The thermal and electrical conductivities of some pure...

206 F. H. Schofield.

P late 5.

F ig.. 3.—Long-crested waves emerging from the front of a catspaw. (Jesus LmH Cambridge, June 29, 1924.) (See p. 201.)

P'jq. 4.__Effect of an increase in the wind-velocity on a swell already established. Thcrests have become sharp and are curling o v er ; the formation of new three si dimensional disturbances is shown by the running together of the crests. (Newnha® a , Millpond, June 15, 1924.) (See p. 201.)

___________________________________ A t

■The Thermal and Electrical Conductivities o f some Pure By F. H. S c h o f ie l d , B.A., B.Sc.

I " ,

(Communicated by Sir Joseph Petavel, F .R .S .— Received October 22, 1924.) H ,

(Physics Department, the National Physical Laboratory.)

I .— I n t r o d u c t io n .

The relation between the thermal and electrical conductivities of metalslA has for a long time engaged the attention of physicists. As far back as 18535 Wiedemann and Franz* propounded the law to the effect that the ratio of the* two conductivities was the same for all metals. In 1872 Lorenzf, both on theo-x retical and experimental grounds, sought to establish that the above-mentioned*9 ratio was proportional to the absolute temperature. On the development of > the electron theory Drude, H. A. Lorentz, J. J. Thomson and othersj have,a| on the basis of various assumptions, arrived at the same conclusion as Lorenz, i Up to 1900, however, the experimental values were too uncertain to allow any c definite confirmation of the theory. In that year Jaeger and Diesselhorst§ % published the result of their investigation, which gave directly the ratio of the a conductivities for a number of metals and alloys over the range 18° to 100° C. I Lees|| has since, by an independent method, confirmed the values of Jaeger and i Diesselhorst for a number of metals at 18° C. and has carried the investigation x * * * §

* * Ann. der Phys.,’ vol. 89, p. 497 (1853).f * Ann. der Phys.,’ vol. 147, p. 429 (1872).% For a critical review of the most recent theories, see Meissner, * Jahrbuch der Radio- 0

aktivitat und Elektronik,’ vol. 17, p. 260 (1920).§ * Abh. der Phys.-Tech. Reichsanstalt,’ vol. 3, p. 282 (1900).

. || ‘ Phil. Trans.,’ A, vol. 208, p. 381 (1908).

on May 24, 2018http://rspa.royalsocietypublishing.org/Downloaded from

http://rspa.royalsocietypublishing.org/

thermal and Electrical Conductivities of some Pure Metals. 207

H\

I

own to —170° C. Meissner* has experimented with some pure metals down is Mo —250° 0. and Onnes and Holstf even lower.

The result of these investigations has been to show that between —100° C.jad -f- 100° C. the value of the function K/ AT (K and A being the thermal and Iectrical conductivities and T the absolute temperature), is sensibly the same

| or the pure metals, with perhaps a slight tendency to fall with decreasing term aierature. Below —100° C., however, the function shows an increasingly rapid all with temperature and a considerable divergence between individual metals. Ibove a temperature of +100° C. very few determinations of thermal con- luctivity have been made, and the object of the present series of experiments las been to measure, in this region, the thermal and electrical conductivities )f a number of metals of the highest purity obtainable commercially.

The materials used have been obtained through the kindly offices of Dr. Hutton, the Director of the British Non-Ferrous Metals Research Association, and were presented by the firms whose names appear below. In setting out the results (see Appendices I to V) it has been thought well to give, in addition to the chemical analysis of the metal, particulars as to the method of preparation and heat treatment. Dr. Rosenhain, Superintendent of the Metallurgy Department of the National Physical Laboratory, kindly undertook to advise as to the suitability of the specimens, and arranged for an examination of the aluminium specimen, of which details are included in Appendix I.

II.—T h er m a l Co n d u c t iv it y .

(a) Theory of Experiment and Reference to Previous Work.The methods which have been adopted for measuring the thermal con

ductivity of metals can be classified under two main heads which, for convenience, may be termed “ electrical ” and “ thermal ” respectively. Under the former a rod of metal is heated by the passage of an electric current and measurements are made of the thermal and electrical potentials along its length. By this means the ratio of the thermal to the electrical conductivity is obtained. The determination of the latter by a separate experiment then enables the thermal conductivity to be deduced. With various modifications this method has been exploited by Jaeger and D iesselhor st, J Callendar,§ Meissner J and others. The method probably presents considerable experimental difficulties at high

* ‘ Deutsch. Phys. Gesell. Verh.,’ vol. 16, p. 262 (1914). f * Proc. Acad. Amsterdam,’ p. 760 (1914).J Loc. cit.§ ‘ Encycl. Britannica,’ 11th ed., art. “ Conduction of Heat.”




temperatures, and above 200° C. appears to have been tried only by Angell,* who in an ingenious way dealt with the radial, instead of the longitudinal gradient of temperature in a bar of metal heated by an electric current.

The purely “ thermal ” methods of measuring conductivity are simple in theory, and generally resolve themselves into a determination of the rate of heat flow through a bar of metal, in which a longitudinal gradient of temperature is maintained.

A method of this description was first used by Forbes in his well-known experiments. Forbes allowed the surface of his bar to be exposed to the atmosphere and determined the heat flow past any point on the bar by the amount given up by radiation and convection from the cooler parts. This procedure, gives rise to considerable uncertainty, not only on account of the difficulty, of accurate measurement of heat flow in the manner indicated, but also because it involves the necessity of estimating the temperature gradient at a particular point. With modern appliances more convenient and accurate methods of measuring the heat flow are available and, if it is possible to insulate the bar" thermally so as to prevent lateral heat loss, the temperature gradient may be; measured over a finite distance instead of at a point. Under the conditions indicated the rate of heat flow Q is given by the equation

Q - - K A t o - e , ) d

where A is the cross-sectional area of the bar, d1 and 02 are the temperatures at a distance d apart, and K is the mean conductivity of the metal between the temperatures 6t and 02, and which is assumed over this range to be a linear function of the temperature.

This is, the principle of the method adopted in the present series of experiments. Before describing the details of the apparatus, it is well to refer briefly to those used by some previous workers who have adopted similar methods, particularly for experiments above atmospheric temperature. For example, Callendar and Nicholson, f when measuring the thermal conductivity of steel, used bars of considerable cross-section (about 4 inches in diameter) and lagged them with a material of low conductivity. In this way the lateral escape of heat was so reduced as to amount to only a small fraction of that conducted by the metal. The bar under test was heated at one end by steam and cooled at the

* ‘ Phys. Rev.,’ vol. 33, p. 421 (1911). f Loc. cit.



Thermal and Electrical Conductivities o f some Pure Metals. 209m h -

other end by a flow of water. Ezer Griffiths* also used a lagged bar with electric heating at one end and water pooling at the other, and obtained the conductivity

i of a number of aluminium alloys up to a mean temperature of 250° C. Wilkesf 111 eliminated lateral heat loss by an application of the guard-ring principle. He

surrounded bis bar with a coaxial pipe of metal, the annular space between the two being filled with a finely powdered insulating medium to prevent convection

j currents. At the hot end of the apparatus the bar and pipe fitted into a common I end-piece of copper maintained electrically at a constant temperature. At | the other end the bar and pipe were cooled independently by water circulations l and the cooling was so adjusted that the same longitudinal temperature distribution was induced in the bar and pipe, thus eliminating lateral loss from the

I former. In the three cases mentioned above, the rate of heat flow (Q) in the test bar was determined by means of a flow calorimeter at the cold end. This

I method of measuring the heat flow is very accurate and convenient, but it limits the temperature to which the conductivity can be determined, since the value is given for a temperature intermediate between those of the hot and cold ends of the bar, generally the mean of these temperatures. If, however, the heat flow is determined from the energy input at the hot end, the cooler end of the bar may be kept at a higher temperature and the value of the conductivity can be obtained at a correspondingly higher mean temperature. Honda and ShimiduJ worked in this way in determining the conductivity of nickel and

t various specimens of steel to over 800° C. In their apparatus the test bar was i divided into two portions centrally to allow the insertion of a small heating

A coil, in a very similar way to that subsequently adopted by the author (see I fig. 1, p. 210). This specimen bar was inserted into a pipe and packed with

kaolin powder, and the whole apparatus was placed inside a furnace maintained at a steady temperature. In conducting an experiment, energy was switched on in the central heating coil and was dissipated at a certain rate for about 20 minutes, at the end of which time the steady rate of heat flow was established in the bar. The temperature difference at two points at a known

• distance apart was then measured by differential thermocouples. Under these conditions a small amount of the energy dissipated in the central heating coil (estimated at 6 per cent.) was conducted into the kaolin surrounding the bar. This amount could not be directly measured, but, on the assumption that the

* Advisory Committee for Aeronautics, Light Alloys Sub-Committee, Report No. 7(Nov., 1917).

t * Chem. and Met. Engineering,’ vol. 21, p. 241 (1919).% ‘ Sci. Reports, Tohoku U niv.,’ vol. 6, p. 219 (1917). The author did not have access

to this paper until after the conclusion of the experiments described below.



Hea

ting

Coi

ls

Sil-o

-Cel

Pow

der


©£

same fraction of heat generated was always lost by diffusion into the kaolin, relative values were obtained from room temperature up to 900° C. While this assumption may not be strictly valid over very wide ranges of temperature, for moderate ranges, at any rate, the method seems to be admirably adapted to the measurement of changes of conductivity with temperature.

(b) Details of Apparatus.In the present series of experiments

the attempt has been made to determine the thermal conductivity in absolute measure by adopting the guard-ring principle. For this purpose a source of heat was applied at the centre of the test bar and a sink at each end in such a way that a steady flow of heat was maintained. The guard ring consisted of a coaxial pipe of metal wilich surrounded the bar and which, like the bar, was heated centrally and cooled at the ends in such a way as to reproduce as closely as possible the same temperature distribution as that obtaining in the bar.

The details of the apparatus are shown in the accompanying diagrams. Fig. 1 represents a section of the apparatus. The test specimen is seen to be divided into two portions (shown shaded in different direction^ in fig. 1) which fit into each other with an overlapping joint. Each of these portions is drilled axially to a certain



Thermal and Electrical Conductivities o f some Pure Metals. 211

fi! I

tepth, so that when they are brought together an enclosed space is formed, bout 7‘5 cms. in length, for the reception of a heating unit. For purpose >f clearness, the latter is not shown in fig. 1, but it appears in the enlarged (rawing of fig. 2, and a full description of it is given below. To the ends of he test specimen are screwed copper extension pieces, and the composite jar thus formed is supported by several uralite rings inside a pipe of metal which, n order to facilitate assembly of the apparatus, is cut into halves longitudinally. The temperatures at a series of points along the bar and pipe are measured by neans of thermocouples fixed at the positions marked Tl5 etc., in fig. 1. These :ouples are of wires of platinum and 10 per cent, iridium-platinum, 0*2 mm. n diameter. In the case of the bar, all the couples, except the central one, vere insulated with capillary tubes of pyrex glass or silica inserted into holes Irilled through the bar. The precise arrangement is shown in fig. 2. In order

to fix the couple in position in the rod the capillary tubes were slightly tapered to ensure a tight fit and the wires were bent over the edges of the tubes in the

jj manner shown. The central couple was fixed in a groove, cut in the rod, by J means of a binding of platinum wire. In the case of the pipe the couples were

attached directly to the metal by means of small pegs.The central portion of the pipe was heated by means of a coil of platinum'

wire wound on a wrapping of mica. The length of pipe covered by the winding was equal to that of the cavity in the centre of the test bar, and in assembling the apparatus care was taken to secure that the ends of the two were in alignment. In order to reduce the heat loss from the pipe the whole apparatus was encased in magnesia-asbestos lagging.

The sinks of heat at the ends of the bar and pipe consisted of the exposed ends HH and KK, to which a number of devices for regulating the heat loss could be applied. Thus in fig. 1 one end of the bar is shown fitted with a movable




sleeve to which radiating fins are attached, in order to increase the heat los When a still greater loss was required the ends could be wound with composs jj tion pipe, through which water was circulated. If, on the other hand, it we ; required to reduce the heat loss, the exposed ends could be covered wit! insulating material, such as asbestos string, or a still greater effect in thi direction could be obtained by means of sleeves on which heating coils wei n wound. An auxiliary heating coil of this kind is shown in fig. 1 on one end o *i the pipe.

As has already been indicated, the lateral interchange of heat between the ba |> and pipe was practically eliminated by maintaining the same temperatur t distribution in the two, but, in order that this device should be effective, it wa ' necessary to secure that no interference should arise from the heating element A* themselves. The respective heating coils were accordingly situated insidb J the rod and outside the pipe. The latter has already been described and pre j sented no difficulty, but some experiment was necessary before a satisfactory 4 design was evolved for a heating coil to be embedded in the rod. To securt 1 ease of assembly it was desirable that leads should emerge close together neai the centre of the heater, while to obtain the requisite efficiency it was important that there should be no obstruction between the incandescent wire of the heaters and the interior surface of the bar.

The design adopted is shown in figs. 2 and 3, which represent respectively >'

a section of the bar and a plan viewed from a position at right-angles to the section. The heater consists of platinum wire, 0-3 mm. in diameter, wound upon a silica tube 5 mm. in diameter. As is shown in fig. 2, the ends of the silica tube are splayed out to prevent contact of the winding with the interior surface of the bar, and 4 knobs of silica, aa and are fused to the tube near the centre. The winding is effected by belaying one end of the wire round the base of the knob a and winding spirally from there to the end of the silica tube. The wire then passes through a nick in the splayed end to the interior of the tube and, emerging in a similar way from the other end of the tube, is again wound spirally toward the centre and belayed round the other knob a. In order to prevent

©

F ig. 3.



overheating of the portion of the circuit inside the silica tube this section con-i isted of two strands of wire in parallel. The function of the knobs is to prevent *1 the short-circuiting of the complete heating coil owing to a slipping of the

Endings in the neighbourhood of either of the knobs a. Incidentally, the knobs ia and bb serve to limit any possible sagging of the silica tube at very high temperatures. I t will be noticed from fig. 2 that the internal surfaces of the two portions of the bar, which are exposed to radiation from the heater, are

ii equal.1 The assembly was effected by passing the loose ends of the heating coil through

the holes cc (see fig. 3) in the right-hand portion of the bar and drawing the heating unit in position. The left-hand portion of the bar, which was provided with a slot for clearing the holes cc, was then slid into position. The ends of the heating

! coil were insulated in the holes cc by means of silica tubes, and current and | potential leads of platinum were attached to them where they emerged from the

tubes.| j In the earlier experiments asbestos wool was used for packing the space

between the rod and pipe, but the material finally adopted was “ Sil-o-cel,” which is a finely powdered diatomaceous earth. This material has the advantage of an extremely low thermal conductivity, while its fine state of division serves to prevent convection currents and reduce the oxidation of the specimen bar.

(c) Method of Experiment.

In carrying out an experiment, adjustments were made of the energy supplied to the heating coils at the centres of the rod and pipe and of the energy absorbed at the ends until the desired gradients were obtained. In all cases the gradients in the tube were made to correspond as closely as possible with those of the rod. Typical distributions of temperature for the specimens of nickel and aluminium are shown in fig. 4 (p. 214). I t will be noticed that in each case the gradients in the rod and pipe are approximately straight lines.

A strict linearity of gradient would, of course, be obtained only where the metals composing the rod and pipe had conductivities not varying with temperature ; where the lateral heat loss from both rod and pipe were negligible ; and where the supply of heat was from sources of zero thickness in a plane at right-angles to the axis. None of these conditions was precisely fulfilled but, as will be seen from fig. 4, the nett effect in producing curvature was negligible. It should, however, be pointed out that the amount of the lateral loss through the lagging from the pipe increased with increasing temperature. The resulting sag which this would tend to produce in the temperature distribution curve





of the pipe was counteracted by using a greater thickness of lagging and bj increasing the quantity of heat flowing through the metal itself. Consequently

Rod Te

Distance In cms. from centre. F ig . 4.

throughout the experiments steeper gradients were employed at the higher temperatures.

As evidence that no systematic error arose from the employment of differing temperature gradients, it may be mentioned that the conductivity measurements for the same mean temperature, but with different temperature gradients, gave results agreeing within the limits of experimental error. (See for example the results in Appendix I for a mean temperature of about 150° C. obtained with temperature differences of 28° C., 35° C. and 50° C. respectively.)

(d) Magnitude of Lateral Heat Loss.Since the theory of the method presupposes the elimination of lateral heat

loss from the specimen, it is important to ascertain the magnitude of any error due to failure to obtain a coincidence of temperatures over the working area of the rod and pipe. Consequently, the following series of experiments were made with the specimen of aluminium. The several temperatures of the rod and pipe were first adjusted to correspond as closely as possible, so as to obtain a value of the true conductivity of the metal. The temperatures along the pipe were then adjusted to differ by a certain amount, either above or below, from the corresponding temperatures of the rod, and when steady conditions had been



obtained the apparent conductivity was calculated. The temperature gradient between the points T2 T4 (fig. 1) was about 40° C. throughout, and the temperature of T3 approximately 160° C. The results obtained are shown in fig. 5,


0° +10° +20°-30°C. -20° H00Temp. Pipe le ss Temp. Bar.

F ig. 5.

and it will be observed that the error due to a mean difference of 1° C. between the rod and pipe was about 1 per cent. I t was estimated that the mean temperature difference between corresponding points on rod and pipe could be adjusted to between 1° C. and 2° C., so that this fixes a definite limit to the accuracy of the method. This limit may be stated to be from 1 to 2 per cent, for the aluminium bar working with a temperature gradient of 40° C. Working with higher or lower temperature gradients or with metals of higher or lower conductivity the accuracy would be correspondingly greater or less. r As a check on the above conclusion, it is possible to make an approximate estimate of the lateral heat loss from the known conductivity of insulating material. No attempt can be made here to give a mathematical solution of the problem under consideration, namely, the flow of heat between coaxial cylinders with a constant difference of temperature between the corresponding points in planes at right-angles to the axis and with a longitudinal gradient in each cylinder, but as an approximation it is proposed to take the case of a constant difference in temperature, but no gradient. The formula for the lateral flow of heat per 1° C. difference would then be

„ 2 • 73KZ ,H = 1------ TTT\ cals/ sec-logio (o/«)

Here a and 6, the diameters of the rod and pipe respectively, are 1-9 and 7-0 cms.; l is taken as 30 cms., i.e., the complete length between Tx and T4, and K, the thermal conductivity of the insulating medium at a mean temperature of 160° C., is about 0-00015 e.g.s. units for “ Sil-o-cel.” Hence we get

H = 0-022 cals/sec.




Now the flow of heat through the aluminium rod for a temperature differenc of 40° C. between T2 and T4 at a distance (d) apart of 20 cms. is given by

H = 7ra2K = 2 -9 5 cals/sec.

So that the lateral heat loss per 1° C. in the case taken is estimated as 0-7 pei cent, of the heat flowing in the rod, a result which is of the same order as tha* obtained by experiment.

I t may be added that the error due to lateral heat loss varies inversely as the square of the diameter of the specimen rod, provided that the ratio of the diameters of the rod and pipe is constant, so that it would be advantageous to use specimens of large diameter. The limit of the dimensions of the present apparatus was decided largely on considerations of convenience and expense.»

(e) Magnitude of Longitudinal Heat Loss.The isothermal surfaces in the lagging being adjusted so as to be approximately

perpendicular to the axis, it follows that there will be a longitudinal flow ol heat in the lagging, which will be contributed mainly by the pipe, but to some extent from the rod. The poorest conductor of all the metals tested, namely, nickel, having a conductivity of the order of 1,000 times that of the insulating material, it was considered safe to neglect the contribution from the rod to the longitudinal heat loss.

III.—E l e c t r ic a l Co n d u c t iv it y .

The measurement of the electrical conductivity of the several metals has been undertaken merely to throw light on its relation to the thermal conductivity. For this purpose an accuracy of 1 per cent, suffices, so that an elaborate investigation has not been called for. The method used consisted in a comparison of the voltage drop on a measured length of the specimen and on a standard resistance arranged in series with it, a constant current being maintained through the two,

Since this method has been adopted by a number of experimenters, a detailed description is not required here, but the following particulars should perhaps be mentioned

The current was led into and out of the specimen rod by copper rods 4 mm. in diameter screwed into the test rod. The voltage drqp was measured by means of thin potential wires pegged into the specimen at a distance of 22 cms. apart. The specimen was fixed centrally in a tubular furnace 1 • 8 metres long wound with nichrome ribbon, and its temperature was measured by 3 thermocouples. The space between the specimen and the furnace tube was packed with “ Sil-o-cel



hermal and Electrical Conductivities o f some Pure Metals. 217

ywder. The current, which was supplied from a large storage battery, was of ie order of 10 amps. In order to eliminate any thermal E.M.Fs. at the potential oints, measurements were made before and after reversing the main current, hile the effects of thermal E.M.Fs. in the potentiometer circuit were iminated by taking readings before and after a simultaneous reversal of the otential leads and the leads supplying the current to the instrument. The tagnitude of the difference due to these two sets of reversals seldom exceeded microvolts, and it was estimated that the volt drop was obtained to better

kan 1 microvolt, a precision amply sufficient to meet the requirements.No special difficulty occurred in applying this method, except in the case of

lagnesium, where at temperatures over 300° C. voltaic effects were likely to ccur, which were eliminated by the use of potential leads of the same metal s the specimen.

IY .— D is c u s s io n of R e s u l t s .

The detailed results of the measurements of thermal and electrical conduc- ivity are set out in Appendices I to V. The values obtained are also shown a figs. 6 and 7 and, since the majority of the metals were also investigated by jees and by Jaeger and Diesselhorst, their values over the respective ranges if —100° C. to 18° C. and 18° C. to 100° C. have been included for purposes of jomparison. Some individual values given by other observers have been shown >n the graphs or are referred to in the text below. For the purpose of dealing vith the relation of thermal to electrical conductivity, the values of Lorenz’s unction have been set out in Table I (p. 218).

In this table the names of the observers have been indicated by initials, their methods of experiment have differed considerably. Thus, as already stated, an “ electrical ” method was used by Jaeger and Diesselhorst, by Meissner md, in a considerably modified form, by Angell. The other observers worked with “ thennal ” methods. Lees, who introduced many refinements, obtained his values in absolute units ; Konno was primarily interested in changes of conductivity on melting, and used a relative method, taking Lees’ values at i8° C. for his starting points ; the method of Honda and Shimidu has already oeen outlined. Detailed comments on the results are appended under the heads of the several metals.



218 F. H. Schofield.«

Table I.—Relation of Thermal and Electrical Conductivity.

Metal. Purity. Observer.

Value of Lorenz’s function K /aT x 108 (K in watts /cm./0 A in reciprocal ohms/cm.) at Temperatures of 1

—100° c. 18° C. 100° c. 200° C. 300° C. O O j

p 1

500° C. 600° C.

r 99 L 1-81 2 1 3J & D 2* 19 2-27 i

Aluminium ........... ^ 99 A 2-25 2*68 3 1 8 3-79 4-48 5-081 K* 2-30 2*25 2-29 2-26 2-23 2-14 2-03H L 99-7 S 2-23 2-36 2-44 2-53r L 2-17 2-32

J & D 2-29 2-32Copper ................... ^ M(l) 2-25 2-33

M(2) 2-26 2-34L 99-9 S 2-31 2-36 2-34 2-37 j 2-34 2-35

Magnesium ............... 99-6 S 2-31 2-32 2-30 2-33

ir 99 L 2-59 2-5997 J & D 2*40 2-44

Nickel ....................«{ 97 A 3-10 2-67 2*24 1-81* 1 97 H & S 2-37 2-53 2-71 2-68 2-71 2-75

l 99-2 S 2-28 2-39 2-65 2-79 2-62 ! 2*64

j L 2-39 2*43Uxrxr* J J & D 2-31 2-33/line ........................< K* 2-45 2-47 2-47 2-41 2-36

j 99*81

S 2*26 2-26 2-29

* Konno’s values of thermal conductivity are relative to those of Lees at 18° C., and for electri j conductivity he has taken those of Tsutsumi (‘Sci. Rep.,’ vol. 7, p. 93 (1918)).

Aluminium.

Like Lees, and Jaeger and Diesselhorst, in their respective ranges, the author finds that the conductivity of aluminium shows a slight increase with tempera- :j ture. I t will be noticed from fig. 6 that, at the points of overlap, the values of j Jaeger and Diesselhorst are considerably lower than the other two, probably j owing to impurity in their specimen. As would be expected, the electrical resistivity found by Jaeger and Diesselhorst is correspondingly higher (see fig. 7). Three other sets of values above 100° C. are available, namely, those of Ezer Griffiths, Angell and Konno. The first mentioned used material of nearly the same purity as that tested by the author, viz., 99*5 per cent., as against 99-7 ̂per cent., and he gave values for his four specimens ranging from 0*50 to O’52 at 100 C., and found a slight tendency to increasing conductivity with temperature up to the limit reached (250° C.). This is in very fair agreement with the results of the present experiments. On the other hand, Angell gives the value



'hernial and Electrical Conductivities of some Pure Metals. 219

i i i i_ — Protonh Fvnorim ^nK

12S . . .g e l l . .. ida 3oSi

I1........ 1908

___ >

A1

=•— =Jk

9 9

ig e r &

i

9 9 (FUDiessel

>peat Readings) horst. .1900_____J___ «*J

-O--- o

Kl

- = A n— = Hor

.......... 1midu...l

9U J 917 H

r-*-*—

CuQi ScateJ- — ---- -4*.—:u(54S cale)------- (

Mq#— 19Z n ------m —♦----4L— Z n

Ni m - * efc----\ n jF -"1—-* >~- - - V - i —< ____

i------ < r

!-200 -100 0 100 200 300 400 500 600 700 800M e a n Tem p. °C.

Fro. 6 .

'/a ScaleP resent Experim ents. J a g e r &. Diesselhorst. 1900 L e e s . 1908 i

500 600 700 800 900300 400100 200

VOL. CVII.--- A. R




as increasing from 0-49 at 100° C. to 1-0 at 600° C. and Konno as decreasing from 0 • 50 to 0 • 36 over the same range.

As to Lorenz’s function, it will be seen that the values of the severa observers are in good agreement at 100° C. Konno gives a nearly constam value throughout, and the others give values rising somewhat with temperature those of Angell showing the greatest change.

Copper.The author’s values for the thermal and electrical conductivity show a satis

factory continuity with those of Lees and of Jaeger and Diesselhorst. The copper used in all three cases seems to have been nearly 100 per cent, in electrical conductivity, according to the international specification.

Further values for copper were obtained by Meissner with two specimens oi the metal. One of these (No. 1) was better than, and the other (No. 2) equal to, the 100 per cent, standard in conductivity. The respective values obtained are as follows :—

Table II.—Thermal Conductivity of Copper.

Observer. Klg K ioo

Meissner (1) 0-94 0-94„ (2) .... ............ 0-92 0-92

Lees 0*918 —Jaeger and Diesselhorst .... 0-918 0*908Present paper 0.90x

Meissner’s* figure of 0 • 94 appears to be the highest reliable value yet obtained for copper. Schottf gives 0 • 98 for a natural crystal of copper, but this value is probably too high, as his figure for pure commercial copper is as large as 0 • 94.

With regard to Lorenz’s function, it will be seen from the table that there is a good agreement at 100° C. and that the author finds a nearly constant value throughout.

Magnesium.The only previous value traced is that of Lorenz, who gives 0*37$ for the

thermal conductivity at 100° 0. According to the present experiments, the value for the same temperature would be about 0 • 336.

The values for electrical conductivity are in fair agreement with those of

* * Ann. der Phys.’ (4), vol. 47, p. 1001 (1915). t * Verh. der Phys. Ges.,’ vol. 18, p. 27 (1916).



1 hernial and Electrical Conductivities o f some Pure Metals. 221

icolai,* the latter being on the average about 3 per cent, higher. For Lorenz’s jiction a nearly constant value is obtained, which does not differ greatly om those found for copper and zinc.

Nickel.As will be seen from Table I, the purity of the specimens used by the several

oservers varied considerably. In correspondence with the purity, the values iven by the present experiments at 100° 0. for the thermal and electrical inductivities are somewhat higher than either those of Jaeger and Diesselhorst, r Honda and Shimidu. The curve for electrical conductivity shows a pro- ounced change in curvature at the change point at about 350° C. The form f the curve agrees closely with those found by Nicolai ,Somerville,f Pecheux,$: nd by Honda and Shimidu, while the absolute values are in close agreement dth that of Pecheux, whose specimen was of 99-6 per cent, purity, as compared dth 99 • 2 for the specimen used in the present experiments. The author’s values or the thermal conductivity show a decrease with temperature between 100° C. nd 300° C., thereafter an approximately constant value to 500° 0., while the wo values obtained in the neighbourhood of 700° 0. show a considerable rise, he results of Honda and Shimidu give a generally similar curve, but their aethod permitted the taking of a large number of values with temperature

i Inferences as small as 30° C., so that they were able to trace a definite minimum f conductivity at about 400° C. With the present dimensions of the apparatus .escribed in this paper and a metal of as low conducting power as nickel it is lecessary to use gradients as high as 100° C. to obtain an accuracy of 2 or 3 per ent. Consequently, the point of inflexion in the conductivity curve could not >e accurately located. This fact probably accounts for the apparently high

■ ralue obtained for Lorenz’s function at a temperature of 400° C. I t will be observed for Table I that the value tends to become constant at about 2 • 6 from 'L^emperature of 300° C. upwards. A similar phenomenon was observed by londa and Shimidu, while Angell found a steady fall in the value with rising emperature.

Zinc.The values obtained for the thermal and electrical conductivity are slightly

»wer than those of Jaeger and Diesselhorst at 100° C. Like Konno, the author finds a nearly constant value for Lorenz’s function.

* ‘ Phys. Zeits.,’ vol. 9, p. 367 (1908).t ‘ Phys. Rev.,’ vol. 33, p. 77 (1911).t * La Lumidre filectrique,’ vol. 10, p. 232.



F. H. Schofield.222

V. S u m m a r y .

The thermal and electrical conductivity of a number of pure metals has h#i measured for mean temperatures ranging to a maximum of 700° C. thermal conductivity of ahiminium was found to increase with rising t<v-S perature, that of nickel to decrease at first and then above 500° C. to showi# increase. The other metals—namely, copper, magnesium, zinc—showed #j the whole slight decreases of conductivity with temperature.

The values of Lorenz’s function for copper, magnesium and zinc we practically constant at all temperatures ; that for aluminium showed a |# with increasing temperature ; that for nickel showed a rise to 300° C., abe® which temperature it remained nearly constant, except for an abnormal vae at 400° C.

In conclusion, the author desires to make his acknowledgments, in additab to those already recorded, to the Director of the National Physical LaboratB and to Dr. Kaye, the Superintendent of the Physics Department, for the a m i facdities placed at his disposal. Further, he is especially indebted to 1c Challoner, observer in the Physics Department, not only for his skill in cd-|i structing the apparatus and suggesting improvements, but also for taking % majority of the observations.

Particulars of Specimen (British Aluminium Co., Ltd.).—The specimen v* prepared as follows:—Billets 6J inch in diameter were cast from a maxima 3 temperature of 700° C., annealed for 2^ hours at 500 C., extruded at tfll perature of 420° C. to f inch diameter, and finally annealed for 2£ hours I 450° C.

In order to test the soundness of the material, transverse and longitudjM sections were taken from the ends of the specimen and were examined in Metallurgy Department of the National Physical Laboratory. These reported to be free from the more serious defects of extruded materials, yfl unsoundness, discontinuities between the core and surrounding layers, inclusfl of dross and oxidised skin.

A p p e n d ix I.

Aluminium.

Density at 21° C. = 2*70. Purity 99’7 Al.



formal and Electrical Conductivities of some Pure Metals. 223,

Thermal Conductivity.

t eanvit nfira* Temperature

Differencet s- t 4

Energy supplied to Bar.Conductivity c.g.s. units.

MeanConductivity c.g.s. units.

s t j

if© atAmps. Volts. Cals/sec.

—

4 c. °c.r08-7 36-7 1-360 16-60 5-38 0-528 0-528

28-6 51-7 1-135 28-95 7-84 0-532 0-5321 C : 5 4 0 60-0 2-585 12-20 7-53 0-528 0-528

'l 49-4 28-1 2-030 8-70 4-22 0-526 148-9 28-1 2-025 8-70 4-21 0-525 y 0-52649 1 28-0 2-025 8-70 4-21 0-527 J

y!54-0 46-9 2-395 12-50 7-15 0-536 1 0-536563-8 46-9 2-395 12-50 7-15 0-536

574-8 80-0 2-845 18-20 12-35 0-544 1u 573-3 80-5 2-840 18-20 12-35 0-540 L 0-542id 571-6 80-3 2-830 18-20 12-30 0-537r| J68 • 8 78-3 2-820 18-20 12-25 0-547 |

146-4 34-8 2-150 10-20 5-24 0-527 1149-4 36-4 2-160 10-30 5-32 0-528 Y 0-528*01149-7 35-5 2-160 10-40 5-36 0-530 J

* Repeat reading.

Electrical Resistivity.

Temperature. Resistivity.|

Temperature. Resistivity.

°c. Ohms per cm. cube. °c. Ohms per cm. cube.16-2 # 2-83 X 10- 6 302-7 6-15 X 10“616-8 2-79 304-4 6-2316-8 2-81 306-2 6-2473-0 3-45 399-0 7-3977-0 3-53 500-0 8-7779-0 3-53 502-4 8-79

160-0 4-474-48

540-7 9-31161-0

A p p e n d ix II.Copper.

Particulars of specimen (T. Bolton & Sons, Ltd., Oakmoor).1 The specimen was prepared as follows :—Billets were cast from a mixture of

cathodes and § electrolytic wire bars immediately after poling. They were >lled hot to 1 inch diameter, drawn cold to f inch diameter, machined and

teolished to § inch diameter, and then annealed.Density at 21° C. = 8-92. Purity 99-9 Cu.



224 F. H. Schofield,


Meantempera

tureTs

TemperatureDifference

T2-T 4

Energy supplied to Bar.Conductivity c.g.s. units.

Mean t? Conductivity c.g.s. units.Amps. Volts. Cals /sec.

° c . ° c .93-8 19-1 2-475 8-30 4-91 0-900 196-2 20-0 2-490 8-50 5-06 0-89095-6 19-9 2-505 8-60 5-14 0-908 ► 0-901 , |96-0 19-4 2-515 8-30 4-98 0-90098-4 20-9 2-590 8-75 5-41 0-907

177-4 43-4 3-215 14-40 11-05 0-893177-9 44-4 3-230 14-60 11-25 0-890172-4 44-0 3-225 14-60 11-25 0-897 Jl ° ‘893 1

266-0 73-6 3-755 20-80 18-65 0-888265-7 73-6 3-750 20-85 18-65 0-890 i[■ 0-888 1265-7 74-0 3-750 20-85 18-65 0-885 J473-1 93-4 3-585 26-76 22-95 0-862473-4 94-5 3-590 26-80 23-00 0-854

jiy 0-858 1472-0 93-8 3-585 26-85 23 00 0-858 J624-8 142-0 3-720 38-40 34-15 0*842 'l624-7 142-1 3-720 38-45 34-20 0-844 1► 0-842 1624-7 142-3 3-720 38-45 34-20 0-839 J151-8 30-7 2-060 16-10 7-93 0-905 0-905* I

* Repeat reading.


Temperature ° C. Resistivity Ohms per cm. Cube. Temperature ° C. j Resistivity Ohms |f

per cm. Cube.I

14-0 1-69 X 10-6 470-0 4*88 X 10~6145-0 2-59 630-5 6-00144-5 2-61 630-0 6 0 7306-0 3-73

A p p e n d ix III.Magnesium.

Particulars of specimen (Magnesium Co., Ltd).—The specimens were extruded to f; inch diameter from a billet 5 inch in diameter, annealed at 360° C. for 6 hours, and allowed to cool slowly.

Density at 21° C. = 1 • 75. Purity 99 • 6 Mg.



• •

'hernial and Electrical Conductivities o f some Pure Metals. 225


MeanTempera

tureTs


T*-T4

Energy supplied to Bar.Conductivity c.g.s. Units.

MeanConductivity c.g.s. Units.Amps. Volts. Cals/sec.

160-4 42-1 1-940 8-00i

3-71 0-328 1157-0 42-2 1-920 8-10 3-71 0-328 1> 0-328156-0 40-4 1-905 7-90 3-60 0-332 1153-2 39-1 1-860 7-60 3-38 0-322 J

264-0 74-7 2-290 11-85 6-48 0-324263-0 76-5 2-300 11-85 6-51 0-317261-7 77-3 2-290 11-80 6-46 0-312 ► 0-318

i 258-3 75-5 2-285 11-60 6-33 0-313| 251-3 72-5 2-275 11-50 6-26 0-322

329-5 102-4 2-495 14-20 8-47 0-308 1322-0 98-6 2-460 14 00 8-23 0-311 y 0-309326-4 103-8 2-510 14-30 8-58 0-308 J

I 456-0 104-8 1-510 24-50 8-84 0-314 \ 0-314( 456-5 104-6 1-500 24-50 8-78 0-314

254-2 70-5 1-370 18-70 6-12 0-323 0-323*253-0 73-0 2-230 11-40 6-08 0-311 0-314*

* Repeat readings with different heating coils.


Temperature ° C. Resistivity Ohms per cm. Cube. Temperature ° C. Resistivity Ohms

per cm. Cube.

20-0 4-59 X 10-« 199-5 8-08 X 10-«101-4 6-19 314-0 10-35101-1 6-21 348-6 11-21101-1 6-18 348-0 11-04199-2 8-17 480-1 13-74

A p p e n d ix IY.Nickel.

Particulars of specimen (H. Wiggins & Co., Ltd.).—The specimen was prepared as follows :—Cast in 3-inch moulds, hot-rolled to 1J inch diameter, reheated and rolled to § inch diameter, close-annealed at 800° C., cold-drawn to -J§- inch diameter, again annealed, drawn to § inch diameter, and finally annealed between 750° C. and 800° C.

Density at 21° C. = 8*79. Purity 99-2 Ni.



226 F. H. Schofield


MeanTempera

tureT,


Ta-T 4

Energy supplied to Bar.Conductivity c.g.s. Units.

MeanConductivity c.g.s. Units.Amps. Volts. Cals/secs.

99-2 47-5 1-420 5-95 2-02 0-146 Z100-8 48-0 1-420 5-95 2-02 0-145 > 0*145

141-6 59-8 1-490 7-00 2-49 0-143 "I141-6 59-9 1-490 7-00 2-49 0-143 y 0*144141-8 60-0 1-490 7-00 2-49 0-145 J196-7 75-3 1-535 7-95 2-91 0-132 -)196-2 75-5 1-560 8-20 3-05 0-138196-4 75-3 1-580 8-15 3-07 0-140 > 0-138196-0 74-1 1-545 8-00 2-95 0-136 J290-2 81-6 1-510 8-45 3-05 0-128 'J289-7 81-5 1-510 8-45 3-04 0-128289-2 80-9 1-510 8-45 3 04 0-129 k 0-128288-4 80-8 1-510 8-45 3 04 0-129 J353-6 . 99-4 1-610 9-70 3-73 0-129 H355-0 100-3 1-610 9-70 3-73 0-128357-3 100-3 1-610 9-75 3-75 0-128 0-128357-2 100-3 1-610 9-75 3-75 0-128 J491-4 105-8 1-595 10-45 3-98 0-129 -v491-0 106-9 1-595 10-40 3-96 0-127 > 0-128703-3 179-6 1-965 16-35 7-67 0-141 0-141733-0 177-3 1-975 16-70 7-88 0-147 0-147166-5 65-1 1-505 7-20 2-59 0-136* 0-136293-7 84-1 1-575 8-70 1 3-27 0-133* 0-133

* Repeat reading.



per cm. Cube.

14-0 10-04 x 10-« 320-5 29 *70 X 10- •111-0 14-60 327-8 30*75142-4 16-17 331-6 31*20148-5 16-57 349-5 32*35149-2 16-62 358-8 33*50200-5 19-73 383-8 33*95227-0 21-57 409-6 35*00229 * 5 22-10 465-2 36*85265-0 25-52 519-4 38*65266-0 25-10 583-5 40*60280-0 25-90 691-1 43*60304-1 28-15 820-7 47*60



thermal and Electrical Conductivities o f some Pure Metals. 227

A p p e n d i x V .

Zinc.Particulars of Specimen (London Zinc Mills).—The specimen was prepared as

>llows :—Billets were cast, were rolled a t 200° C., sawn into strips and drawn old.Density at 21° C. = 7*13. Purity 99*8 Zn.


Mean temperature at

T,


t 2- t 4

. Energy supplied to Bar.Conductivity Mean

Conductivity c.g.s. Units.Amps. Volts. Cals/sec.

c.g.s. Units.

| °C. ° c.87-5 25-0 1-520 4-90 1-78 0-25687-7 25-0 1-520 4-85 1-77 0-25687-587-5

25-825-1

1-5451-530

5-054-95

1-861-81

0-2590-259 * 0-258

87-5 26-0 1-540 5-05 1-86 0-25687-8 25-0 1-540 5-00 1-84 0-264 --

160-5 54-4 1-910 8-10 3-70 0-244160-3 53-2 1-900 8-05 3-65 0-246 1l 0-246160-3 53-4 1-905 8-10 3-68 0-247160-2 52-8 1-910 8-00 3-65 0-249

227-5 80-5 2-155 10-60 5-46 0-243 >227-1 80-0 2-160 10-30 5-32 0-239227-1 79-9 2-145 10-60 5-44 0-243 * 0-241224-5 79-5 2-150 10-45 5-37 0-242223-5 78-3 2-130 10-30 5-25 0-240

284-1 102-6 2-325 12-40 6-89 0-240 1288-5 102-7 2-320 12-40 6-88 0-239 l 0-238290-8 103-9 2-320 12-40 6-88 0-237 i291-6 104-6 2-330 12-40 6-91 0-236 1117-9 47-8 1-950 7-30 3-40 0-255 1117-7 48-6 1-955 7-30 3-40 0-251 0-253*117-1 49-0 1-920 7-50 3-44 0-252 1

* Repeat reading.



per cm. Cube.

35-0 6-08 X 10~6 105-0 8-08 X 10-•107-0 8-15 200-8 10-47106-0 8-10 200-0 10-48105-0 8-09 350-2 14-50



The thermal and electrical conductivities of some pure...

Documents

Transcript of The thermal and electrical conductivities of some pure...