CHANDLER LECTURE The Chandler Lecture for 1935 was delivered a t Columbia University, Xew York, on May 28, 1936, by William Francis Giauque, of the University of California. P r o f e s s o r Giauque’s announcement, in 1929 in collaboration with H. L. Johnst’on,of Ohio State University, that three kinds of oxygen existed instead of one, each variety or isotope having a different weight, stimulated world-wide research on all of the lighter elements, including hydrogen, nitrogen, and carbon, and led ultimately to the identification component of of a new isotope of hydrogen-deuterium, “heavy water”-by Harold C. Urey, of Columbia University. Of equal importance is Professor Giauque’s work with very low temperatures and entropy measurements, of which he is said to have made the most systematic study of anyone in the world. His method of obtaining low temperatures through the use of a magnetic engine has enabled chemists to reach temperatures one hundred times as low as could previously be attained. The Charles Frederick Chandler Foundation was established in 1910 when friends of Professor Chandler presented to the trustees of Columbia University a sum of money, and stipulated that the income was to be used to provide a lecture
by an eminent chemist and also a medal t o be presented to this lecturer in further recognition of his achievements in the chemical field. The previous lecturers and the titles of their lectures are as follows: 1914 1916 1920 1921 1922 1923 1925 1926 1927 1928 1929 1931 1932
1934
L. H. Baekeland W. F. Hillebrand
Some Aspects of Industrial Chemistry Our Analytical Chemistry and Its Future The Littlest Things in Chemistry W. R. Whitney F. G. Hopkins Newer Aspects of the Nutrition Problem E. F. Smith Samuel Latham Mitchill-A Father in American Chemistry R. E. Swain Atmospheric Pollution by Industrial Wastes E. C. Kendall Influence of the Thyroid Gland on Oxidation in Animal Organism The Constitution of Coal-Having S. W.Parr Special Reference to the Problems of Carbonization Moses Gomberg Radicals in Chemistry, Past and Present Chemistry and Leather J. A. Wilson Electrochemical Interactions of TungIrving Langmuir sten, Thorium, Caesium, and Oxygen James B. Conant Equilibria and Rates of Some Organic Reactions George 0. Curme, Jr. Synthetic Organic Chemistry in Industry The Stuff of Life Jacob G . Lipman
Temperatures below 1”Absolute W. F. GIAUQUE Department of Chemistry, University of California, Berkeley, Calif.
HE adiabatic demagnetization method of producing very low temperatures resulted from a series of investigations relating to the third law of thermodynamics. This important natural law enables us to determine the conditions of chemical equilibrium from calorimetric data alone, and the practical advantages and economy which result are well known. The third law of thermodynamics1 (26)states that all substances in the perfect crystalline state are without entropy a t the absolute zero of temperature. Thus if the absolute zero be taken as a limit of integration, the entropy of a substance may be evaluated by means of the expression,
s
=AT$
Principally for this reason, a number of chemical laboratories are actively engaged in low-temperature calorimetric investigations. However the absolute zero of temperature cannot be attained and extrapolation is unavoidable in evaluating entropy by means of Equation 1. Until some twelve years ago such extrapolations were simply and somewhat too confidently based on the assumption that no appreciable calorimetric effects occurred in the temperature region below 1’ absolute. In 1924 Nelson W. Taylor and the writer collaborated in conducting a seminar on magnetism a t the University of California. I n the course of this seminar the writer presented a thermodynamic treatment of magnetic phenomena, and in considering certain available magnetic data it became evident that magnetic fields could remove large amounts of entropy
dT
where C , = heat capacity T = absolute temperature 1 A discussion of the historical development of the third law of thermodynamics leading to the accepted statement of Lewis and Gibson is given by Lewis and Randall.
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744
VOL. 28, NO. 6
INDUSTRTAL AND ENGINEERING CHEMISTRY
stances are concerned] their magnetic systems are substantially a t the absolute zero condition, even a t ordinary temperatures. A somewhat similar situation holds for ferromagnetism. Ewing (4) advanced the idea that the elementary magnets, through mutual i n t e r a c t i o n , formed groups with the total magnetic moment acting as a unit. This qualitative idea agrees we11 with the facts of ferromagnetism. It may be said that ferromagnetism corresponds to a crystallization of the elementary magnets into an ordered arrangement within the groups. The groups increase in size and perfection as the temperature is lowered, a n d even a t ordinary temperatures the magnetic system 0 of iron, for example, appears to have attained a state 0 I 2 3 4 5 6 of nearly zero entropy, although other degrees of MH/RT freedom are still active. Langevin (91) explained paramagnetism in terms FIQURE 1. COMPARISON OF WOLTJER AND KAMERLINGH ONNES’DATA WITH THE THEORETICAL CURVEON THE INTENSITY OF MAGNETIZATIONof the random orientation of atomic or molecular OF GADOLINIUM SULFATE OCTAHYDRATE magnets. He obtained, from classical theory, an equation for the intensity of magnetization, I , as a function of the field strength, H : from some substances a t temperatures so low that it had formerly been assumed that no appreciable entropy remained. H Z = M coth M RT Faraday was the first to realize that all substances are affected by magnetic fields, although only those classed as where M = molal magnetic moment ferromagnetic exhibit large effects a t ordinary temperatures. R = gas constant He gave the name “diamagnetic” to those substances which Langevin’s equation leads to magnetic saturation at infinite are weakly repelled by a magnet and “paramagnetic” to those attracted. By far the larger number of subptances exhibit field strength. Curie’s law, which applies only to the initial diamagnetism. The magnetic susceptibility of this class is, magnetic susceptibility, is a special case of Equation 4. as a first approximation, independent of temperature. HowOne of the important consequences of the work of Curie and ever a large group of compounds, including most of those of of Langevin was the realization that ideal paramagnetism is titanium] vanadium, chromium, manganese] iron, cobalt, a function of H / T . In such a case, for example, a magnetic nickel, copper, and the rare earth elements, are paramagnetic. field of 30,000 gauss acting a t 1” absolute will produce t h e same efiect as a field of about 9,000,000 gauss a t ordinary An outstanding characteristic of paramagnetic substances is that they approximately follow the law, temperatures. This behavior stimulated experimental investigations of magnetic phenomena a t low temperatures, xT = C = constant (2) particularly by Kamerlingh Onnes and his associates a t the University of Leiden. The best example was an investigadiscovered experimentally by Curie (1). x may represent tion by Woltjer and KameTlingh Onnes (26). They measured the gram magnetic susceptibility, or, in connection with a the intensity of magnetization of gadolinium sulfate octahyphysical interpretation, it is preferable to consider the molal drate a t fields up to 22,000 gauss and a t temperatures as low as susceptibility. Paramagnetic susceptibilities should be cor1.3” K. At this temperature i t was possible to approach rected for the universally present, but masked, diamagnetism within 5 per cent of magnetic saturation. It was principally before applying Curie’s law. Ferromagnetic materials always these data which led to the deduction, mentioned above, become paramagnetic a t higher temperatures] the transforthat magnetic fields can remove comparatively large amounts mation usually occurring over a range of temperature. A of entropy from paramagnetic substances even in the region well-developed ferromagnetic situation undergoes little change near 1O absolute. with temperature. From thermodynamics we know that the temperature coefFROM the second law of thermodynamics we have the ficient of the reversible work, or free energy, required in any equation, process is equal to the negative of the resulting entropy change. Since the work required to magnetize a substance is
(
4;)
0
it is evident that our present interest is concerned with paramagnetism. Only in this case does the susceptibility have an appreciable temperature coefficient and the substance have a corresponding change in entropy on magnetization. Both diamagnetic and ferromagnetic substances appear to be without appreciable entropy as far as their magnetic systems are concerned. Diamagnetism is a second-order effect which remains when the electron systems of atoms and molecules attain an ordered state with complete cancellation of their individually powerful magnetic moments. This ordered arrangement corresponds to the situation characterized by zero entropy. In other words, as far as diamagnetic sub-
and the conclusion was based on the application of Equation 6 to the low-temperature magnetic observations. Since the entropy was shown to decrease when a magnetic field is applied, an amount of heat corresponding to TAS, where AS is the entropy accompanying isothermal magnetization, must be evolved. If the magnetized substance is then thermally isolated from its surroundings and the magnetic field is removed, the demagnetization will occur adiabatically with a corresponding reduction in temperature. Calculation of orders of magnitude from the data of Woltjer and Kamerlingh Onnes was so promising that adiabatic demagnetization was proposed (5, 6 ) as a practical method of producing formerly unattained temperatures in the region below 1” absolute. Debye (2), working independently] later announced similar conclusions.
,
It was evident that Langevin's equation and Curie's law were inconsistent with the third law of thermod?namics, From the latter and Equation 5, we obtain
in which A 8 becomes infinite instead of zero at the ahsolute
zero of temperature. Further, the application of Equation 5 tu Langevin's equation shows that it would hc necmsaq io remove Sn infinite amount of entropy in producing magnetic sat.uration. Langevin had, of course, used the methods known as classical theory in deriving his equation, and it was clear that the snhntitution of a finite number of qiiaiitum states would remove this difficulty, which is a general characteristic of the classical method of treatment. In fact this change had been proposed hy Pauli (%5) in connection with an atrtempt to interpret initial susceptibility on a quantmn basis. Thermodynamics does not inquire concerning the meclranism of a process, but quantum statistics often goes far m interpreting complicated results in tenns of coinparatively simple elementary mechanisms. Figure 1 shows the data of Woltjer end Kamerlingh Onnffi? (9%) compared with a curve calculated from quantum statistics. The agreement is remarkably good, especially in view of the fact that the calculation is in no way dependent on the data which it ropresents. The equation (0)for the curve given in Figure 1 is
where the summations cover four tenns with the values of cos H equal t.o 1, 5/7, 3/7, and 1/7, respectively. In the derivation it was considered that each trivalent gadolinium atom is an elementary magnet with 7 Bohr units of magnetic 1110merit due to electron spin. Each elementaw magnet was assumed to act independently under the influence of the esternal field. We know that the last assumption is only approximately true and that interactions must, in accordance with the third law of tlierniodynamics, produce a very cornplete deviat,ion from Equation 7 near the absolute zero. In fact Kiirti arid Simon (18) showed by means of beat capacity measurements on gadolinium sulfate octalrydrate that deviatiolln were hecorning appreciable even above 1" K. BEFORE proceeding with the adiabatic demagnetiza0 tion . esperiments i t was necessary to enlarge the facilities for the liquefaction of hydrogen, and build equipment for thr liquefaction of hrlium and a suitable magnet. Space does not perniit R det.ailed description of the many interesting ieatores of these developiiients, which, although started early in 1925. did not reach a sufficient state of completion to perniit the use oi adiahstic deinngoetization in atPl0"ilE 2. ( F o p ) t a i n i n g temperatures below 1°K. INTERCHANGERS (7, 3 ) until March 19, 1933. HowAND GLASSDEWAR TUBES OF THE H Y ever. Figures 2 to 8 give some idea DROGEN ~ A I Q U E F ~ E R of blre equipment used. $11 apparat.w was designed with t,he idea of utilizing tho iow- temperatures prodiiced for useful scient,ific investigat,ion rather than to attain low tanixirature as an end in itself: I.'igurr 2 pictures 1hr h y d r o g e n iiqiwfirr twkeri :Lpnvt. It i~ Iae;it.ed under :i vcntilnt.ing I t o d The liquefirr is monntrd on :I hylmuli? elwritor irr t,lie cent,ri. On ritlwr sidr of tlir c m t e r , in ordrr. isre intwchavprs, sil-
746
INDUSTRIAL AND ENGINEERING CHEMISTRY
vered glass Dewar tubes, Dewar cases, and outer metal cases. The expansion valve is on the left and the interchangers above remove the cooling effect from Ohat fraction of the hydrogen gas which returns to the compressor. On the right the lower coils are immersed in liquid air boiling under reduced pressure. After evaporation of the liquid air, the gaseous air transfers the remaining cooling effect to the interc h a n g e r s above and l e a v e s the top a t approximately room temperature. The several sections of the right and left interchanger systems are connected by means of high-pressure 1i n e s i n s i d e the supporting bridge a t the top. A high vacuum is main. tained in the bridge to protect the cold hydrogen gas from heat leak. Figure 3 shows the hydrogen liquefier assembled and ready for operation. On the left, attached to the liquid hydrogen outlet, is shown a metal Dewar vessel. Such containers, of the type ordinarily used for liquid air, are satisfact o r y f o r transporting liquid hydrogen. On the right is a Dewar vessel from which liquid air is drawn into the liquefier as needed. B o t h t h e 1 i q u i d hydrogen and liquid air are transferred by v a c u u m - j a c k e t e d tubes above the liquefier. The rate of liquefaction may be observed on the gas gage a t the FIGURE 5. BACKVIEW OF MAGNET right.holder Against the wall WITH SECTIONS CUT A W A Y a t the left are simple but e f f e c t i v e low-messure safety valves of rubber tubing. The liquefier is operaied a t a pressure of about 170 atmospheres and produces approximately 25 liters of liquid hydrogen per hour. After the liquefier has been cooled, a little over 1 liter of liquid air is required for each liter of liquid hydrogen produced. Figure 4 shows the adiabatic demagnetization apparatus and the helium liquefier. The helium liquefier is directly behind the steps, to the left, in order, are the magnet, a container of liquid air, a water rheostat used to avoid arcing when the magnet current is reduced, and various operating switches. The liquid air supply and helium liquefier are connected to the apparatus within the interior of the magnet by vacuum-jacketed transfer tubes shown above the magnet. T o the right of the helium liquefier is a 50-liter Dewar vessel of liquid hydrogen which is transferred to the interior of the liquefier where it is used to cool the compressed helium gas t o 14" K. A magnetic valve on a vacuum pump line automatically kee s the liquid hydrogen boiling a t a pressure of about 5.5 cm. o?mercury, corresponding t o about 14" K. On the right is the two-unit helium purifier. The helium gas is freed of oil vapor from the compressor and any air impurity on each passage through the cycle. Oil and readily condensed gases are removed by contact with a large interchange surface in one of the units, and air is removed by means of adsorption on charcoal in the other, both units being cooled to liquid air temperatures. Figure 5 represents a back view of the iron-free solenoid (7) with a section cut away to show the sample tube within the liquid helium bath. The liquid helium is protected by glass
VOL. 28, NO. 6
D e w r tubes and liquid-air cooling coils. Approximately 0.9 cubic meter (25 cubic feet) of cooling oil per minute is circulated over the bare conductors of the solenoid. The magnet is ordinarily operated a t 40-50" C. to allow the use of a moderate-sized external cooling system. Throughout a comparatively large working space in t,he center, the magnet produces a very homogeneous field of 8000 gauss with a power input of 100 kw. It would produce about 25,000 gauss if the necessary power were available. Figure 6 shows a two-stage rotary vacuum pump which is used for evaporating liquid ajr or liquid hydrogen from the hydrogen and helium liquefiers, respectively. Although of moderate size it can remove approximately 19 cubic meters (525 cubic feet) of gas per minute a t a pressure of 2 em. of mercury (its limiting pressure is about 1 mm.). The pump was designed and built by George F. Nelson, chief mechanician of the department. The liquefaction equipment shown previously was constructed in the department shops under his supervision. To the left may be seen the small centrifugal oil pump used in the magnet cooling system. The larger compressor in Figure 7 is used in connection with the liquefaction of air. At the right nea,r the wall are two ammonia compressors. The larger one is used for precooling air to be liquefied, and the smaller one to remove readily condensable impurities, such as water and compressor oil vapor, from hydrogen. In front of the ammonia-condenser pipe system, which is near the wall, may be seen one end of the somewhat similar concentric-pipe oil cooling system of the magnet. Figure 8 shows the helium compressor in the foreground, and behind the four gages the hydrogen compressor is partly visible. These two vertical compressors were specially designed with the generous cooperation of the builder, the Rix Company of San Francisco. High-speed operation, which we consider economical and desirable for hydrogen and helium compressors, permitted the use of smaller machines. Provision was made to prevent leakage or contamination of the pure gases by air. The high-pressure storage cylinders ,for helium and hydrogen are shown a t the right. Figure 9 shows a typical magnetic cooling apparatus of the type introduced by D. P. MacDougall and the writer. The glass sample tube containing the paramagnetic substance is surrounded by a bath of liquid helium, but they may be isolated from each other by means of an insulating vacuum space. Liquid helium boils a t 4.22" K., but it is not difficult to maintain temperatures as low as 1.5" K. by means of reduced pressure. The bath temperature is readily measured by means of helium vapor pressure thermometers shown near the top and near the bottom of the sample. T h e procedure in obtaining temperatures below 1" K. is
as follows: A small amount of helium gas is admitted to the insulating vacuum space to permit the conduction of heat. The magnetic field is then applied, and the heat evolved during magnetizat,ion conducted to the bath, boiling away a small amount of the liquid helium. Keeping the field constant, the helium gas is pumped from the insulating vacuum space. When the sample has been thermally insulated by a vacuum, the removal or decrease of the magnetic field produces adiabatic lowering of the temperature, To obtain still lower starting temperatures, we have found it convenient either to liquefy a small amount of helium in the sample tube or in a small chamber located a t the top of the sample tube as shown in Figure 9. The glass line leading from the chamber is connected to a mercury diffusion pump which permits the attainment of lower pressures than those obtainable on the bath. Figure 10 shows a more recent type of apparatus being used by J. W. Stout, C. W. Clark, and the writer. This apparatus permits liquid helium to be kept above the sample tube even when the liquid level is well down in the Dewar vessel. The upper helium chamber can be filled with liquid a t will by forcing the helium from below through the vacuum-jacketed transfer tube by means of a very small difference in pressure since the density of liquid helium is 0.125 gram per cc. a t 4" K.
WE HAVE stated that adiabatic demagnetization pro-
P
duces very low temperatures, b u t one m a y well ask how we actually know this t o be true. An essential of thermometry is that some property of the measuring device must vary with temperature and this property must then be calibrated in terms of t h e thermodynamic scale. Woltjer and Kamerlingh Onnes (ZB),in reporting their work
oo gadolilliuiri sulfate, remarked that magnetic susceptibility could be used as a variable for thermometric purposes. This property was used for thermometry in all the early admhatic demagnetization experiments below 1 X . In order to measure the magnetic susceptibility, a coil consisting of many thousand turns of h e copper wire was placed about the sample but was separated from i t by the insulating vacuum space as shown in Figures 9 and 10. Although the coil has no direct connection with the sample, the magnetic susceptibility of the material may be deduced from the inductance of the coil. This is possible because of thp
F I Q U R E7. (Right) C o r p n E s s o n s Fon LIQVEFACSI~N OF Am Ii'IQUED-8,
(BChO) AND IfIQH-PAESSUflE GAS
CorPREsSoE8
STORAQE FOR LIQUEFACTION 01 HYDROQEN AND HELIUM ~ ~ l G l n t k ~ l (Above)Vncu-L.:\I $. 1'1.311' FOl' )1:VAPOH4TINO
that, wheii 11 coil d inductance L" is placed in a niediuin magnetic permeability, p, the inductance heconies
fact of
L
=
L"&L= I,*
*a
(1 + -
(8)
where V and x represent the molal volume arid molal magnetic susceptibility, respectively. Equation 8 corresponds to im idealized arrnngeiireiit since soine of the space apprecial)ly affecting the inductance of the coil cannot be occupied by the magnetic sul~tance. It is neccsvry t.o apply a moderate correctiou to olkain :hmlute values of the maguetic soseeptihility. The inductancc can he measured hy well-known electrical inetliods. ht first tlrn nixgiietic siisceptibility was used in couiicction with Curie's law, T = C/x,to estimate the ion- ternperhires imKtiind. Iltiioiigh Cnric'i law is incnnsiqtrnt vith t,lie 727
third law tliermodyirairiics, nnd must fail as the 82,solute zero is approached, its use %orapproximate extrapolation was justified hg the accuracy with which i t was obeyed down to I" K. 111 the first adiabatic demagnetization cooling experiaienbs MacI)ouga11 and the xrit,er (7, 8, .9) used gadolinium sulfate octahydrate. \ W h a starting temperature of 1.5" IC.and a ficld of 8o(X, paiiss, a temperature of 0.25" was obt,aiiled. Later they r?xtendedthe investigat.ion to the more dihrte gadolinium eniiipounds---gadoliiiiurn nitruhenzene sulfonate heptahydrate, gadolinium aiithraqninone wlfoiiate (both hydrated and imhydrous), and gadolinium phosphoinoI yhdnto tridecahydratc. The lowest temperature,0.097", v a s (htainetl m T i t i i gadolinium nitrolmmne sillionate; Iiowevrr, gidoliriinni pI~ol;plioniolyl~~Inio vas foiind to be :I more ideal substance and it would produce a lower temper&triretliaii any of the ot.hcr gadolininni conrpounds mentinned under similar starting conditions. Later de Haas, \Viersma, and Kramers (18), working at, t h o University of l.eiden, used cerium fluoride in tlreir first esperitnonts. They :ikn invest,igated dysprosium otliyl sulfate and crrium ethyl sulfato, obtaining a temperature of 0.085" I(. with the latter substance. A magnetic field of 27,600 giiii~swas used. More recently de Haas and Wiersma ( 1 1 ) used potassium chromium alum and a mixed salt consisting of potassium chroii~inrn d u m diluted with potassium aluminum alum. \Vith the latter substance they ohtairicd a temperaturc of 0.00444". Kiirti and Simon ( I O ) , working at Oxford University, inventigated manganese ammonium sulfate, iron ammonium aloin, gadolinium sulfate, ani1 clironiiurn pntassium a l ~ m . With a starting temperat,ure of 1.23" K. and a ficld of 14,100 gauss, a temperatiire of 0.038" was obtained n-itb iron amrnonium alum.
INDUSTRIAL AND ENGINEERING CHEMISTRY
748
'0 0 0 0
0 0
0 0 0 0
0 0 0 0 0
I
I
0 0
0 0
All of the temperatures given above by the several groups of experimenters were e s t i m a t e d by means of a Curie's law extrapolation.
I N 1848 K e l v i n (14) 6 proposed the establishment of an absolute scale of t e m p e r a t u r e , based on Carnot's principle, and "quite independent of the physical p r o p e r t i e s of any specific substance." Later (16) he suggested the particular centigrade absolute (Kelvin) or thermodynamic scale now in common use. Kelvin stated that "the absolute values of two temperatures are to one another in the proportion of the heat taken in to the heat rejected in a perfect thermodynamic engine working with a source and refrigerator a t the higher and lower of the t e m p e r a tures respectively." The application of Kelvin's method of determining absolute temperature to the low temperatures p r o d u c e d by reversible demagnetization is obvious. I n d i f f e r e n t i a l form,
0 0 0 0 0 0
0 0 0 0 0 0 0
0 0
I
where Q and X refer to the heat a n d e n t r o p y , respectively. Since changes of entropy and heat are readily measurable quantities, any temperature which can be produced by a reversible process can be evaluated. MacDougall and the writer (IO), Keesom (13), and Debye (3) commented on the fact that temperatures in the region below 1 " K. may be placed on t h e thermodynamic scale. MacDougall and the writer (8) carried out calorimetric experiments on gadolinium phosphomolybdate tridecah y d r a t e i n order to ccmpare the t r u e t h e r m o d y namic t e m p e r a t u r e s with
R FIGURE9. MAGNETIC COOLIXQ APPARATUS SHOWINQ A SAMPLETUBEAND INDUCIAINCECOIL SusPENDED IN A DEWAR VEOSEL
VOL. 28, NO. 6
those obtained from Curie's law. The two temperature scales agreed to within 0.01 'a t all temperatures down to 0.3 ", but a t 0.25' Curie the estimated temperature was 5 per cent too low; a t 0.20", 11 per cent too low; and a t 0.15", 22 per cent too low. Kiirti and Simon (19) have since carried out similar experiments with ferric ammonium alum, and they also found that the Curie extrapolation gives temperatures which are too low. The general expectation had been that temperatures obtained from a Curie extrapolation would be tou high rather than too low. MacDougall and the writer used an inductance heater for the calorimetric measurements on gadolinium phosphomolybdate tridecahydrate. Current was induced in a single turn of gold wire by means of an alternating magnetic field. A small amount of silver was added to the gold to increase its resistance. A recent investigation of gold silver alloys by J. W. Stout a n d t h e w r i t e r indicates that heaters of this material can be used t o i n t r o d u c e measured q u a n t i t i e s of energy w i t h a p r e c i s i o n of a f e w hundredths per cent. It is of some interest to consider the orders of m a g n j t u d e involved in typical c a l o r i m e t r y below 1' K. For example, in the measurements on g a d o l i n i u m phosphomolybdate mentioned above, a sample weighing 89 grams was used, and it was found that this amount would require only about 0.03 calorie to heat it from absolute zero to 1"K. However, the heat leak can be so reduced that observations a t temperatures below 1" K. are possible f o r s e v e r a l hours after a single cooling. The amount of energy introduced for a heat capacity determination was about 0.001 to 0.002 calorie, and this was measured-64th a n a c c u r a c y of t h e order of 1 per cent. As little as 0.01 mg. of ordinary dust falling down the vacuum line attached to the calorimeter would introduce a quantity of energy c o m p a r a b l e with the total amount used for a heat capacity measurement. The apparatus was tested to ensure that possible vibrations transmitted from machinery did not introduce energy. H o w e v e r , we c a n n o t regard the present results as more than preliminary since we believe that the accuracy can be considerably increased. Kiirti and Simon (17,19) used the heat effect from the absorption of y radiation in their calorimetric measurements on ferric ammonium alum. FIQURE
THE f i s t heat capacities in the Q t e m p e r a t u r e r e g i o n below 1' a b s o l u t e w e r e o b t a i n e d by a d i a b a t i c d e m a g n e t i z a -
NETIC
10.
MAQ-
COOLING AP-
MADE OF GLASS; CHAMBER PARATUS
FOR LIQUID HELITJM
SHOWN
NEAR
TOP
THE
JUNE. 1936
INDUSTRIAL A h D ENGIhTEERING CHEMISTRY
-4TOM OF
GADOLINIUM
tion from various fixed entropies. These data, together with the thermodynamic equation
c
dS -__ d In T
determine the heat capacity in terms of the temperature estimated by Curie's law. Figure 11 shows the heat capacities of a number of gadolinium compounds measured in this way by MacDougall and the writer ( 7 , 1 0 , 2 4 ) . The heat capacity is due to interactions of the gadolinium atoms in each case. The effects of magnetic dilution and crystal structure are evident from the differences among the several curves. The extensive magnetic investigations of Kamerlingh Onnes and his associates a t the University of Leiden indicate that dilution of the magnetic atoms leads to more ideal magnetic behavior. Figure 12 was scaled from a preliminary heat capacity graph published b y Kurti and Simon (19). They suggest that the rapid rise in heat capacity a t the lowest temperatures is due principally to mutual interactions of the magnetons, while a t higher temperatures the interaction is concerned primarily with the electric field of the crystal lattice. It is evident that earlier assumptions of zero heat capacity in the region near and below one degree absolute are far from correct in the cases mentioned above. Although the investigations made possible by adiabatic demagnetization are just beginning, a number of results, in addition to those mentioned above, have been obtained. Kiirti and Simon (16, 20) have carried out an interesting investigation on supraconductivity by cooling mixtures of various powdered metals with paramagnetic salts. They found that copper, gold, germanium, bismuth, and magnesium are not supraconducting down to 0.05'. Cadmium (0.54'), zirconium (0.70'), and hafnium (0.35') do become supraconductors a t the temperatures given. MacDougall and the writer ( 7 , s )showed that the magnetization of the five gadolinium compounds referred to above was very reversible. This conclusion was based on the fact that within the limit of accuracy, the susceptibility was independent of frequency to 1000 cycles per second and also on calorimetric observations on the samples whiIe they were subjected to alternating magnetic fields. Expressed in terms of the energy (xH*,,,./Z) transferred to the substance by the field a t the maximum of the sine wave, approximately 5 parts in 10,000 were converted into heat a t 0.15" K. when the frequency was 550 cycles per second. This effect became even smaller a t higher temperatures, and a t 0.35" it was less than 5 parts in 100,000, the limit of accuracy.
749
With a similar precision no effect could be detected with a frequency of 60 cycles per second. The above figures apply approximately to all of the gadolinium compounds mentioned here. Gadolinium sulfate octahydrate was not investigated with a frequency of 550 cycles per second. The high degree of reversibility of the adiabatic demagnetization process places its practical approach to ideal thermodynamic effectiveness almost in B class by itself. In some respects the apparatus may be compared favorably with the ideal engines found only in textbooks. At the low temperatures concerned, the walls of the container are practically without heat capacity, and heat radiation has become inappreciable. Moreover a t the lower temperatures the insulating vacuum becomes more nearly perfect than that obtainable in any other way. It was also of interest to determine whether any permanent magnetism was left after demagnetization to iow temperatures. Gadolinium phosphomolybdate tridecahydrate was investigated for this purpose down to 0.15' K. and it was found that less than 0.02 per cent of the saturation magnetic moment of this substance could have been left as permanent magnetism. I N CONCLUSIOS some unpublished investigations and 0 some work in progress will be mentioned briefly. MacDougall and the writer (23) also developed a method of determining the intensity of magnetization from differential susceptibility measurements:
Starting a t known temperatures, observations of ( a I 1 / 3 H ) ~ by the inductance method are made during the course of adiabatic demagnetization. Similar observations can be made during remagnetization from the low temperature to the initial conditions. These data, combined with Equation 11, determine the intensity of magnetization. This method has been used to determine 1 . the i n t e n s i t y of magnetization of gadolinium phosphomolybdate tridecahydrate to 75 per cent of saturation. The results are in close agree/ ment with t h e theoretical predictions of Equation 7 which w a s p r e I , I sented graphically L 0.10 T 0; in Figure i i n conFIGURE12. HEATCAPACITY IN CALOn e c t i o n with the RIES PER DEGREEPER MOLE, DATA OF KURTIAND SIMON (19) gadolinium sulfate data. The above method does not require evaluation of the intermediate temperatures used. However, an important application of differential susceptibilities is in the determination of thermodynamic temperatures below 1' K. A sufficiently complete description by means of differential susceptibilities, a t various fields combined with data obtained above l o , will permit the determination of any low temperature produced by adiabatic demagnetization. This method of determining thermodynamic temperature, which is suitable either in the presence or absence of magnetic fields, will be of
INDUSTRIAL AND ENGINEERING CHEMISTRY
730
VOL. 28, NO. 6
t-
50000
Carbon Thermometer Heater
-
45000.
R Ohms. 40000-
350001 0
I
T”K
4
Figure 13 shows the resistance, in the absence of a magnetic field, of a thermometer-heater made from amorphous carbon, Unlike ordinary resistance thermometers, its temperature coefficient of resistance increases greatly a t lower temperatures where the increased significance of a n increment of temperature makes this especially desirable. It is probable that other semi-conducting substances will prove useful in low-temperature thermometry. A few preliminary measurements indicate that the resistance of carbon increases somewhat in the presence of magnetic fields, but this acts to increase still further the high sensitivity of the thermometer. The development of a technic for measuring accurate absolute values of differential magnetic susceptibility is one of the more important problems now in progress. With this and other methods and apparatus mentioned above, we expect to explore further the many interesting phenomena of heat, electricity, and magnetism in the temperature region below 1 absolute.
FIGURE13. RESISTANCE OF A CARBON THERMOMETER AT Low TEMPERATURES
importance in some cases since it avoids the difficult problem of establishing thermal equilibrium between a calorimeter and its contents a t the low temperatures reached. The necessary equations have been given previously (7). Although adiabatic differential susceptibilities can be combined with other data for the accurate determination of low temperatures even in the presence of strong magnetic fields, it has been found that (bI/bH)s, by itself, is not very useful as a variable for indicating temperatures except in the region of initial susceptibilities. In strong fields it has been shown experimentally that the adiabatic differential susceptibility tends to small values which do not change much with temperature. This is a consequence of the fact that in an ideal paramagnetic system, without heat capacity, both the intensity of magnetization and the entropy depend only on the distribution of magnetons in the various magnetic quantum levels. Thus constant S implies constant I and zero ( b I / b H ) s . Because of the difficulties inherent in magnetic thermometry in strong fields, we have sought a resistance thermometer which will permit measurements of high precision at very low temperatures. J. W. Stout, C . W. Clark, and the writer have been investigating the properties of carbon for thermometric purposes in the region below 1°K. A material of very high specific resistance was selected because it is desirable to avoid the introduction of heat by eddy currents during experiments with alternating magnetic fields. Another important consideration is that electrical leads of much higher resistance may be used when the thermometer is of large resistance. This makes it possible to minimize heat leak from the surroundings. It has been found practicable to conduct the current to the thermometer by means of platinized strips on glass. As is frequently the case with other low-temperature resistance thermometers, the carbon thermometer may also be used as a calorimetric heater.
Literature Cited (1) Curie. J. .ohus.. 4. 197 (1895). (2) Debye, A n n . - P h y s h , 81,‘1154 (Dee., 1926). (3) Debye, Physik. Z., 35, 923 (1934). (4) Ewing, PTOC. Roy. SOC.(London), 48, 342 (1890); Phil. Mug.. [51 30, 205 (1890). (5) Giauque, A. C. S., Calif. Section, San Francisco, Calif., April 9, 1926; author’s adiabatic demagnetization, method was presented by W. M. Latimer. (6) Giauque, .T. Am. Chem. SOC.,49, 1870 (1927). (7) Giauque and MacDougall, Ihid., 57, 1175 (1935). (8) Giauque and MacDougall, paper presented before joint meeting of Calif. Section of A. C. 5.and Am. Assoc. for Advancement of Sei., Berkeley, June 18. 1934; Phys. Rew., 47.885 (1935). (9) Giauque and MacDougall, Phys. Rev., 43, 768 (1933). (10)Ibid., 44,235 (1933). (11) Haas, de, and Wiersma, Physicu, 2, 335 (1935). (12) Haas, de, Wiersma, rand Kramers, Ibid., 13, 175 (1933),and [N.S.1,1, 1 (1933): Nature, 131, 719 (1933); Nutumissenschuften, 21, 467 (1933); Compt. rend., 196, 1975 (1933). (13) Keesom. J. phus. radium, 5. 373 (1934): Phusik. 2.. 35. 928
Keivin,’Proc. Cumhridge Phil. SOC.,1, 66 (1848); Phil. Mag., [3] 33, 313 (1848). Kelvin, Trans. Roy. SOC.Edinburgh, March, 1851, and May, 1854; Phil. M u g . (4), 1852; “Mathematical and Physical PaDers. Thomson (Kelvin),” Vol. 1, p. 235, Cambridge - Univ. Press, 1882. Kurti and Simon, Nature, 133,907 (1934),and 135,31 (1935); Proc. Roy. SOC.(London), A149, 152 (1935). Kurti and Simon, Nature, 135,763 (1935). Kurti and Simon, Nuturzoissenschuften, 21B, 178 (1933). Kurti and Simon, paper presented before meeting of Roy. Soc. London, May 30, 1935; Proc. Roy. Soo. (London), A152, 21 (1935). Klirti and Simon, Proc. Roy. SOC.(London), A151,610 (1935). Langevin, Compt. rend., 140, 1171 (1905). Lewis and Randall, “Thermodynamics rand tho Free Energy of Chemical Substances,” New York, McGraw-Hill Book Co., 1923. MacDounall - and Giauaue. data to be published. MacDougall and Giauque; J . Am. Chhem. SOC.(in press). Pauli, Physik. Z . , 21, 615 (1920). Woltjer and Kamerlingh Onnes, Communicution.cr Phys. Lab. Univ. Leiden 167c (1923). RECEIVED May 1, 1936.
