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CRYOGENIC THERMOCOUPLE TABLES- PART I11
MISCELLANEOUS AND COMPARISON MATERIAL COMBINATIONS
Larry L. Sparks and William J. Hall
U. S. D E P A R T M E N T O F COMMERCE NATIONAL BUREAU OF STANDARDS
BOULDER LABORATORIES Boulder, Colorado
A BUREAU OF STANDARDS REPORT
NBS PROJECT NBS REPORT
27503-2750439 972 1 January 1969
CRYOGENIC THERMOCOUPLE TABLES - PART I11
MISCELLANEOUS AND COMPARISON MATERIAL COMBINATIONS
Larry L. Sparks and William J. Hall
Cryogenics Division Institute for Basic Standards
National Bureau of Standards Boulder, Colorado 80302
IMPORTANT NOTICE
N A T l O N A L B U R E A U OF STANDARDS REPORTS are usually preliminary or progress accounting documents intended for use within the Government. Before material in the repsrts is formally published it is subjected to additional evaluation and review. For this reason, the publication, reprinting, reproduction, or op,en-literature listing of this Report, either i n whole or i n part, is not authorized unless permission is obtained i n writing from the Office of the Director, National Bureau of Standards, Wash~ngton, O.C. 20234. Such permission IS not needed, however, by the Government agency for which the Report has been specifically prepared i f t l ~ a t agency wishes to reproduce additional copies tor its own use.
U.S. DEPARTMENT OF COMMERCE N A T I O N A L BUREAU OF STANDARDS
List of F i g u r e s Page
Figure I Thermoelectr ic voltage for Chromel vs -
at . 70 i ron . . . . . . . . . . . . . . . . 12
Figure 2 Thermopower for Chromel vs gold-0.02 at . '$0 i ron. . . . . . . . . . . . . . . . 13
Figure 3 Thermopower derivative for Chromel vs gold-0.02 at . ojb i ron. . . . . . . . . . . . . . . . 14
Figure 4 Deviations between calculated and experimental values of thermoelectr ic voltage for
. . . . . . . . . Chrome1 vs gold-0.02 at. 70 i ron 15
Figure 5 Thermoelectric voltage for copper vs gold-0.07 at. 70 i ron. . . . . . . . . . . . . . . . 19
Figure 6 Thermopower for copper vs
F igure 7 Thermopower derivative for copper vs . . . . . . . . . . . . . . . gold-0.07 at . 70 i ron. 21
Figure 8 Deviations between calculated and experimental values of thermoelectr ic voltage for copper vs gold-0.07 at. 70 i ron . . . . . . . . . . 22
Figure 9 Thermoelectr ic voltage for copper v s . . . . . . . . . . . . . . . gold-0.02 at . % i ron. 2 6
Figure 10 Thermopower for copper vs gold- 0.02 at. 70 iron. . . . . . . . . . . . . . . . 27
Figure 11 Thermopower derivative for copper vs gold-0.02 at. % i ron. . . . . . . . . . . . . . . . 28
Figure 12 Deviations between calculated and experimental values of thermoelectr ic voltage for copper vs gold-0.02 a t , 70 i ron . . . . . . . . . . 29
Figure 13 Thermoelectric voltage for platinum vs gold-0.02 at . 70 iron. . . . . . . . . . . . . . . . 33
Figure 14 Thermopower for platinum vs gold-0.02 at . 70 i ron. . . . . . . . . . . . . . . . 34
Figure 15 Thermopower derivative for platinum vs gold- 0.02 at. % i ron. . . . . . . . . . . . . . . . 35
List of Figures (coiitinued) Page
Figu re 16 Deviat ions between calcula ted and exper imenta l values of t he rmoe l ec t r i c voltage fo r plat inum v s gold-0.02 at. 70 i r o n . . . . . . . . .
Figu re 17 The rmoe l ec t r i c voltage fo r "normal" s i lve r v s gold-0.02 at. yo i r o n . . . . . . . . . . . . . .
Figu re 18 Thermopower fo r l l n o r m a l l l s i l ve r v s gold-0.02 at. yo i r o n . . . . . . . . . . . . . . .
Figu re 19 Thermopower der ivat ive f o r "normal" s i l ve r v s gold-0.02 a t . yo i ron . . . . . . . . . . . . . .
Figu re 20 Deviat ions between calcula ted and exper imenta l va lues of t he rmoe l ec t r i c voltage f o r "normal" s i lve r v s gold-0.02 at. 70 i r o n . . . . . . . . . .
Figu re 2 1 The rmoe l ec t r i c voltage fo r Chromel ( 1 ) v s Chromel (2 ) . . . . . . . . . . . . . . . . . .
Figu re 22 The rmoe l ec t r i c voltage fo r Ch rome l (2 ) v s Chromel ( 3 ) . . . . . . . . . . . . . . . . . .
Figu re 23 The rmoe l ec t r i c voltage f o r Ch rome l (1 ) v s Chromel ( 3 ) . . . . . . . . . . . . . . . . . .
Figu re 24 Deviation of individual the rmovol tages f r o m group average fo r Chromel . . . . . . . . . . .
Figu re 25 The rmoe l ec t r i c voltage f o r copper ( 1 ) v s copper (2 ) . . . . . . . . . . . . . . . . . . . .
Figu re 26 The rmoe l ec t r i c voltage f o r Alumel (1 ) v s Alumel ( 2 ) . . . . . . . . . . . . . . . . . . .
Figu re 27 Thermoelec t r i c voltage fo r constantan (1 ) v s constantan ( 2 ) . . . . . . . . . . . . . . . . .
Figu re 28 The rmoe l ec t r i c voltage fo r constantan (2 ) v s constantan ( 3 ) . . . . . . . . . . . . . . . . .
Figu re 29 The rmoe l ec t r i c voltage fo r constantan (1) v s constantan ( 3 ) . . . . . . . . . . . . . . . . .
Figu re 30 Deviation of individual thermovol tages f r o m group average fo r constantan . . . . . . . . , .
List of F i g u r e s (continued) Page
Figure 31 Thermoelectr ic voltage for gold-0. 07 at. 70 i ron vs gold-0.02 at. 70 iron. . . . . . . . . . . . . . 54 -
Figure 32 Thermoelectr ic voltage for annealed platinum vs unannealed platinum . . . . . . . . . . . . . 55
Figure 33 Thermoelectr ic voltage for annealed "normal" s i lver vs unannealed "normal" s i lver . . . . . . 56
List of Tables Page
Table 1
Table 2
Table 3
Table 4
Table 5
Table 6
Table 7
Table 8
Table 9
Thermal voltage, thermopower , and thermo - power derivative for Chromel vs gold-0.02 at . yo i ron. . . . . . . . . . . . . . . . 9
Thermal voltage, thermopower , and thermo - power derivative for copper vs
Thermal voltage, thermopower, and thermo- power derivative for copper vs
. . . . . . . . . . . . . . . gold-0.02 at. % i ron. 23
Thermal voltage, thermopower , and thermo - power derivative for platinum vs
. . . . . . . . . . . . . . . gold-0.02 at. 70 i ron. 30
Thermal voltage, thermopower, and thermo - power derivative for "normal" silver vs
. . . . . . . . . . . . . . . gold-0.02 at. yo iron. 37 - . . . . . . . . . The orthonormal polynomials Fn(T) 5 7
Coefficients for a polynomial expansion representa- tion of the thermocouple data for Chromel v s gold-0.02 at. Yo i ron, copper vs gold-0.07 at . 7'0 iron, copper vs gold-0.02 at. 70 iron, platinum vs gold-0.02 at . yo i ron , and "normal" silver v s gold-0.02 at . yo i ron. . . . . . . . . . . . . . . . 59
Standard deviation (in microvolts) for various o rde r s of polynomial expansions for Chrome1 vs gold-0.02 at. yo i ron, copper vs gold-0.07 at . 70 iron, copper v s gold-0.02 at. '$0 i ron, platinum vs gold-0. 02 at. Yo i ron, ' and "normal" silver vs gold-0.02 at. 70 i ron . . . . . . . . . . 60
Number of digits necessary in computations to reduce round-off e r r o r s below certain l imits for Chromel vs gold-0.02 at. 70 i ron, copper vs gold-0.07 at. yo iron, copper vs gold-0.02 at. YO iron, platinum vs gold-0.02 at . 70 i ron , and "normal" silver vs gold-0.02 at. 70 iron. Decimal digits not in parentheses, binary
. . . . . . . . . . . . . . digits in parentheses
CRYOGENIC THERMOCOUPLE TABLES - - PART III
MISCELLANEOUS AND COMPARISON MATERIAL COMBINATIONS*
L a r r y L. Sparks and William J . Wall
The thermovoltage, thermopower, and thermo - power derivative a r e presented i n graphical and tab- ular fo rm for a ) Chromel, copper, platinum and "normal" silver vs - gold-0.02 at. yo i ron, and b ) cop- pe r vs - gold-0.07 at. % iron. The experimental tern- pera ture range i s f rom 4 to 280K fo r each combina- tion. The experimental data have been extrapolated f r o m 4 to OK. The thermopower of Chrome1 vs - gold- 0.02 at. % i ron i s higher than that of Chrome1 vs - gold- 0.07 at. 0/o i ron below- 12 K. Copper, platinum, and "normalf1 s i lver vs gold-0.02 at. yo i ron a r e reason- ably sensitive below- 15 K. In this temperature range the pure mater ia ls , copper and platinum, have high thermal conductivities and their thermopower s a r e ve ry dependent upon t r a c e impuri t ies of iron. Thermoelectric comparisons a r e made graphically for Chromel, Alumel, constantan, "normal" silver and platinum. The resul t s of these comparisons indicate the degree of noninterchangeability that exis ts between wires f rom different manufacturers.
Key Words: Cryogenics, thermocouples, inter- changeability.
rt, .I.
This work was car r ied out at the National Bureau of Standards under
the sponsorship of the NASA-Space Nuclear Propulsion Office (SNPO-C),
Contract R-45.
T h i s , the third and final r epor t of the "Cryogenic Tl~errulocouple
Table" se r i e s , contains the remainder of the data acquired f rom the f i r s t
set of t e s t mater ia l s . The f i r s t report of the series[I1contained refer-
ence data for thermocouple types T , E, K, and ~ h r o m e l t v s gold-0.07
at. '$0 i ron . These four thermocouple types a r e the most commonly used
low tempera ture combinations. The second report'21contains thermo - e lec t r ic comparisons between reference mater ia l s and pract ical thermo-
couple alloys. Thermoelectr ic propert ies of any combination of the
thermocouple alloys may b e a r r ived at f rom the data in the second report .
The combinations now being reported a r e the miscellaneous and compar - ison types. The miscellaneous combinations a r e usable, pract ical com-
binations of mater ia l s which have not received wide general usage. In
some cases , however, the miscellaneous combinations may have impor-
tant advantages over the m o r e widely used combinations. A1 so included
in this repor t a r e graphical comparisons of wires with the s a m e nominal
composition. These comparison data a r e intended to present a qualita-
t ive picture of how s imi lar ma te r i a l s deviate thermoelectrically.
t Authors' Note: The words Chromel and Alumel a r e reg is te red t r ade
names of Hoskins Mfg. Co. The ASA, ASTM, ISA, designations for the relevant thermocouple combinations and mater ia l s a r e a s follows:
me Elements Mater ials , Trade Names
E EP (+) Chromel, Tophel, T - 1
EN ( - ) constantan, Advance, Cupron
K P ( f ) Chromel, Tophel , T - 1 KN ( - ) Alumel, Nial, T-2
T P ( f ) copper TN ( - ) constantan, Advance, Cupron
Names a r e usually given in this a r t ic le because relatively few people a r e famil iar with the designations KP, KN, etc. However, the use of the t rade names does not constitute an endorsement of one manufac turer ' s products. Al l ma te r i a l s manufactured in compliance with the established standards a r e equally suitable.
The n~iscel laneous thermocouple corribina,tioli,. be ing reyrorted are
( a ) Gbrornel, copper, "normal" silver, and platinum vs ---- gold-0 , 02 a,t, ?&
iron and (b) copper vs gold-0,0? a"c ,ole iron, Calibration data Sor these
p a i r s a r e given in tables I th ru 5 and figures 1 thru 20 , A discuss ion of
experimental e r r o r s i s given i n a previous report!'] The tempera ture
sca les being used a r e IPTS-68[31for temperatures above 20K and the
NBS acoustical scale fo r tempera tures below 20K. The data have been
extrapolated to 0 K. These data m a y be m o r e meaningful after a m o r e
thorough study of the propert ies of dilute - gold-iron alloys, The Chrome1
vs gold-0.02 at. 70 i ron thermocouple exhibits the same general charac-
t e r i s t i c s a s the Chromel v s gold-0.07 at. Yo i ron thermocouple which was
reported ear l ie r . The sensitivity of the C h r ~ m e l v s gold-0.02 at. '$0 i ron
thermocouple i s slightly higher than that of the Chromel vs gold- 0.07 at.
70 i ron thermocouple below- 12 K and slightly lower f rom- 12 K to room
temperature. This ag rees with the general rule for gold-iron alloys that
decreasing the solute concentration increases the low tempera ture sensi-
[ 4 y 51 The principal t ivity and decreases the high tempera ture sensitivity.
advantage of gold-0.02 at . yo i ron over - gold- 0.07 at. % i ron l i e s below the
range of our present calibration sys tem ( 4 to 280K). Chromel v s gold-
0.02 at. % i ron has been tested below 4 K by Rosenbaum!61 The remain-
ing thermocouple combinations which utilize the gold-iron alloys have
received much l e s s general use. The pure ma te r i a l s , platinum and cop-
pe r , a r e not suitable for ve ry low temperature use because of the i r t he r -
moelectr ic dependence upon t r a c e impuri t ies of i ron and their high the r -
ma1 conductivities a t ve ry low temperatures . Since the thermopower of
the gold-iron alloys drops rapidly above 20K, the platinum o r copper vs
gold-iron combinations a r e only sensitive i n the range where platinum
and copper should not b e used. "Normal" silver does not suffer the
thermal conductivity and t race impurity problems of copper and platinum,
The thermopower of "normal" silver i s small; however, when used with
gold-iron alloys below- 15 K the high thermopower of the gold-iron P
makes the combinations usable.
The degree of noninterchangeability that exists between thermo - couple ma te r i a l s f r o m different manufacturers i s i l lustrated i n f igures
21 th ru 33. The data presented i n these figures a r e for Chromel v s
Chromel, Alumel vs Alumel, copper vs copper, constantan v s constan-
tan, gold-0.07 at. TO i r o n vs gold-0.02 at. 70 i ron , annealed platinum v s
unannealed platinum, and annealed "normal1' s i lver v s unannealed "nor-
mal" s i lver . F o r Chromel and constantan, t h ree wires were intercom-
pared; f igures 24 and 30 show the deviation of the individual thermovolt-
age f r o m the group average for these mater ia l s .
Noninterchangeability of thermoelements represents a ser ious
problem to thermocouple users . This i s par t icular ly t rue i n the cryo-
genic tempera ture range where a small discrepancy in the output volt-
age can cause a relatively l a rge e r r o r in the tempera ture determination.
This problem was discussed briefly i n connection with the reference m a -
t e r i a l s presented in the second repor t of this series!21 The control of
thermoelectr ic variations found between wires of the same nominal com-
position can b e increased by comparing the thermocouple mater ia l s to
the proper reference ma te r i a l s , i. e. , thermovoltage with respect to
s i lver -28 at. D/o gold below 50 K and platinum above 50 K. Specifications
for replacement wires may be given so that the new thermocouple sys -
t e m i s within cer ta in tolerances of the original system.
The comparison data presented in this repor t a r e for s imi lar
171 mater ia l s f r o m different manufacturers. In an ea r l i e r a r t ic le com-
parisons were made between different spools of s imi lar mater ia l f r o m
the same manufacturer. The resul ts f rom these in-house comparisons
show about $ of the variation observed wlaen cornparing wires from d j i -
Eerejnt manufac"curers,
The method used to analyze and represent the experimental d a t a
for the miscellaneous mater ia l s i s quite different f r o m the usual l e a s t
squares power s e r i e s method. The experimental values for the volt-
ages of each thermocouple combination a r e approximated by a s e r i e s of
orthonormal polynomials in the La norm ( least squares) , that i s ,
where
E ( T ) - - thermocouple potential in microvolts;
T - - temperature i n degrees Kelvin;
L - - the highest order for a bes t f i t , different
for different combinations:
A, - - constants to b e determined by the fitting
approximation; and
Fn(T) = orthonormal polynomials, orthonormal
on the data points over the range of - variation of the independent variable, T.
The orthonormal polynomials a r e taken to b e the truncated power s e r i e s
n Fn(T) =jZl Cjn TJ
where the C a r e determined f rom the orthonormality conditions at the j n
measured tempera tures . It should b e s t r e s sed that the Fn a r e de te r -
mined by the values of the independent variable T only. The Fn(T) a r e
therefore the same fo r all thermocouple combinations. The coefficients
a r e determined by values of the dependent variable E and a r e differ-
ent for each thermocouple combination. The highest o rde r , L, neces-
sa ry for a bes t fit i s also different for each combination.
The general polynon~ia l s F,(T) are given in table 6 . F o r eom-
p u t e r economy- t h e factored fo rma t used in "cable 6 i s preferable to an
unfactored f o r m , The values of and L for each thermocouple corn-
bination a r e given in table 7 with sufficient digits so that no significant
precis ion i s los t in the calculation of E(T) .
An advantage of the orthonormal representation i s that the func-
tion may be simplified by lowering the o rde r of the f i t without having to
determine new A, for the lower o rde r . The lower o rde r function uses
the same A, and represents the bes t fit for that order . The s tandard
deviation of the fit increases as the o rde r i s reduced a s i s shown i n
table 8. Another method of simplifying the computation i s to reduce the
number of digits ca r r i ed in the calculations. Table 9 shows the l imi t s
of e r r o r to be expected when using various numbers of digits in the ca l -
culation of E ( T ) . When reducing either the number of coefficients used
o r the number of digits ca r r i ed one must consider both the e r r o r s found
in table 8 and table 9. Fo r example, if one wishes to generate the data
for platinum v s gold-0.02 at. O/o i ron with a precision bet ter than 1p V,
table 8 shows that n = 11. Table 9 shows that to achieve this precis ion
11 decimal digits (34 binary b i t s ) should b e car r ied . The thermocouple
calibration data given in tables 1 thru 5 was computed using 2 4 digits
(84 binary b i t s ) and the highest order fit given for each thermocouple
combination a s given in table 7.
The following example i s included to i l lustrate the use of the da ta
in tables 6 and 7. Tables 8 and 9 cannot be applied to the resu l t s of this
example since table 8 requires at l eas t four polynomial coefficients and
table 9 requi res at leas t eight decimal digits.
EXAMPLE - For purposes of illustration consider the calculation of E 2,
with 1. = 2. E ( T ) = zz, &Fn(T) = Al Fl ( T ) i- A, F2 (T). From table 6,
F1 = 2. 627 X 1 0 - ~ 7 ( and Fa = (3 .216 X ~ o - ~ T - 1 .117 X ~ O - ~ ) T * Now,
E ( T ) = A l ( 2 . 6 2 7 X 1 0 - ~ ~ ) + A 2 ( 3 . 2 1 6 X 1 0 - ~ ~ - 1 . 1 1 7 X 1 0 - ' ) ~ ~ At
t h i s point t he calcula t ion m a y b e used f o r any of t he m a t e r i a l cornbina-
t ions s i nce t h e s a m e F n ( T ) appl ies t o all p a i r s . Assume that the p a r t i c -
u la r combination of i n t e r e s t is Chrome l v s gold-0.02 at. 70 i r o n at 100K.
F r o m tab le 7, Al = 6903.629 and A2 = 561.689. The solution using only
two t e r m s at lOOX is then E ( T ) = E(100K) = 1813.6 - 446.8 = 1366.8pV.
The t abu la r va lue f o r Chromel v s gold-0.02 at. 70 i r o n is 1377.33pV.
The 0 .8% d i f fe rence is due to t h e low o r d e r (L = 2 ) used i n t h i s ca lcu-
lat ion.
References
Larry L, Sparks, Robert L. Powell, and William J , Hall,
"Cryogenic Thermocouple Tables" , NBS Report 9712 (July , 1968).
L a r r y L. Sparks and Will iam J. Hall, "Cryogenic Thermocouple
Tables - Part 11, Refe rence Mater ia l s v s Thermocouple Alloys",
NBS Repor t 9719 (Dec. 1968).
To b e published in Metrologia - 5, (1969).
R. B e r m a n , J. C. F. Brock , and D. J. Huntley, " P r o p e r t i e s of
Gold t 0.03 percen t (at.) I ron Thermoelement Between 1 and
300°K and Behavior i n a Magnetic Field", Cryogenics - 4, 233
(1964).
D. K. F innemore , J. E. Ostenson, and T. F. S t romberg ,
"Secondary The rmomete r fo r the 4 to 20°K Range", Rev. Sci.
I n s t r . - 36, No.9, 1369 (Sept. 1965).
R. L. Rosenbaum, "Some P r o p e r t i e s of Gold-Iron The rmo-
couple Wires" , Rev. Sci. Ins t r . - 39, 890 (1968).
L . L. Sparks and R. L. Powell , "Cryogenic Thermomet ry" ,
Measu remen t s and Data - 1 , No.2, 82-90 (Mar . -Apr. , 1967).
Table 1 T h e r m a l voltage, thermopower , and ther lnopower der iva t ive fo r Chromel v s gold- 0 . 02 at. 7' i ron .
Table 1 (cont , ) T h e r m a l voltage, t he rmopower , and t h e r m o - power der iva t ive f o r Chrome1 vs gold-0, 0 2 a t , Ojo i r o n
10
Temp.
Table 1 (cont. ) Thermal voltage, thermopower, and the rmo- power derivative for Chrome1 vs gold-0.02 at. 70 i ron
F i g u r e 1 T h e r m o e l e c t r i c vo l t age f o r Chrome1 v s go ld -0 . 02 a t . 70 i r o n
Figure 2 Thermopower for Chrome1 vs gold - 0 . 02 at. 70 i r on
b 3
T e m p e r a t u r e ( K l
Figu re 3 Thermopower der ivat ive fo r Chrome1 v s gold - 0 . 02 at. 70 i ron
The rmocouple KP v s Au-ZFe
C C
C
4 C
Temperature (K)
Figu re 4 Deviations between calcula ted and exper imenta l va lues of t he rmoe l ec t r i c voltage fo r Chrome1 v s - gold-0. 02 a t . 70 i r o n
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'I'abl e 2 (cant, ) Tlzermal. volta,ge, ther rnopower , and therrno- power derivative for copper vs gold- 0-07 at, % i r o n
Tab le 2 (cont . ) T h e r m a l vol tage, t h e r m o p o w e r , and t h e r m o - power de r iva t ive f o r coppe r vs gold-0.07 a t . 70 i r o n
Tempera tu re (K)
Figu re 5 Thermoelec t r i c voltage for copper v s ., gold-0. 07 a t . 70 i r o n
Temperature (K)
F i g u r e 6 T h e r m o p o w e r f o r copper vs gold-0 . 07 at. % i r o n -
Temperature (K)
F i g u r e 7 T h e r m o p o w e r de r iva t ive f o r copper v s gold -0. 07 at. 7 0 i r o n -
.- La-.
V
W
Temperature ( K l
F i g u r e 8 Devia t ions be tween ca lcula ted and exper imen ta l va lues of t h e r m o e l e c t r i c vol tage f o r copper v s - go ld -0 .07 .. a t ,% i r o n
Table 3 Thermal voltage, thermopower, and the rmo- power derivative fo r copper vs gold-0.02 at. 70 i ron
~ n t . ) T h e r m a l voltage, t he rmopower , power der iva t ive f o r copper 0 , 0 2 a t , yo i r o n
and t h e r m o - vs gold-
Table 3 (cc
Table 3 ( cont, ) Thermal voltage, thermopower , and the rmo- power derivative for copper v s gold-0. 02 a t , i ron
Temperature (K)
F i g u r e 9 T h e r m o e l e c t r i c vol tage f o r copper v s go ld -0 -02 a t . % i r o n
Figu re 10 Thermopower fo r copper vs gold-0. 02 at. yo i r o n
T e m p e r a t u r e ( K )
F i g u r e 11 Thermopower der iva t ive f o r copper v s gold - 0. 02 at . 70 i r on
The rmocoup 1 e TP vs Au-2Fe
T e m p e r a t u r e (K)
F i g u r e 12 Dev ia t ions b e t w e e n ca l cu la t ed and e x p e r i m e n t a l v a l u e s of t h e r m o e l e c t r i c vo l t age f o r c o p p e r v s go ld -0 .02 a t . (ro i r o n
Table 4 The r m a l voltage, thermopower , and thermopower der iva t ive for platinum v s gold- 0. 02 at. (ro i r o n .
Table 4 (cont, j Thermal voltage, thermopower, and the rmo- power derivative for platinum vs gold-0.02 at. Ole i ron
Table 4 (cont , ) Thermal voltage, thermopower, and the rmo- power derivative for platinum v s gold-0.02 a t , D/o i ron P
Tempera tu re (K)
F i g u r e 13 T h e r m o e l e c t r i c voltage f o r p la t inum v s gold-0. 02 at, % i r o n
T e m p e r a t u r e ( K l
F i g u r e 14 T h e r m o p o w e r f o r p l a t inum vs gold-0 . 02 at-70 i r o n
Temperature (K)
Figu re 15 Thermopo-*;rer de r iva t ive fo r plat inum v s gold-0, 02 a t . 70 i r on
The rmocoup 1 e P t v s Au-2Fe
T e m p e r a t u r e (K)
Figu re 1 6 Deviations between calculated and exper imenta l va lues of t he rmoe l ec t r i c voltage fo r plat inum v s gold-0. 02 a t . 0jo i r on .
Temp, VnI lupn"F ~ B S - d S d 4 M u\B m V l K ~ v / K "
Table 5 T h e r m a l voltage, tbermopower, and thermopower derivat ive f o r "normalv s i lve r vs gold-0.02 a t , 70 i ron ,
Table 5 (cont. ) Thermal voltage, thermopslwer, and t he rmo- power derivative fo r "normal" s i lver v s gold-0,02 at. yo i ron
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Temperature ( K )
F i g u r e 17 T h e r m o e l e c t r i c vo l t age f o r " n o r m a l " s i l v e r v s go ld -0 , 02 a t . 70 i r o n
Figure 18 Thermopower for "normal" silver vs gold-0, 02 at. Djo iron
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Temperature (K)
Figu re 20 Deviat ions between calculated and exper imenta l va lues of t he rmoe l ec t r i c voltage for "normal" s i lve r vs gold-0. 02 a t . % i r on .
T e m p e r a t u r e
Figure 21 The r r i oe l ec t r i c volts-ge for Chrome1 (1) v s Chrome1 ( 2 )
T e m p e r a t u r e (K)
F i g u r e 2 2 T h e r m o e l e c t r i c vol tage f o r Chrome1 ( 2 ) v s Chrome1 ( 3 )
. "I
T h e r m o c o u p 1 e
0 0
T e m p e r a t u r e ( K )
Figu re 23 Thermoelec t r i c voltage fo r Chrome1 (1) v s Chrome1 ( 3 )
I DEVIATION FROM 0.02 AVERAGE THERMBMOLTAGE
0.0 1
TEMPERATURE ( K )
Figu re 2 4 Deviat ions of individual thermovol tages f r o m croup average fo r Chromel .
T h e r m o c o u p l e TP v s VP
T e m p e r a t u r e (Kl
Figu re 2 5 The rmoe l ec t r i c voltage for copper (1) v s
copper ( 2 )
Figu re 2 6 Thermoelec t r i c voltage for Alumel (1) vs Alumel ( 2 ) .
4 9
T e m p e r a t u r e 1 K l
F igu re 2 7 The rmoe l ec t r i c voltage fo r constantan (1) v s constantan ( 2 )
- 0.05 40 €30 120 160 200 240 280
TEMPERATURE ( K ) Figu re 30 Deviation of individual thermovolatge s from
g r o u p average for conetantan
T h e r m o c o u p l e P t v s P t
T e m p e r a t u r e ( K )
Figu re 32 Thermoelec t r i c voltage fo r annealed platinum vs unannealed plat inum
T e m p e r a t u r e ( K )
Figu re 33 Thermoelec t r i c voltage fo r annealed "normal" s i lve r v s unannealed " n ~ r r n a l ' ~ s i lve r
Table 6 The orthonormal polynomials Fn(T)
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