed to expand, cooling it further. This colder helium was then used to cool more compressed helium, which was then allowed to expand, producing even colder helium. Through a sequence of such steps, the temperature of the helium could be lowered to the point at which it began to condense as a liquid. Using this system, Kamerlingh Onnes succeeded in liquefying helium on July 10, 1908, becoming the first scientist to do so.
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