Chapter18

Chapter18 - CHAPTER THE QUEST FOR LOW TEMPERATURES We have...

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Unformatted text preview: CHAPTER THE QUEST FOR LOW TEMPERATURES We have seen that the gaseous and liquid states are only distant stages of the same condition of matter, and are capable of passing into one another by a process of continuous change. A problem of far greater difficulty yet remains to be solved, the possible continuity of the liquid and solid states of matter. The fine discovery made some years ago by James Thomson, of the influence of pressure on the temperature at which liquefaction occurs, and verified experimentally by Sir. W. Thomson, points, as it appears to me, to the direction this inquiry must take; and in the case at least of those bodies which expand in liquefying, and whose melting—points are raised by pressure, the transition may possibly be effected. But this must be a subject for future investigation; and for the present I will not venture to go beyond the conclusion I have already drawn from direct experiment, that the gaseous and liquid forms of matter may be transformed into one another by a series of continuous and unbroken changes. Thomas Andrews, Philosophical Transactions of 1869 18.1 COOLING OFF How do you make something colder? Making something hotter is easy. For example, if you need to warm yourself on a chilly night, you can build a fire with little or no technology. But to cool yourself on a hot day is quite another matter. The difference between heating and cooling is reflected in our history: we’ve had the use of fire ever since Prometheus let the secret slip long before the dawn of history. But the secret of making things colder — refrigeration — is barely older than the oldest living person. 343 344 THE QUEST FOR LOW TEMPERATURES Nonetheless, some techniques of cooling are somewhat old. The ancient Sumerians used porous jugs for cooling household water. As some water seeped out it evaporated and cooled the rest, a technique used today in bottled water dispensers. Later in history, slaves were sent to bring snow from the mountains in summer. And later still, Leonardo da Vinci invented a form of air conditioning using air blown over a block of ice that had been stored since winter. As we turn to the past to see how low temperatures were reached, we find that the quest for low temperatures is closely tied to the history of understanding the basic states of matter — solid, liquid, and gas. As it turns out, the Sumerians had the right idea: evaporation, that is, the change of a liquid into its gaseous form, cools the liquid. That’s not the only method, but it is powerful and convenient for most purposes. However, to make something very cold — temperatures in the range 10—100 K (—263 to — 173°C) — further knowledge of the behavior of matter is needed. With the quest for low temperature came the discovery that all elements can exist in each of the basic states under the right conditions of temperature and pressure. We turn now to find what conditions govern the states of matter. Questions 1. Explain why you feel cool when you step out of the shower and into another room to dry yourself. 2. Explain why hot, humid weather is more uncomfortable than hot, dry weather. 3. When a frost is expected in Florida, why do citrus growers often spray their trees with water? 18.2 THE STATES OF MATTER That all matter can exist in three basic states — solid, liquid, and gas — is a discovery less than a century old. But the idea of the states of matter can be traced back to ancient Greece. The elements of Aristotle’s universe — earth, air, water, fire — also demonstrated the basic states of matter. The element earth reflected the solid appearance of matter, water generalized the liquid state, and fire and air represented the gaseous state. What was unknown to Aristotle and to others until the late nineteenth century was that any particular substance can exist in each of the three basic states. What conditions produce different forms of the same substance? The physical state or phase of a substance depends on both its temperature and its pressure and can be illustrated visually by a phase diagram such as that in Fig. 18.1. For example, at low temperatures and high pressures a substance such as H20 tends to be solid ice. At high temperatures and low pressures it tends to be gaseous, such as steam or water vapor, and somewhere in the intermediate range of temperatures and pressures it tends‘to be liquid. The curve that separates the solid and liquid regions on the phase diagram is called the melting curve. The curve between the liquid and gaseous states is the vapor-pressure curve, and that between the solid and gaseous states is the sublimation curve. Only on these curves can the respective phases coexist in equilibrium, and if two phases are in 18.2 THE STATES OF MATTER 345 Critical point Triple point Gas T Figure 18.1 A typical pressure—temperature (phase) diagram illustrating regions in which a substance exists as either solid, liquid, or gas. equilibrium, then specifying either the temperature or the pressure alone is sufficient to define the state. When a substance crosses one of these curves it is said to undergo a phase transition. When the phase transition is from solid to liquid, the substance melts. The structure changes from an ordered, crystalline array of molecules and atoms to a less-ordered configuration. To achieve this change of phase a certain amount of heat must be added which goes entirely into changing the phase and does not raise the temperature. If heat Q is required to melt a substance of mass m, then the ratio Q/m is called Lf, the latent heat of fusion. Hence Q = mLf- (18.1) The latent heats of fusion for several substances are listed in Table 18.1. As the phase diagram indicates, a substance can go directly from solid to gas without passing through the liquid state. This process, known as sublimation, also is accompanied by a latent heat. The most common example is the sublimation of dry ice: solid carbon dioxide sublimes at atmospheric pressure. That’s why dry ice is never wet. When a substance crosses the vapor-pressure curve, boiling occurs as liquid is changed into vapor. In this case the structure of the substance does not change radically as in the Table 18.1 Phase Transitions and Their Temperatures and Latent Heats for Various Substances at 1 atm Substance Melting point (K) LV (kJ/kg) Boiling point (K) Lv (kl/kg) Hydrogen 14 59 20 452 Nitrogen 63 26 77 200 Oxygen 55 14 90 213 Ammonia —- — 240 1369 Water 273 334 373 2257 Lead 600 25 2023 858 346 THE QUEST FOR LOW TEMPERATURES solid—liquid transition. Instead the molecules and atoms increase their separation distance. Just as in the case of melting, once a substance is at the boiling point, a certain amount of heat must be added to change the phase from liquid to vapor. If Q is the amount of heat necessary to vaporize a mass m of liquid at the boiling point, the ratio Q/m is called L, the latent heat of vaporization. Thus we have Q = va. (18.2) The boiling points and latent heat of vaporizations of a few substances are also listed in Table 18.1 Two points of special interest on the phase diagram are the triple point and the critical point, which are shown in Fig. 18.1. The triple point is a unique pressure and temperature where the three coexistence curves meet and at which all three phases can coexist. By international agreement, the triple point of water, occurring at 273.16 K and a pressure of 0.006 atm, is used as the fixed point in the absolute temperature scale. Triple-point temperatures and pressures for several other substances are listed in Table 18.2. The critical point signals the end of the vapor—pressure curve and it also occurs for a particular pressure Pc and temperature Tc. At any higher pressure and temperature, there is no distinction between liquid and gas; there is only a homogeneous fluid phase. A thorough study of the critical point of carbon dioxide was made by Thomas Andrews in the mid-nineteenth century. In an attempt to solve one of the great problems of his time — the liquefaction of gases - Andrews discovered what was to be a general property of all matter: above a critical temperature, no distinction between gas and liquid exists. This discovery, among others of the time, prompted physicists to investigate what dis- tinguishes one phase from another. Table 18.3 lists the critical temperatures and pressures for several substances. In Fig. 18.2, the same phases as in Fig. 18.1 are shown on a PV diagram. Here we find the solid state at high pressure and low volume and the gas at low pressure and large volume. In the shaded regions of the graph more than one phase can coexist. The triple point of the pressure—temperature diagram corresponds to the single, horizontal isotherm Table 18.2 Triple-point Temperatures and Pressures for Several Gases Substance Temperature (K) Pressure (105 Pa) Hydrogen 13.84 0.070 Nitrogen 63.18 0.125 Oxygen 54.36 0.002 Ammonia 195.40 0.061 Carbon dioxide 216.55 5.17 Water 273. 16 0.006 182 THE STATES OF MATTER 347 Table 18.3 Critical Temperatures and Pressures for Several Gases Substance Temperature (K) Pressure (105 Pa) Hydrogen 33.3 13.0 Nitrogen 126.2 33.9 Oxygen 154.8 50.8 Ammonia 405.5 112.8 Carbon dioxide 304.2 73.9 Water 647.4 221.2 labeled TP. On the other hand, the critical point is also a single point on this diagram that occurs at the maximum of the gas—liquid coexistence curve, indicating that there is a critical volume as well as a critical temperature and pressure. Figure 18.2 Phases of a given amount of a substance on a pressure— volume diagram. The states of a substance in equilibrium depend on three quantities — pressure, temperature, and volume; the mathematical relationship between these variables can be extremely complicated. Nonetheless we can represent the state graphically by a surface on a pressure—volume—temperature plot. Such a representation is shown in Fig. 18.3. The region under the PV curve shown in Fig. 18.2 is a projection of this surface on a plane T = const. Questions 4. Can a liquid boil and freeze at the same time? Support your answer by reference to a phase diagram. 348 THE QUEST FOR LOW TEMPERATURES Vaporization curve Sublimation \\curve Pressure ——> Figure 18.3 The state of a given amount of a substance can be represented by a surface in a plot of temperature, volume, and pressure. 5. For the phase diagram shown below, explain what happens as the substance changes states from (a) A to B, (b) C to D, (d) E to F, (e) G to H. 6. Can liquid become gas without passing through a phase transition? Can solid change into gas without passing through a phase transition? Explain your reasoning. 7. To raise the temperature of 1 kg of ice 1°C requires 2.0 kJ of heat; to raise the temperature of 1 kg of water 1°C requires 4.2 k] of heat. Using this information, plot a graph of temperature versus heat added for 1 kg of ice taken from — 10°C to vapor at 100°C. 18.3 BEHAVIOR OF WATER Let’s consider the states of a substance without which‘life on earth would not exist — water. The phase diagram for H20 is illustrated in Fig. 18.4. Imagine an ice cube inside 18.3 BEHAVIOR OF WATER 349 Pressure (atm) Critical 218 point 0 0.01 100 Temperature (° C) Figure 18.4 Phase diagram for H20. a sealed container that is much larger than the cube and from which the air has been evacuated. Even at very low temperature, sufficient water vapor exists inside the container to create the pressure called for by the sublimation curve. As we heat the container, the ice cube warms up, and the gas pressure increases slightly as water molecules evaporate from the surface. As this process occurs, the ice remains on the sublimation curve with the solid and gas states in coexistence. As we continue to heat the container, the temperature eventually reaches that of the triple point. At this point no further increase in temperature occurs until all the ice has melted. The added heat goes entirely into changing the phase from ice to water. Once all the ice has melted, the water can be heated further, thereby creating more water vapor. Since the water remains on the vapor—pressure curve, just enough water evaporates with every increase in temperature as called for by the curve (the amount depends on the size of the container). If we continue to warm the container, it eventually reaches 100°C, at which point the vapor pressure is equal to one atmosphere. If you opened the container at this point, the pressure of water vapor inside and the air outside would just balance. If you were to open the container and continue to heat it, you would have the same situation as a pot of water on a kitchen stove. Whereas before, the pressure could change because the can was sealed, now the pressure is kept constant and equal to that of the atmosphere. So heating will make the water evaporate without any change in temperature — that’s boiling. On the other hand, if you kept the container sealed, the water would pass through 100°C without any apparent effect, and the pressure would continue to rise as well. This is what happens inside a pressure cooker. There is nothing special about the boiling point, 100°C for water, except the accidental fact that at that point the vapor pressure of water happens to be equal to atmospheric pressure on the planet Earth, at sea level, on an average day. Table 18.4 lists the boiling point for water at various pressures. The phase diagram for water is slightly different from the typical diagram we saw earlier in that the melting curve bends backward. This peculiarity of water makes it possible to ski or ice skate because, at a temperature below 0°C, ice can be melted by simply applying pressure. The force of the skis or ice skates melts the ice at that particular place and the liquid lubricates the path. Otherwise, skiing on snow would be like skiing on concrete. 350 THE QUEST FOR LOW TEMPERATURES Table 18.4 Vapor Pressures of Water for Various Temperatures Temperature (°C) Pressure (105 Pa) 0 0.006 20 0.023 40 0.073 60 0.199 80 0.473 100 1.01 120 1.99 140 3.61 160 6.17 180 10.0 200 15.5 Questions 10. 11. 12. 13. 14. . In a car radiator the coolant water is under pressure. When the radiator cap is removed after the engine has been running for some time, why does the water boil and create a miniature geyser? . On hot, humid days why does a cold glass of lemonade “sweat”? That is, why do water droplets form on the outside of the glass? A real-estate developer proposes to create an artificial lake on the moon by filling a large crater with water. Would you invest in such a venture? Explain why or why not. Can it be too cold to ice skate? Explain. During extremely cold winters in places like Chicago, snow “vanishes” even though the temperature never rises above 0°C. What happens to the snow? Use the phase diagram for water to explain how a snowball is formed. In the “mile high” city of Denver (1 m cook. Explain why. 1.6 km), a 3-min egg takes longer to 18.4 LIQUEFACTION OF GASES 351 18.4 LIQUEFACTION OF GASES At the turn of the nineteenth century, a handful of scientists may have understood the phases of water, but even fewer saw a generalization to the states of matter. The idea crystallized through research into the liquefaction of gases. Earlier a Dutch scientist, Martin Van Marum, had accidentally liquefied ammonia gas under pressure while using it to test Boyle’s law; however, he didn’t grasp the significance of this first liquefaction. Until 1823, the liquefaction of gases remained tenuous. In that year, at the Royal Institution of London, a young chemist made an explosive discovery. While heating a compound in a sealed glass tube, Michael Faraday produced an oily-looking substance. When he filed the tube open to investigate the substance, the tube promptly exploded. But Faraday realized that he had liquefied chlorine gas. This great intuitive genius of the nineteenth century would later become famous for his researches in electromagnetism, but he revealed his talents in this early episode. Unlike Van Marum, Faraday understood perfectly the significance of his discovery, and immediately undertook a quest to liquefy other gases. Using an inverted U tube of glass, in one leg of which he could heat reagents to evolve the gas in question, while the other leg, under pressure, could be cooled, if necessary, to form the condenser, he succeeded in liquefying many gases. With that success, Faraday reached the plausible conclusion that all forms of matter could exist in each of the fundamental states, given the right conditions of temperature and pressure. The next great advance in understanding the states of matter came in 1835 when the French scientist Thilorier managed to solidify carbon dioxide (C02). The phase diagram of carbon dioxide is shown in Fig. 18.5. Although the phase diagram appears like the ones we discussed earlier, peculiar things happen because of the relation between the characteristic temperatures and pressures of C02 and the temperature and presssure at which human life on earth flourishes. Pressure (atm) Critical 73 point 56 5.11 —78.5 —56.6 20 31 Temperature (°C) Figure 18.5 Phase diagram for carbon dioxide, C02. At atmospheric pressure and temperature, carbon dioxide is commonly a gas. How— ever, if it is compressed without allowing its temperature to rise above room temperature, carbon dioxide will condense into a liquid. On the phase diagram this compression 352 THE QUEST FOR LOW TEMPERATURES corresponds to moving from room temperature and atmospheric pressure directly up the line to the coexistence curve, where liquid C02 coexists with gaseous C02 at high pressure. Liquefying gases is what Faraday had already accomplished. The advance made by Thilorier comes when, starting from these conditions, the pressure is reduced too quickly for heat from the surroundings to keep the temperature constant. We can imagine opening a valve on the container of liquid plus gaseous C02 that leads directly into a room at atmospheric pressure. And whoosh, a high-pressure jet of C02 blows forth into the room. Inside the container liquid C02 still coexists with gaseous C02, but now at reduced pressure. Since the two phases coexist, the carbon dioxide must be on the coexistence curve of the phase diagram. And to be on that curve at reduced pressure means that it must also be at reduced temperature. In other words, the liquid and gas in the container are cooled by evaporation. The process works for C02, or for that matter any other substance, just as it does for water. We can summarize this observation as follows: To stay on the coexistence curve, temperature must decrease when pressure is allowed to decrease, just as the pressure must rise when a substance is heated. As gas escapes from a container, liquid evaporates in order to try to replace the gas. The result of the evaporation is cooling. We can describe the same process in a more subtle way. Gas is a state of higher entropy than liquid. The entropy is higher not because the gas has a different internal structure from the liquid but because the gas is less dense. Each molecule of the gas has more space in which to move around, and that in itself is a form of disorder. In any case, when liquid evaporates to become a gas, the entropy per molecule increases. If this occurs at temperature T, then there is a corresponding transfer of heat equal to the heat of vaporization, Q = M, (18.2) and the change in entropy in going from liquid to gas is AS = —. (17.2) Example 1 Compare the change in entropy for 0.1 kg of ice melting at the triple point with that of the same mass of liquid H20 vaporizing at the boiling point. As Table 18.1 indicates, when ice melts it releases 334 kJ/kg of heat. Since AS = Q/T the change in entropy for this process is AS = (0.1kg)(334 X 103 J/kg)/(273 K) = 122 J/K. On the other hand, vaporization releases 2257 kJ/kg and the associated change in entropy is AS = (0.1kg)(2257 X 103 J/kg)/(373 K) = 6050 J/K. The entropy change is much greater in the liquid—vapor transition than in the solid—liquid transition. This comparison indicates that for water the increase in distance between molecules accompanying the liquid—vapor transition is more effective in increasing the 18.4 LIQUEFACTION OF GASES 353 entropy than the change of form from crystalline array to liquid, which occurs at nearly constant density. There is yet another way to describe this process. At any given temperature, the C02 molecules have the same kinetic energy, on the average, no matter whether they are in the liquid or the gas. According to Eq. (15.12) this energy is equal to % kT for each atom making up each molecule. The molecules of liquid, however, have lower potential energy than those of the gas; it is precisely this potential energy that binds the molecules together, causing the liquid to form. Condensation is a consequence of the electric force of attraction between the molecules when they are close together in the liquid state. Therefore, when molecules evaporate from liquid to gas, they are increasing their potential energy by escaping the attraction of their neighbors. If the gas plus liquid are isolated from contact with the rest of the world, so that overall energy must be conserved, the increase in potential energy must be balanced by a decrease in kinetic energy. But we’ve already seen that kinetic energy is equivalent to temperature, and so the temperature falls. On a molecular level this is why evaporation causes cooling of the gas. In the next section we’ll return to this explanation. Escape from the attractive forces of other molecules explains why the gas is cooled, but what cools the liquid? Inside the liquid, the average kinetic energy per molecule is % kT, but in fact, some molecules have more kinetic energy than that, and some less. The fastest-moving molecules are the ones most likely to escape into the gas. That leaves behind the slower, cooler molecules. That’s why the liquid cools. Of course, all of these different versions are not opposing views, but rather alternative descriptions of a single coherent understanding of the states of matter. The change in potential energy and the latent heat of fusion are really the same quantity viewed on different levels. _ Any liquid, not just C02, can coexist with its own vapor. But carbon dioxide differs from most other substances in one peculiar respect: its vapor pressure at the triple point is above 1 atm. When Thilorier opened his valve and allowed liquid C02 to cool by evaporation, as the pressure dropped, the mixture froze before it reached atmospheric pressure. C02 sublimes directly from the solid at a pressure of 1 atm. That’s why dry ice never becomes a liquid under ordinary circumstances. Thilorier’s discovery led him to a method of producing even lower temperatures. By mixing ether with carbon dioxide and pumping away the vapor to reduce the pressure below one atmosphere, Thilorier produced a temperature of — 110°C. Armed with this new advance in technology, Michael Faraday returned to the problem of liquefaction in 1844. Within a year he succeeded in liquefying all the known “permanent gases” except those he really wanted. Three elements — oxygen, nitrogen, and hydrogen — and three compounds — carbon monoxide, nitric oxide, and methane — failed to yield to his tech- niques. The quest to liquefy these permanent gases now took on the character of an open scientific challenge. To succeed where the great Faraday had failed was no small matter. The story of that quest is filled with twists and ironies. For example, the liquefaction of oxygen was accomplished in 1877 by Louis Paul Cailletet and Raoul Pierre Pictet, who achieved success within a few days of each other 33 years after Faraday’s failure set the 354 THE QUEST FOR LOW TEMPERATURES stage. The basic process was a kind of cascade in which one bath was used to liquefy another bath under pressure. This second bath in turn was further cooled by released pressure, and so on. In the final step, the pressurized oxygen gas (Pictet achieved a pressure of 250 atm at a temperature of — 130°C) did not liquefy. The critical point of oxygen hadn’t been reached. However, when the pressure was subsequently released, both Pictet and Cailletet found that a cloud of partially liquefied oxygen was produced. The liquefaction had occurred because expansion of a gas by itself produces cooling. Questions 15. Explain why the mist coming from an aerosol spray can is cool to the touch. 16. Formulate a simple theory of fog formation by citing the conditions that induce fog and the physical process that occurs. 17. Using the data in Table 18.1, calculate the entropy change associated with (a) lead melting, (b) ice melting, (c) nitrogen vaporizing, (d) carbon dioxide vaporizing. 18. Offer an explanation for the comparative difference in your answers to parts (c) and (d) in Question 17. 18.5 THE JOULE—THOMSON EFFECT Beginning in 1845 and culminating in 1862, Joule, and later Joule and Thomson (the same Thomson who later became Lord Kelvin), conducted a series of experiments to test the interchangeability of work and heat. Their investigations showed that under certain circumstances the expansion of a gas into a chamber held at a constant pressure would produce cooling. The physical reason turns out to be the same one that causes a liquid to cool when it evaporates. The cooling effect they discovered, known as the Joule—Thomson effect, provided experimental evidence for the existence of intermolecular forces between gas molecules. It is these forces that account for the structural changes in a substance as it passes through different phases as well as for the deviations of real gases from the ideal-gas law (which were discussed in Chapter 15). Further research revealed that intermolecular forces consist of two different interactions between pairs of molecules. One force is a weak, relatively long-range attractive force known as the Van der Waals force. The second force is a strong, short-range repulsive force which prevents molecules from coming too close together. The regions in which each force dominates are indicated in Fig. 18.6 where the potential energy of a molecule is plotted as a function of the distance between two interacting molecules. These forces are electrical in origin and depend on the structure of the particular molecule. In their experiments, Joule and Thomson kept a gas at constant pressure and allowed it to flow continuously through a porous plug of tightly packed cotton, as shown in Fig. 18.7. As the gas flows from the left chamber at pressure P1 into the right chamber at lower pressure P2, the pistons move, changing the volume, so as to keep the pressures constant. The porous plug, or nozzle, merely supports the pressure difference and the entire apparatus is isolated so that the process is adiabatic. 18.5 THE JOULE—THOMSON EFFECT 355 L/(r) / repulsion equilibrium separation —+ r intermolecular separation Potential energy \ attraction :— l | | | l | | | | Figure 18.6 Potential—energy diagram for a molecule in a real gas. The force is repulsive at small r where U(r) slopes down, and attractive at larger r where U(r) slopes up. Let’s discuss why the Joule—Thomson effect indicates the existence of intermolecular forces. As the gas is pushed from the left chamber of Fig. 18.7, decreasing its volume from V1 to zero, the work done by the gas is simply W1 = —P1V1 because the pressure is held constant. On the other side of the nozzle the piston does an amount of work W2 = P2 V2 as the volume expands from zero to V2. According to the first law of thermody- namics, Q = W + AU, (16.3) porous plug Figure 18.7 Schematic of the Joule—Thomson porous plug apparatus. and since the process is adiabatic, Q = 0. Therefore, the change in internal energy of the gas is equal to the negative of the net work done by the gas: AU = U2 _ U1 = _W = —(_P1V1 + P2V2) = P1V1 _ P2V2. From this we see that there is a conserved quantity for the process: U1 + P1V1 = U2 + P2V2. Now if we assume an ideal gas, then both the internal energy and PV are functions only of temperature: U = quT, (15.13) PV = NkT. (15.9) 356 THE QUEST FOR LOW TEMPERATURES Consequently, the temperature of the gas should remain constant during the process. But the observation is that the Joule—Thomson process produces a cooling of the gas. This departure from ideal gas behavior is attributed to intermolecular forces. The intermolecular forces contribute potential energy, so the internal energy of the gas is not simply due to the kinetic energy of individual molecules. Let u denote the potential—energy contribution due to intermolecular forces. Then the internal energy of the gas is given by U = quT + u. (18.5) According to Eq. (18.3), we should have When the gas cools, the right-hand side of this last result is found to be positive, that is, PIVI —P2V2>0, which in turn implies Au > —quAT. (18.7) Since AT is negative, this means Au is positive. As the gas expands, the potential energy of the molecules increases, because the molecules are pulling away from each other’s attractive potentials. This is exactly what happens when a liquid evaporates. The increased potential energy is balanced by a decreased kinetic energy, or slower atoms, so the gas is cooler. If the initial temperature and pressure are high enough, the repulsive part of the intermolecular force may be dominant. In this case, Au is negative, so the gas should actually warm. Warming of the gas is not only expected, but also observed under these conditions. Of course, intermolecular forces are responsible for change of phase as well. The difference between a gas and a liquid is that the molecules of a gas on the average are too far apart to have much influence on each other, while in a liquid, they are close enough for the Van der Waals forces between them to cause them to attract and condense. Expressed in energy terms, liquid molecules have more negative potential energy. This potential energy is the latent heat. The Joule—Thomson effect creates a decrease in temperature that is found to be nearly proportional to the difference between the pressures of the two chambers and provides a practical method for liquefying gases. In 1895 the German chemist Karl von Linde adapted the process for the large-scale liquefaction of gases. His process did away with the cascade effect and makes use only of the gas to be liquefied, for example, nitrogen. Cooled, compressed nitrogen passes through an inside tube and through a Joule—Thomson ex- pansion valve and back through an outer tube. The gas that is not liquefied is returned to the compressor by means of a heat exchanger, where the incoming compressed gas is cooled to a lower temperature by the outgoing cold product. Questions 19. Using the potential-energy curve in Fig. 18.6, indicate how the potential energy decreases as molecules of a gas come closer together. 18.6 A FINAL WORD 357 20. Use a potential-energy curve like the one in Fig. 18.6 to explain why a gas cools when it expands. 21. In the Joule—Thomson process, determine whether net work is done on the gas or by the gas, if (a) the gas is ideal, (b) cooling occurs, (c) warming occurs. What is the connection between net work and intermolecular forces? 18.6 A FINAL WORD After nitrogen and oxygen had been liquefied, only one permanent gas remained — hydrogen. Scientists knew that if it could be liquefied at all, doing so would be a great achievement. And so two men set out in a race to liquefy hydrogen. They were Sir James Dewar, who was Faraday’s successor as Professor at the Royal Institution in London, and Heike Kammerlingh-Onnes at the University of Leiden, in the Netherlands. Each of these two great scientists spent decades pursuing the quest. In the end, Sir James Dewar won the race. He gained the lead by inventing the double-walled evacuated flask to retain cold liquids. It is known in scientific circles as the Dewar flask and in popular terms as a thermos bottle. However, in a final twist of irony, the rules of the race changed just before the finish line. In 1895, just before Dewar succeeded in producing liquid hydrogen, his countryman, William Ramsay, isolated terrestrial helium, an element previously known only to exist in the sun. Kammerlingh-Onnes, knowing that he had lost the race for liquid hydrogen, immediately abandoned the pursuit and laid plans for an assault upon helium. That siege lasted another thirteen years. To undertake it made sense only because of the work of one of his countrymen, Johannes Diderik van der Waals. In the 1870s, Van der Waals developed a theory of the fluid state that took into account the fact that a compressed gas, especially above its critical point, could have potential energy. Such a gas, he argued, would not obey the ideal-gas law, PV = NkT. [See Eq. (15.10).] In fact, by careful observation of the deviations from that law, he concluded that it would be possible to deduce the strength of the forces between the molecules. But those forces were responsible for the Joule—Thomson cooling, and in fact, liquefaction itself. Thus, by careful measurements of the properties of helium gas, even well above its critical temperature, it would be possible to predict both the conditions under which the Joule—Thomson cooling would be effective, and the temperature and pressure that had to be reached in order to liquefy it. The results of this analysis, which Kammerlingh-Onnes carried out, gave him three indispensable pieces of information. First, helium did behave like other gases; in other words, it could be liquefied. Although the effort was daunting, it would not be wasted. Second, when liquefied, the temperature of helium would be much lower than that of liquid hydrogen. So if he succeeded, he and not Dewar would be the winner of the quest in history’s eyes. And finally, by giving him in advance the values of temperature and pressure he would have to attain, the analysis made it possible to undertake the job in a rational and orderly way. 358 THE QUEST FOR LOW TEMPERATURES Kammerlingh-Onnes and his research group succeeded in liquefying helium on 10 July 1908. The critical temperature turned out to be, as predicted, only 5 K — just five degrees above absolute zero. The last “permanent” gas had been liquefied. For his research into the properties of matter at extremely low temperature, Kammerlingh-Onnes was awarded the Nobel prize in physics in 1913. Today, liquid helium is made in huge commercial plants for use in scientific labo- ratories and industry as is liquid nitrogen and oxygen. The cost is low: a liter of liquid nitrogen costs about as much as a liter of milk, and a liter of liquid helium costs about as much as a liter of vodka. ...
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This note was uploaded on 03/30/2010 for the course PH 1a taught by Professor Goodstein during the Fall '07 term at Caltech.

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Chapter18 - CHAPTER THE QUEST FOR LOW TEMPERATURES We have...

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