Physics. - Establishment f an Abslute Scale fr the herm-electric Frce. By G. BOR ELlUS. W. H. KEESOM. C. H. JOHANSSON and J. O. LND E. Supplement N0. 69b t the Cmmunicatins frm the Physical Labratry at Leiden. (Cmmunicated at the meeting f January 30. 1932.) he results btained fr the therm-e1ectric frces f Pb and Sn at liquid helium temperatures and higher 1) tgether with the assumptin made prbable by thse results. that the HOMSON-heat a is zer in the supracnducting state 2). render the establishment f an abslute scale fr therm-e1ectric frces pssible. he H OMSON thery gives the frmula de al dy - - 02 which n accunt f the N ERNS therem gives?y integratin ' e=.[~ d-.[id. (2) 0 he integrals may be called the abslute therm-e1ectric frces per degree fr each f the tw metals. and they are f curse f mre interest than the therm-electric frce f the cupe. t is bvius frm (2) tha t if the integral is knwn fr ne metal. it may he determined fr any ther metal at any temperature by measurement f the therm-electric frce against the first. get the value f the integral fr that ne metal. it is. hwever. necessary t knw the values f al cntinuusly frm dwn t the lwest temperatures. Frtunately the measurements seem t give such a knwledge with a fairly gd degree f accuracy. Belw the critical pint f Sn at 3.72 0 K al is by assumptin zer fr Sn as weil as fr Pb. Frm 3.72 t 7.2 0 K it is zer fr Pb. and may be calculated fr Sn and fr the special silverally wire called "nrmal" in the Cmmunicatin mentined 3) by the aid f equatin (1) frm the thermc1ectric frces against Pb. Abve 20 0 K al is knwn fr the nrmal frm the direct measurements f the HOMSON heat made by BOR ELlUS. KEESOM and JOHA NSSON 4) and may be calculated fr Pb and Sn fr m thc measurements f Cmm. N. 217c. All these values have been determin~d graphically ') G. BORELlUS. W. H. KEESOM. C. H. johansson and j. O. LNDE. hese Prc. 34. 1365. 1931. Cmm. Leiden N O. 217c. 2) Cf. 3 Cmm. Leiden N O. 217 c. 3) Cf. Cmm. Leiden NO 217 c. 4) hese Prceedings 31. 1046. 1928. Cmm. Leiden N O. 196a. (1)
11 and are shwn in Fig. 1 by the full lines. Between 7.2 and 20 K ther~ is an interval. where n values culd be directly calculated frm ur measurement. As will be seen frm the diagram in the case f Sn the gap can. hwever. quite easily be filled up by cnnecting the curves n its sides. As t Pb and the nrmal the shape f the curves between 7.2 and 20 is rather unfit fr a graphical interplatin. he dtted lines in the figure were derived frm the therm-electric frces against Sn accrding t equatin (1). At the critical pints the curves are simply drawn as if there were a discntinuity in defd. thugh in fact we nly knw. thilt there is a rapid change. As hwever the curves are btained here by graphical derivatin this detail will have n influence n the result f the ABLE. Numerical values t Fig. J. OK. "- 10 8 vlt per (degree)2 Sn31 Pb31 Nrmal <3. 7 0 0-3. 7-1.7 0 +0. 1 5 1.9 0 0. 1 6 2.3 0 0. 2 7 2. 55 0 0.2 7.2 - - 14.3 0.2 10 3.3 15.0. is 12.5 3. 7 5 i.2 3.5 15 i.o 0.6 3.5 5 17. 5 i.o 0.3 2. 17 20 3.8 0.37 1.55 30 2.9 +0. 18 0.80 io 2.15 - O.Oi 0.25 50 0.86 0.09 - O.Oi 60 0.51 0.05-0.03 70 0.-44 0.13 +0.03 80 0.36 0. 15 0.10 90 0.2i 5 0.38 5 0. 155 100 0.19-0.21
12 graphical integratin in the fllwing. he numerical values cnnected with Fig. 1 have been cllected in able. Fig.. a de.b. dt fr Sn31. Pb31 and silverally-nrmal in vlt p~r (degree)2. he curves in Fig. 1 have been graphically integrated, and the abslute therm-electric frces per degree eab. =.[ ~ d (3) th us btained are given in Fig. 2 and able 11. he even frm f these curves as cmpared with the curves in Fig. 2 f Cmm. N0. 217c, see~s t cnfirm the crrectness f the graphical interplatin fr Sn between 7.2 and 20 K and als demnstrate the usefulness f the abslute scale. " e ~/O 10 20 JO ';0 50 60-1. 0 ),ver-,.. _u. V ---- '1\ l~ 1\ t'--.. Pb ""--- ~ -... ~ r--- 7f-~ -90-2.0 Fig. 2. herm-electric frce in vlt per degree fr Sn310 Pb3 and silverallynrmal in th~ abslute therm-electric scal~.
13 ABLE l. hermelectric frces in micrvlt per degree in the abslute the-rm-electric scale. OK Sn31 < 3.7 Pb31 Nrmal +0.01 3.7 0 0 0.01 5-0.023 0 0.01 6 Oi2 0 0.01 7 0.067 0 0.01 7.2 0.073 0 0.01 5 la 0.15 5 - O.iO 0.030 12.5 0.25 0.68 5 0.096 S 0.3is 0.73 5 0. 185 17.5 0.44 5 0. 74 0.26 20 0.5is 0.75 0. 30 5 30 0.88 5 0. 74 i2 ia 1.13 0. 73 0.i7s 50 1.28 5 0. 74 0.i8 60 1.3i 0.74 5 0.i7 5 70. 39 0.75 0.i7s 80.ii 0.76 0.i8 90 1.46 5 0.79 5 0.i9 5 100 1. 48 5 0.83 5 0.51 5 With further use f the measurements f BORELlUS. KEESOM and JOHANSSON n the HOMSON heat f the nrmal the e abs f this wire are calculated further up t 300 0 K and are given in table 111 fr the same temperatures as are used in ur interplated tables fr therm-electric frces per degree in the earlier papers 1). We es ti mate the errr in these abslute therm-electric frces at rm temperature at abut -+- 0.1 micrvlt per degree. ') hese Prceedings 33. 17 and 32. 1930. Cmm. Leiden NO. 206a and b.
ABLE 111. herm-e1ectric frce in micrvlt per degree fr the silverally-nrmal in the abslute therm-electric scale. (e abs = J; d) OK e eab.s 11 K e 2-271.1 +0.00 5 73. 1-200 0.i8 i 269.1 0.01 83.1 190 0.i9 6 267. 1 0. 01 93. 1 180 0.50 8 265. 1 0.01 5 103. 1 170 0.52 10 263. 1 0.03 113. 1 160 0. 5i 13.1 260 0. 12 133. 1 1i0 0.61 18.1 255 0. 27 153. 1 120 068 23.1 250 0. 35 5 173. 1 100 0.76 28. 1 2i5 0.i0 5 193.1 80 0.8i 5 33.\ 2040 0. 41 213.1 60 0.93 38.1 235 0.i6 5 233.1 io 1.02 i3.1 230 0.i8 253.1 20 1.11 53.1 220 0.i8 e ab 273. 1 0 1. 20 63. 1 210 0.i8 293. 1 +20 1.29 5 We at last wish t pint ut that the pssibility f using the measurements n the supracnductrs fr the establishment f the abslute scale was nt quite dear t us at the time as the measurements were perfrmed. he results are therefre nt in details the mst cnvenient fr this purpse. t is prbable that the scale can be mre exactly determined by measurements n an extended number f supracnductrs. Summary. he authrs intrduce eab. =.J' ~ d (a = HOMsON-heat) as the therm-electric frce per degree f a metal in the abslute therm-electric scale. hey calculate this quantity fr tin, lead, and the silverally-nrmal they used, n the basis f their measurements f the therm-electric frces and f the HOM SO N-heat, f the assumptin that a = 0 in the supracnducting state, and f an interplatin fr tin between 7.2 and 20 K.