(Communicated at the meeting of January ).

Transcription

1 Physics. ~ The Speci{ic Heats of Solid Substances at the Temperatures Attainable with the Help of Liquid Helium. I. Measurements of the Atomic Heat of Lead. By Prof. W. H. KEESOM and Dr. DONALD H. ANOREWS 1). (Communication No. 185a from the Physical Laboratory. Leiden. (Communicated at the meeting of January ). 1. Introduction. In the range of temperatures which can be reached with the help of liquid helium there have been scarcely any measurements of the specific heats of solids. KAMERLINGH ONNES and HOLST 2) published a few preliminary measurements of the specific heat of mercury. which we re made in order to find out whether a discontinuous change in the specific heat occurs at the temperature at which mercury becomes superconductive. KAMERLINGH ONNES and HOLST concluded from these measurements. which however were not very exact that na such discontinuity occurs. In the present communication there are discussed same measurements of the specific heat of lead between the temperatures 2 K. and 20 K. We selected lead as the initial substance for the study of specific heat at extremely low temperatures. primarily because lead belongs to th ase elements. whose specific heat falls oef least rapidly with the lowering of the temperature. thus enhancing the accuracy of observation; besides this it seemed desirabie because same exact observations 3) of the specific heat of lead had been made in the reg ion of temperature just above the range which we planned to investigate. Particularly at the lowest temperatures. our measurements do not have the accuracy which we hoped they would and we plan to repeat them and continue them; but in the meantime by the departure of one of us it seems desirabie to publish the results which we have al ready secured. 2. Method. We employed the methad of NERNST and EUCKEN for determining specific heat. in essentials in the way already followed by 1) Nationa1 Research Fellow (U. S. A.) with a fellowship of the International Education Board. 2) These Proc ; Comm. Leiden NO. 112c. 3) W. H. KEESOM and H. KAMERLINGH ONNES. These Proc ; Comm. Leiden NO Cf. a1so F. SIMON. Zs. physik. chem

2 435 KEESOM and KAMERLINGH ONNES 1) for determining specifk heats at the temperatures which can be reached with the help of liquid hydrogen. For these experiments th ere was constructed a combination unit for measuring temperature and for heating(see Fig. 2 Comm. N.143) consisting of two concentric cylinders of copper the outer being threaded on the outside. On the inner cylinder there was wound bifilarly a coil of insulated constantan wire and the remaining space between the two cylinders was filled with amalgam as described in Comm. No This constantan coi! served for the heating as weil as for measuring temperature. It consisted of three parts one of one ohm one of one hundred ohms and one of ten ohms. The wires leading to the coil we re so arranged th at any one of these parts could be used at will. In these experiments only the 100 ohm coil was used. The measurements of resistance for determining the course of temperature before and af ter heating were made with the help of a potentiometer. During the heating this was disconnected. The heat imparted was calculated from the mean resistance of the heating coil from the current strength as read on a milliammeter and from the time as adjusted by the switching device described in Comm. No. 143 Fig. 7. The switch was actually controlled by an electric impulse sent out by the dock as was the case in the measurements of Comm. No For acontrol the time was read from a watch. The current used for measuring temperature was about 0.5 ma. and that for heating from 10 to 50 ma. The heat from the measuring current was taken into consideration as was necessary. The vacuum within the calorimeter jacket was secured and maintained by a three stage diffusion pump from LEYBOLD. 3. Accuracy of the Measurements. a. A factor of uncertainty is introduced in that the resistance of the constantan heating coil during heating is taken to be the mean of the resistances before and aft er heating. Since there is but a very small change in the resistance of the constantan for a rise even of ten degrees the error due to the temporary rise in temperature during heating cannot exceed some few percents. The temperature-time curve gave no reason for conduding that the temperature of the wire during heating rose very high above that of the surroundings moreover our results at higher temperatures are in accord with those of KEESOM and KAMERLINGH ONNES indicating that the above assumption is permissible within the calculated limit of error. Considering that at lower temperatures much smaller currents were used for heating it does not appear likely th at this sort of error could have been greater in that region. 1) These Proc ; Comm. Leiden NO Also These Proc ; Comm. Leiden NO. 147a. 29*

3 436 b. The apparent decrease in the resistance immediate1y af ter heating at the lowest temperatures (see 5) makes the measurements be10w 4 K. somewhat uncertain. Above 4 K. this cause of uncertainty does not appear to be significant. c. The measurements of the heat capacity of the core are less accurate apparently because its heat capacity is so smal!. For just this reason however. the core has a relative1y unimportant part of the total heat capacity in the measurements of the specifk heat of lead. d. A number of measurements is uncertain because the course of the temperature af ter heating was not observed over a long enough period to permit an accurate calculation of the temperature rise following the heating. e. The following table gives an estimate of the order of magnitude of the different sources of error expressed in percent of the atomie heat capacity of lead. Factor I 2-4 K. I 4-8 K K. I. Weight of the lead block 0.05 % 0.05 % 0.05 % 2. Temperature. ri se Energy Imparted (current) Resistance Time Part of the heat capacity due to the core O. J Tota! 19 % 9 % 6 % Average deviation of the results from the mean 20 % 7 % 2 % I Uncertainty in the heat capacity of the core 50 % 20 % 3 % For some measurements the deviation is considerably greater without th ere being any evident cause. 4. The resistance thermometer. The data for the calibration of the constantan resistance thermometer are given in Tables Ia and Ib. The temperature of the liquid helium was read off a graph based on

4 437 the formula for the vapor pressure by KAMERLINGH ONNES and WEBER 1). excepting the lowest three temperatures which were calculated from the formula of VERSCHAFFELT. given in Comm. Leiden. N p. 18. note 1 2). I TABLE Ia. Calibration of constantan thermometer in liquid helium. Date Vapor pressure Temperature Resistance of He mmo Hg ok. Ohms 20 November March ) Between liquid helium and liquid hydrogen temperatures interpolation was made with the help of a graph. 1) These Proc ; Comm. Leiden NO. H7b 7. 2) The newer formula of VERSCHAPPELT. Comm. Leiden Suppl. NO. 49. p. 26. gives temperatures. which are 0.06 higher. 3) During the hour preceding this measurement there was no current passing through the constantan wire ; for the fifteen minutes just before the next measurement there was a current of 1 milliampere. This explains the somewhat higher value of the resistance according to thc second measurement. as the re sult of the slightly higher temperature in the thermometer core due to the heating effect of the current.

5 438 TABLE Ib. Calibration Constantan Thermometer in Iiquid hydrogen Date Vapor Pressure Temperature Resistance H 2 mmo Hg ok. Ohms 5 November *) AFril **l I 'i. 115 **) *) Secured from simultaneous readings with Platinum thermometers Pt32 and Pt36' **) Secured from the vapor. pressure of hydrogen accordmg to Comm. Lelden I N O. 156b 1). 5. The Heat Capacity of the Heater~Thermometer~Core. Table II gives the data secured from the measurements of the heat capacity of the heater~thermometer~core. A number of observations. not included in the table did not give good results. For several of these. especially at the lowest temperatures. the energy added was too small to give a good measurable temperature rise. In some cases the behaviour of the galvanometer was as if the temperature was actually lowered by heating. The cause of this irregularity is as yet unknown to us. For a number of measurements shown in the table. the deduction of the corrected flnal temperature af ter heating from the different successive readings of the galvanometer was uncertain. These measurements are marked with an *. In this connection it should be noted that. af ter the current for heating has passed. the heating wire has a temperature appreciably higher than that of the surrounding metal. There is in most cases about ten minutes before the temperature of this wire. serving also as thermometer. is the same as the temperature of the block of metal. Only wh en the tempera tu re of the bath (in whieh it was impossible to use a stirrer 2)) remained sufficiently constant over a time long enough to provide a regular change in temperature for the block. was it possible to get the flnal temperature reading for the calorimetrie calculation with sufficient accuracy. These remarks apply also to the measurements of the heat capacity of the lead block communieated in 6. 1) J. PALACIOS MARTINEZ and H. KAMERLINGH ONNES. Arch. Néerl. (3A) Comm. Leiden NO. 156b. 2) To promote uniformity of temperature in the bath. the calorimeter vessel was encased in a copper cylinder. cp. These Proc. 20. p ; Comm. Leiden. NO. 153a. 1.

6 439 TABLE 11. Date NO. :x: Ol Ol.~ ë "':.:: roö~ e El :.:: ::l ~ ~..c:. ~e~~ ~ ~O Time <'J '" <IJ <'J U 0> i5... <IJ '" ~~~ U 1;;.5 g ~.- ~ sec '" <'J '" I'i '" '"... ~ e- :r: 0 0.." +ol 0.:0... <'J U e Ü:? 0> <'J "'<'J ::l '" I'i U ~2 1-< '"." '" ~ Ü :C ''6 ~ 21 May 1926 I A XIV XV * XVI * B XII * XIII (332) XIV * XV * XVI * XVII XVIII June 1926 XIX XX i XXI C XVIII * XX * XXI I * D III ** VI * VII * VIII * For the bracketed readings in Tables 11 and 111 th ere were other reasons for uncertainty. e. g. that for the measurement the temperature rise was not sufficiently large. The results are shown in Fig. 1. The points within broken circ1es are those indicated in Table 11 as less accurate. For the calculation of the specific heat of lead in 6 we used the line drawn through the points. (shown in the uncertain region as a dotted line).

7 The Atomie Heat of Lead. The results of the measurements are given in Table IIl. The lead block 1) weighed grams. 4 B 12 Fig T 20 OK c ei 1. '':: f':\' 12~------~ r ~ ; Pb '0 9B~------~ ~ ; I o " 04~ ~I:l~ C.~:_' ~ -+ ~ Fig. 2. For remarks on the order of certainty of the results cf. 5. The results are shown graphically in Fig. 2 (dotted circles indicating less accuracy). The D. D. mark the points secured from the accurate measurements of 1) The same bloek as that which served for the measurements of these Proc ; Comm. Leiden NO. 143 diminished by a strip which served for the resistanee measurements given in these Proc no te ; Comm. Leiden NO. 147a p. 6 note 3.

8 441 Date NO. TABLE 111. Atomie Heat Capacity.. "-0.:!l El '"... :.:.. '" lil.. lil - In ~ El B 0.0'" -0 ~..c: u 1:11;; " lil u- lil 0::0 Time lil... ~ ~ ~ ï Q "x: U... 0 ~ sec. ~.ï: ~ ~ 0 El B '" tl '" ::E ~ o.. lil U El Ol 'iiî ~è... < -0 U ::E~ E-< E-< ::r:'~ '"..c: u 0. " '" tl '" '" '" '" 30 March 1926 In bath of liquid helium IV V VI [0.728] VII H VIII IX April In bath of solid or liquid hydrogen I III IV varled [1.713] V [2.300] 30 April In bath of liquid helium. III IV V VI IX XI XII XIII XIV May In bath of liquid helium. VI VlIl IX * XII H* XIll [0.422*] XIV XV XVI I) The difference between cp and Cv is negligible.

9 442 KEESOM and KAMERLINGH ONNES in the liquid hydrogen range. The agreement is re1atively satisfactory. considering our calculated accuracy. The broken line denotes the values for the atomie heat capacity (at constant volume) as calculated from the formula of DEBIJE with (J = 88. In the first place we note that with lead th ere is no indieation that at the transition to the super~conductive state there occurs a discontinuous change in the atomie heat. even as KAMERLINGH ONNES and HOLST found with mercury. Further it appears from our measurements that the atomie heat of lead at the lower temperatures is much greater than that calculated from the formula of DEBIJE. employing a value of (J whieh reproduces approximate1y the observed values at higher temperatures. The first indieation of this deviation in the case of lead was observed in the results of the measurements of KEESOM and KAMERLINGH ONNES (l.c.) whieh at the lowest temperatures obtainable with liquid hydrogen indieated that the atomie heat of lead is greater than would be calculated from the formula of DEBIJE with (J = 88 (see their Fig. 10. as weil as Fig. 2 of this communieation); or otherwise expressed. the value of (J below 18 K. gets somewhat smaller than 88 (see Fig. 11. Communieation No. 143). Also SIMON l.c. at the temperatures 9.85 to K.. finds (J smaller than 88. At the temperature of liquid helium this deviation has become so great that the atomie heat there is several times greater than that calculated from the formula of DEBIJE with (J = 88. A similar behaviour in the case of mercury. since confirmed at temperatures above 9 K. by SIMON I). was found by KAMERLINGH ONNES and HOLST (l.c.). in connection with the measurements of POLLITZER 2}. A further investigation will be immediately undertaken to see whether this behaviour is also characteristie of substances whieh are not super~conductive. for example. bismuth. It is not clear from our measurements whether one would expect that. in approaching 0 K.. the atomie heat capacity approaches zero or a positive value. It still seems likely from our measurements that the atomie heat capacity approaches zero but at a considerably smaller rate than the T3 rule of DEBIJE would lead us to expect. Our results do not show clearly whether the case of lead is explained by the assumption of SIMON 3} that the deviation. whieh occurs in the case of gray tin and silicon. is due in these atoms to the existence of two different quantum states with small energy difference. Should this be the case th en it would follow from our measurements that (Ju = 2.25 approximate1y. This would give at 1 0 K. t: C = at 2 K at 3 K N ow it should be observed that several of the more uncertain I) F. SIMON. Zs. f. physik. Chem ) F. POLLITZER. Zs. f. Elektrochemie ; see also ) F. SIMON Berlin Sitz. Ber p. 477.

10 443 measurements at about 3 K. give rather large values for the heat capacity. 0.7 and 0.4 (see also the values for the core. fig. 1). On the other hand. the more certain measurements give values of about 0.2. It is desirabie to secure new measurements in order to be sure of this point. It is a pleasure to record our hearty thanks to Mr. CHESTER W. CLARK of the University of California for his valuable help in securing the measuï.'ements and in calculating the results.