NBS

PUBLICATIONS

A UNITED STATES DEPARTMENT OF COMMERCE

PUBLICATION

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NAT'L INST OF STANDARDS & TECH R.I.C.

A1 11 009901 90

/NBS monograph QC100 .U556 V124;1972 C.1 NBS-PUB-C 1959

NBS MONOGRAPH 124

Reference Tables

for Low-Temperature

Thermocouples

U.S.

PARTMENT

OF

COMMERCE

National

Bureau

of

Standards

I oo

*US3h

no. \9Ji

ft. A
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and

technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measure- ment system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety.

The Bureau consists of the Institute for Basic Standards, the Institute for Materials

Research, the Institute for Applied Technology, the Center for Computer Sciences and

Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent system of physical measurement; coordinates

that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of a Center for Radiation Research, an Office of Measurement Services and the following divisions: Applied Mathematics—Electricity—Heat—Mechanics—Optical Physics—Linac

Radiation2—Nuclear Radiation2—Applied Radiation2—Quantum Electronics3—

Electromagnetics3—Time and Frequency3—Laboratory Astrophysics3—Cryogenics3

. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research lead- ing to improved methods of measurement, standards, and data on the properties of

well-characterized materials needed by industry, commerce, educational institutions, and

Government; provides advisory and research services to other Government agencies;

and develops, produces, and distributes standard reference materials. The Institute consists of the Office of Standard Reference Materials and the following divisions: Analytical Chemistry—Polymers—Metallurgy—Inorganic Materials—Reactor

Radiation—Physical Chemistry.

THE INSTITUTE FOR APPLIED TECHNOLOGY provides technical services to pro- mote the use of available technology and to facilitate technological innovation in industry and Government; cooperates with public and private organizations leading to the development of technological standards (including mandatory safety standards), codes

and methods of test; and provides technical advice and services to Government agencies

upon request. The Institute also monitors NBS engineering standards activities and

provides liaison between NBS and national and international engineering standards

bodies. The Institute consists of the following divisions and offices: Engineering Standards Services—Weights and Measures—Invention and

Innovation—Product Evaluation Technology—Building Research—Electronic

Technology—Technical Analysis—Measurement Engineering—Office of Fire Programs.

THE CENTER FOR COMPUTER SCIENCES AND TECHNOLOGY conducts re- search and provides technical services designed to aid Government agencies in improving cost effectiveness in the conduct of their programs through the selection, acquisition,

and effective utilization of automatic data processing equipment; and serves as the principal focus within the executive branch for the development of Federal standards for automatic data processing equipment, techniques, and computer languages. The Center

consists of the following offices and divisions: Information Processing Standards—Computer Information—Computer Services —Systems Development—Information Processing Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination

and accessibility of scientific information generated within NBS and other agencies of

the Federal Government; promotes the development of the National Standard Reference

Data System and a system of information analysis centers dealing with the broader

aspects of the National Measurement System; provides appropriate services to ensure

that the NBS staff has optimum accessibility to the scientific information of the world,

and directs the public information activities of the Bureau. The Office consists of the following organizational units: Office of Standard Reference Data—Office of Technical Information and

Publications—Library—Office of International Relations.

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

2 Part of the Center for Radiation Research.

3 Located at Boulder, Colorado 80302.
OCT 4 1972

c Reference Tables

' for Low-Temperature Thermocouples

Larry L. Sparks, Robert L. Powell, and

William J. Hall

Institute for Basic Standards

(j . National Bureau of Standards

Boulder, Colorado 80302

U.S. DEPARTMENT OF COMMERCE, Peter G. Peterson, Secretory

NATIONAL BUREAU OF STANDARDS, Lawrence M. Kushner, Acting Director

I ssued June 1972
Library of Congress Catalog Number: 74-186212

National Bureau of Standards Monograph 124

Nat. Bur. Stand. (U.S.), Monogr. 124, 61 pages, (June 1972)

CODEN: NBSMA6

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. C 13.44:124). Price 60 cents. Stock Number 0303-0952
Table of Contents

1. Introduction j 2. Material Specifications 2

3. Preliminary Selection and Inhomogeneity Tests 3

4. Apparatus 4

5. Experimental Design and Technique 9

6. Data Analysis ] ] 7. Error Analysis 13

8. Standard Tables and Functions 15

9. References 55 Appendix A. Standard Designations for Thermocouples 55

List of Figures

Figure Page 1. (a) Short-range inhomogeneity probe, (b) Medium-range, long-range, and inter-lot homogeneity probe, (c) Dif- ferential thermocouple probe 4

2. Schematic of thermocouple calibration cryostat 6

3. Flange and trough arrangement for using low melting point solder to make cryogenic vacuum seals 7

4. Schematic of thermal and electrical placement of thermometers in the calibration system 8

5. Block diagram of thermocouple calibration instrumentation 8

6. Four object measurement graph 9

7. Measurement graph used for calibration of thermocouple materials TP, KP (or EP), KN, TN (or EN), Pt, Ag-0.37

at% Au, and Ag-28 at% Au 11

8. Graph of | A„ | versus number of coefficients for thermocouple Type T 12

9. Least squares approximations to typical data before the range shift constants are applied 13

10. Characteristic propagated standard deviation (ag) in voltage for the thermocouple calibrations 13

11. Illustration of the nonzero thermoelectric voltage at 1=0 K which results when experimental data are ex- trapolated from 5 K to OK 16

12. Thermoelectric voltage for primary thermocouple types E, K, and T 26

13. Seebeck coefficient for primary thermocouple types E, K, and T 26

14. Derivative of the Seebeck coefficient for primary thermocouple types E, K, and T 26

15. Thermoelectric voltage for thermocouple materials versus Pt 39

16. Seebeck coefficient for thermocouple materials versus Pt 39

17. Thermoelectric voltage for thermocouple materials versus Ag-28 at% Au 50

18. Seebeck coefficient for thermocouple materials versus Ag-28 at% Au 50

List of Tables

Table Page

1. Total inventory of tested materials for thermocouple types E, K, and T and the reference materials Ag-28 at%

Au and Pt 2

2. Range of chemical compositions for the tested thermocouple wires 2

3. Physical characteristics of some typical thermocouple test wires 3

4. Thermocouple wire inhomogeneity data 4

5. Comparison of differential thermocouple dip test data with previously published data and with data from NBS

internal reports 5

6. Kink and strain effects on thermocouple wires 6

7. Average values of the standard deviations for the main thermocouple combinations 14

8. Average values of the standard deviation of the secondary thermocouple combinations, average values for the standard deviation of the adjustment constant, and the overall standard deviation resulting from the combined

effect of these uncertainties 14

9. Estimates of systematic errors in temperature measurements 14

10. Estimated systematic errors in thermocouple voltage readings 15

11. Total uncertainties in thermocouple calibrations 15

12. Type E—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS{T) . 18

iii
List of Tables—Continued

Table Page 13. Type K—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) 20

14. Type T—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) 22

15. Type E—reduced precision tables, E(T) 24

16. Type K—reduced precision tables, E(T) 24

17. Type T—reduced precision tables, E(T) 25

18. Type E—reduced precision tables, T(E) 27

19. Type K—reduced precision tables, T(E) 29

20. Type T—reduced precision tables, T(E) 30

21. Type KP (or EP) versus Pt—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) 31

22. Type Pt versus TN (or EN) —thermoelectric voltage, E{T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) 33

23. Type Pt versus KN—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck

coefficient, dS(T) 35

24. Type Pt versus TP—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) ._ 37

25. Type KP (or EP) versus Ag-28 at% Au—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) 40

26. Type Ag-28 at% Au versus TN (or EN) —thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) 42

27. Type Ag-28 at% Au versus KN—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) 44

28. Type TP versus Ag-28 at% Au—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) 46

29. Type Pt versus Ag-28 at% Au—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) 48

30. Orthonormal polynomials, Fn (T) 51

31. Orthonormal polynomial coefficients for thermocouple types T, E, K, Pt versus TP, KP (or EP) versus Pt, and

Pt versus KN; E=f{T) 52

32. Orthonormal polynomial coefficients for thermocouple types Pt versus TN (or EN), KP (or EP) versus Ag-28

at% Au, Ag-28 at% Au versus KN, TP versus Ag-28 at% Au, Ag-28 at% Au versus TN (or EN), and Pt versus Ag-28 at%Au; E=f(T) .77 .77. 52

33. Standard deviations (^V) of reduced order fits for thermocouple types T, E, K, Pt versus TP, KP (or EP) versus

Pt, and Pt versus KN; E=f(T) 53

34. Standard deviations (/iV) of reduced order fits for thermocouple types Pt versus TN (or EN), KP (or EP) versus Ag-28 at% Au, Ag-28 at% Au versus KN, TP versus Ag-28 at% Au, Ag-28 at% Au versus TN (or EN), and Pt versus Ag-28 at% Au fE~=f(T) 77. ~Z 53

35. Number of digits necessary in computations to reduce round-off errors below certain limits for thermocouple

types E, K, and T 53

36. Power series coefficients for thermocouple types T, E, K, Pt versus TP, KP (or EP) versus Pt, and Pt versus KN; E=f(T) 54

37. Power series coefficients for thermocouple types Pt versus TN, KP (or EP) versus Ag-28 at% Au, Ag-28 at% Au

versus KN, TP versus Ag-28 at% Au, Ag-28 at% Au versus TN (or EN), and Pt versus Ag-28 at% Au; E=f(T) 54

iv
Reference Tables for Low-Temperature Thermocouples*

Larry L. Sparks, Robert L. Powell, and William J. Hall

Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302

The experimental program to establish low-temperature reference tables for the commonly used thermocouples has been completed. Details of the experimental system, instrumentation, data analysis, error analysis, and materials tested are given in order to allow the user to better evaluate and apply

the results. The results presented here include:

(1) Reference tables for thermocouple types E, K, and T, both as E=f(T) and T=f(E). The

shorter f(E) tables have a 0 °C (273.15 K) reference temperature while all other tables have a 0 K reference temperature.

(2) Reference tables for Pt and Ag-28 at % Au vs the materials used in thermocouple types

E, K, and T. These data are presented as E=f(T) only.

(3) Orthogonal polynomials and the associated coefficients necessary to generate the data with reduced order approximations.

(4) Power series coefficients for full precision reproduction of the reference data. The data presented in the E=f(T) tables cover the temperature range from 0 to 280 K. The T—f(E)

tables cover the temperature ranges from 273.15 K down to the lowest temperatures allowed by table resolution.

Key words: Cryogenics; homogeneity tests; liquid helium; liquid hydrogen; liquid nitrogen; thermocouples.

1. Introduction

The rapid expansion of cryogenic technology in the last 20 years has created a need for standardized

thermocouple calibrations in the cryogenic temperature range. Therefore, an extensive experimental

program was initiated at this laboratory to provide

the necessary reference data. The overall thermoelectric thermometry program had several objectives: (1) to establish standard thermoelectric refer- ence tables between 4 and 280 K for thermocouple

types E, K, and T1

; (2) to select and test a material

for use as a thermoelectric standard below 50 K;

(3) to compare materials of the same nominal composition to determine the degree of thermoelectric

interchangeability; and (4) to test new thermocouple

combinations for possible advantages in specific situations. Results for the first three goals are dis- cussed in this paper; further research must be done

on the newer combinations before they can be considered standard materials. In order to establish thermoelectric values which

are representative of thermocouple materials cur- rently being used, we obtained wire from all major

thermocouple wire producers in the United States. Most manufacturers submitted two or three spools

* This work was carried out at the National Bureau of Standards under the sponsorship of the National Aeronautics and Space Administration, Space Nuclear

Propulsion Office (SNPO-C). Order Number R-45 and W13.300.

1 The letter designations for thermocouples are explained in Appendix A. Any

material manufactured in compliance with an established standard is equally suitable.

of wire which were representative of each material

requested. Exhaustive preliminary testing was done

to determine which of the wires were to be used in the detailed calibration. The final reference values

in this report are based on the characteristics of

individual wires; they do not represent averages of

all the similar wires from the many different companies. Members of the E-20 committee of the

American Society for Testing and Materials (ASTM)

and the thermocouple wire producers were extremely

cooperative throughout the program; the wide selec- tion of representative wires and the chemical analysis of the melts would have been difficult to obtain

without their cooperation.

Traditionally, platinum has been used as the thermoelectric reference standard for production control. For temperatures above approximately 50 K, it re- tains the thermoelectric properties of a good reference

material. Below 50 K, however, the thermopower of platinum becomes very dependent upon trace chemical impurities—notably iron. Since trace impurities

of iron are difficult to remove from platinum, a thermoelectric reference material which is not as sensitive to trace impurities is needed to replace

platinum below 50 K. An alloy of gold in silver has

been tested in this laboratory, and it appears to meet

the requirements for a low temperature thermoelectric reference material.

1
The design of our experimental system and of our

data acquisition procedure produced a large amount

of information on secondary combinations, such as intercomparisons of similar wires from different producers. Knowledge of the comparative thermoelectric behavior of similar wires is of critical importance when adjusting standard reference data to represent a particular thermocouple.

The purpose of this monograph is to present recently

acquired data for low temperature thermocouples.

Details of the cryostat, measurement scheme, error

analysis, analytical representation of the experimental data, etc., are included to allow the individual user to judge the creditability of the data and to further understand the extent and limitations of the

experiments.

2. Material Specifications

Materials to be used in the thermocouple calibra- tion program were requested from all major United

States producers. Each company was asked to furnish

representative samples of the thermocouple materials

that they distribute. Multiple spools of each material were requested whenever different melts were available. A list of the wires received for initial testing is given

in table 1. The number of participating manufacturers and the total number of spools of each material

are also indicated in this table. The complete inventory

of wires was tested to determine the degree of thermoelectric homogeneity and interchangability. Results

of these preliminary tests are of considerable practical

interest and are discussed in detail in the following

section. The wires to be included in the detailed

calibration from 4 to 280 K were selected after considering the results of the preliminary tests. Whenever possible, one test wire of each type from each

company was included—the one most homogeneous

and closest to the accepted high-temperature standard

values. Only one wire of each type, however, was considered to be the primary wire. The primary wire was used in all appropriate thermoelectric combinations, while the secondary wires were only compared

thermoelectrically to the primary wire of the same

nominal composition.

Table 1. Total inventory of tested materials for thermo- couple types E, K, and T and the reference materials

Ag-28 at% Au and Pt

ASTM desiimation or Number of Number

nominal composition manufacturers of represented spools

EP or KP 3 9 EN or TN 4 10 KN 3 9 TP 2 4

Ag-28 at% Au 3 4

Pt 1 2

The chemical compositions and physical conditions

of the calibrated wires are given in tables 2 and 3, respectively. The compositions shown in table 2

are the extremes found in the various spools tested. These data were furnished by the cooperating manufacturers. No attempt will be made here to predict

the specific thermoelectric effect of each of the components or impurities in the wires. A method of

making such a prediction, in principle at least, is

Table 2. Range of chemical compositions for the tested thermocouple wires

Chemical composition of test wires (wt%)

Letter designation

C Mn Si Cr Cu Fe Co Al Mg Zr Ca Ni

EP or KP 0.03 0.03 0.39 9.09 0.0 0.3 0.0 0.0 0.0 0.01 0.0 89.63

to to to to to to to to to to to to 0.06 0.06 0.41 9.50 0.01 0.5 0.10 0.01 0.01 0.03 0.01 89.80 EN or TN 0.0 0.86 0.01 0.0 53.66 0.03 0.17 43.73

to to to to to to to to 0.01 1 .88 0.04 0.01 54.73 0.37 0.28 44.21 KN 0.0 1.60 1 .03 0.0 0.05 0.50 1 .00 0.01 0.0 93.42

to to to to to to to to to to 0.01 2.45 1 .70 0.01 0.26 0.62 2.25 0.02 0.05 95.20

Ag-28 at% Au 58.4 wt% Ag, 41.56% Au; 2X10-" wt% Fe and Si; 5X10~5 Al, Ca, and Mg; 3X10"6 Cu and

Pb; 2X10-5 Ni.

Pt 4X10"4 wt% 0; 1X10-4 Au, Mg, Ni and Pb; 7X10"8 Fe; 2X10-6 Pd and Rh; lXlO"8 Ag,

Cu and Zr.

2
Table 3. Physical characteristics of some typical thermocouple test ivires

Wire size Insulation Heat

Averagegrain

intercept diameter

Maximum

Thermocouple

AWG Diameter (mm)

coating* treatment grain diameter

Grain orientation

EP or KP 32 0.20 glass fiber PVF

PVF

as received 7 . 1 iim 6.4 5.014 /im 1312no preferred direction 32

32

.20 .20as received

as received

slight axial preference

slight axial preference

EN orTN 32 .20 glass fiber PVF

PE

PTFE

as received 6.3 10 slight axial preference no preferred direction

slight axial preference

slight axial preference

323030

.20

.25

.25

as received

as received

as received

6.9

5.6 7.4

1214

13 KN_. 32 .20 PVF as received 8 .2 16 slight axial preference no preferred direction

slight axial preference 3232

.20 .20 PVF

glass fiber

as received

as received 5.7 6.2

9

15 TP 32 .20 PTFE as received 4.8 14 slight axial preference 30 .25 PE as received 6 .0 15 slight axial preference

Ag-28 at% Au___ 32 .20 PI (Lab) 1 h /air/400 °C

Pt 32 .20 PTFE(Lab) 1 h/air/400 °C

* Abbreviations: PE—polyethylene; PI—polyimid; PTFE—polytetrafluoroethylene; PVF—polyvinyl formal resin; (Lab) —coating was applied in our laboratory, air dried, and baked under infrared lamps.

given by MacDonald [l]. 2 The grain size is significant

because it is indicative of the heat treatment history

of the wires. As shown in table 3, all of the wires

except Pt and Ag-28 at% Au were tested in the "as- received" condition.

The platinum and silver-gold alloys are both avail- able as Standard Reference Materials for thermometry

from the Office of Standard Reference Materials,

National Bureau of Standards, Washington, D.C. 20234.

3. Preliminary Selection and Inhomogeneity Tests

An exhaustive series of preliminary tests were per- formed on our complete inventory of wires for thermocouple types E, K, and T. These tests were necessary

in order to determine the homogeneity characteristics of each type of wire and to determine the most

representative wires from each company. The dip

test program performed on these materials was de- signed to provide information on short range, medium

range, and long range inhomogeneities and to compare the present materials to existing or proposed

standards. No thermal voltage is developed when a loop of

homogeneous wire is subjected to a temperature

gradient. Similarly, no voltage is generated when two

identical wires are joined and the pair of wires is placed in a temperature gradient. The problem in practical thermometry is, however, that the ideal characteristics "homogeneous" and "identical" are not sufficiently well approximated for real thermocouple materials. Actually, a loop of wire placed in a

large temperature gradient will usually produce a

resultant voltage, sometimes as large as 10 microvolts

(mV) for poor materials. If wire from one spool is con- nected to wire from a different spool of the same

nominal composition, their junction is placed in a

2 Figures in brackets indicate the literature references at the end of this paper.

cryogenic fluid, and the free ends are held at room

temperature, then a significant voltage may result; we have observed readings as large as hundreds of

microvolts for poorly controlled alloys. These variable spurious voltages caused by inhomogeneities, physical

imperfections, and chemical impurities are usually

the main source of imprecision and inaccuracy in thermocouple systems.

For descriptive convenience, we have divided in- homogeneities into four categories based on their distance of separation:

(1) Short-range inhomogeneities occur in a single

wire and are separated by less than five meters, often being within a few centimeters of each other.

(2) Medium-range inhomogeneities occur in wires

that are from a single spool but are more than five meters apart.

(3) Long-range inhomogeneities are found in wires

that are from the same general stock but are from

different spools.

(4) Inter-lot variations in chemical composition,

thermal treatment, and handling occur in materials

produced by different manufacturers, or even in wire

produced by the same manufacturer at different times. The latter categories of inhomogeneities lead to much larger spurious voltages in cryogenic systems.

3
Well-prepared thermocouple wire can have short- range inhomogeneity effects as low as 0.1 /xV; poorly

controlled alloys often have inter-lot variations as large as 100 pN.

Two kinds of probes, shown in figure 1, were used

to investigate the various effects of the four cate- gories of inhomogeneities. The first probe configuration, shown in figure 1(a), consisted of a single wire

about 4 or 5 meters (m) long, part of it attached to a

plastic tube. It did not need to have a large number

of coils, even straight lengths of wire would have

been satisfactory. This probe was used to test for short-range inhomogeneities. The second probe configuration, shown in figure 1(b), consisted of two

wires, each 2 or 3 m long, that were coiled on a

plastic tube and joined at the bottom. This probe was used to test for the last three categories of in- homogeneities. The essential difference between the

two kinds of probes (besides the junction) was in

their manner of thermal tempering; the second kind

had tightly wound coils of wire near the junction in order to prevent a thermal gradient across the junction, which often contained dissimilar materials.

For both kinds of probes, the loose ends of the

wires were connected to a potentiometer or highresistance voltmeter; the probes were then dipped

into dewars containing cryogenic fluids, usually liquid

helium or nitrogen. The first type of probe was dipped

in two different manners, one way for static tests, another way for dynamic tests. For static short-range inhomogeneity tests, the

probes were immersed to a given depth in the cryogenic

Table 4. Thermocouple wire inhomogeneity data

Material Lot code

Short length 1 Medium length 2 Different spools 3

Equilibrium Dynamic Equilibrium Equilibrium

Liq N, Liq He L.q N2 Liq N2 Liq He Liq N2 Liq He

A 0 .5 MV 0 .9 mV 5 .5 ,xV 2.2 MV 2 .2 MV 28 .0 MV 33 .4 MV

EP, KP B 1 .0 1 .2 6 .9 1 .0 1 .0 38.0 39.1 C 2 .6 2 .6 8 .2 4.5 4 .5 4.4 6.1 D 0 .9 1 .2 1 .3 1 .6 1 .7 6.6 6.6 EN, TN E 3 .0 3 .0 5 .1 2.4 2 .5 26.0 27.7 F 2 .8 2 .8 8 .3 10.8 12 .5 36.0 44.4

G 1 .6 2 .1 6 .8 5.8 5..8 H 0 .7 0 .7 13 .7 3.8 4 .9 42.0 45.4 KN I 1 .9 2 .4 14 .1 2.2 2 .2 1 .7 2.8

J 2 .0 2 .0 21 .4 2.6 2 6 4.6 4.6 TP K 0 .4 0 .4 1 .0 0.4 0 7 0.5 0.5

L 0 .2 1 .4 1 .1 1 .9 7 6 4.1 37.9

Pt M 0 .3 2 .4 3 .4

Ag-28 at% Au N 0 .3 0 3 1 .8 0 3 0.3

* Reported data are maximums.

1 Continuous length of wire—approximately 5 meters.

2 Compares front and back ends of a single roll—30 to 150 meters.

3 Widely separated lengths of wires from different spools.

To Measuring

Instrument

Continuous

Length of Wire

PROBE TYPE

1

To Measuring ^ \~V—— Instrument K^WireA

-Plastic Tube PROBE TYPE

2

- Tempering Coil ^—Junction of Wires A and B

(a) (b)

Plastic Tubes -

Wire A

Junction of Wires A and B

Copper Extension Wires To Measuring

Instrument

PROBE TYPE

3

- Junctions of 1) Wire A and one

Extension Wire and 2) Wire B

and the other Extension Wire

(c)

Figure 1 . (a) Short-range inhomogeneity probe, (b) Mediumrange, long-range, and inter-lot homogeneity probe, (c) Differential thermocouple probe.

4
Table 5. Comparison of differential thermocouple dip test data with previously published data and with data from NBS internal reports

Thermocouple type

Percentage deviations'

Ice temperature to liquid N2 Liquid Nj to liquid HeNBS Circ. 561 2 Interim tables3 Interim tables'

E +0.38 to +1 .29 -0.45 to +0.23

-0.11 to +0.31

-0.19 to +0.72

+2.14 to +2.27

+0.89 to +1.31

-1 .68 to +1.07

-0.54 to +2.3

-2.07 to -1.70

K

T

1 In comparing the present experimental data to past data, a positive percentage indicates that the experimental data were higher in absolute value than the paM data. The

values used here are the maximums found in testing several thermocouples of each type.

2 National Bureau of Standards Circular 561, Reference Tables for Thermocouples. Reference 2. The voltages corresponding to the liquid nitrogen temperature had to be

extrapolated. No values were available for the He to N2 range.

3 Interim values are from low temperature thermocouple tables by R. L. Powell, et al., of the Cryogenics Division, National Bureau of Standards, Boulder, Colorado, dis- tributed Summer, 1965, as an informal report.

fluid and the temperature gradient was allowed to come to equilibrium before readings were taken. In

order to obtain more representative values, readings were usually taken at three different levels for each

test.For dynamic short-range inhomogeneity tests, the

probes were lowered into the fluid at a constant speed.

Erratic output voltages were usually observed in these

tests because large temperature gradients were de- veloped over different, relatively short lengths of

wire as the depth of immersion was changed. The

magnitude of the output depended on the type of

thermocouple wire, the specific specimen, and, to some extent, the rate of immersion. Since comparable

results were desired, a constant immersion rate, 0.5 meter per minute, was used for our tests. The dynamic, short-range tests were sensitive be- cause large temperature gradients were established over short sections of wire which could contain sig- nificant chemical and physical defects. However, when

the thermal gradients were allowed to diffuse, as in the static short-range tests, the random thermoelectric voltages tended to cancel one another and

the extreme readings became smaller. The static tests were therefore less sensitive indicators of inhomogeneities.

Short-range inhomogeneity tests were useful for selecting homogeneous wire that had a minimum

amount of spurious voltages. Results from the tests also gave a good preliminary estimate for the imprecision that could be expected for temperature

measurements in the actual cryogenic system. Results

from dynamic tests were most appropriate for systems

with rapidly fluctuating temperatures or liquid levels; results from static tests were most appropriate for

stable cryogenic systems like our laboratory cryostat.

Wire that exhibited unusually high spurious thermal

voltages (typical values are given later in this section)

could be detected and rejected before costly installa- tion in the specialized cryostat. For tests on medium- or long-range inhomogeneities, or inter-lot variations, the probe configuration

shown in figure 1(b) was used. The only differences were in the methods for selection of wires that were

assembled in the test rig. The selection criteria were

simply those implied in the basic definitions of the

three categories of inhomogeneities. The manner of

joining the wires was not critical as long as good electrical contact was obtained and the materials were not

strained or thermally treated more than a few centi- meters away from the junction. The assembled probes were dipped into a cryogenic fluid in the same manner

as in static short-range inhomogeneity tests. Medium- and long-range inhomogeneity tests were

useful for determining the variations that occurred

in selected lots of thermocouple wire. The deviations

in voltage usually became progressively larger as the

original positions of the wires became more widely

separated. If the material varied beyond acceptable

limits, then it was not used in the final calibrations. The third kind of probe, shown in figure 1(c), was

a simple differential thermocouple that was used to determine the thermoelectric voltages at fixed points

for the standardized wire types in our inventory.

One of the criteria used in selecting wires for the detailed calibrations was that the wire's voltage should

be reasonably close to the values given in the former

standard tables contained in NBS Circular 561 [2]. Table 4 lists typical results for the four kinds of

standardized thermocouple wires tested in this pro- gram. The values were obtained using Probe Types- 1 and 2 at liquid nitrogen and helium temperatures.

Table 5 gives the range of deviations that were ob- tained for Types E, K, and T thermocouples tested at liquid nitrogen and helium temperatures using Type

3 Probes.

A number of samples of each material were given

special tests to determine the effect of accidental

kinking or straining. The test samples for this case were obtained by deliberately inducing short radius

bends (kinks) in the test wire for the "kink" tests and by elongating one leg of the test sample by 2

5
Table 6. Kink and strain effects on thermocouple wire

(VI atpna 1 J.TJ. a l CI lul T nt pnnp

Kink 1 Strain 2 Undamaged3

Equilibrium Dynamic Equilibrium Dynamic Equilibrium Dynamic

Liq He Liq N2 Liq IN 2 Liq He Liq N2 Liq IN 2 Liq He Liq N2 T • AT Liq IN 2

A 6.0 MV 6.0 MV 10.5 yuV 8.5 MV 7.2 MV 9.0 MV 0.4 MV 0.4 /tV 4.2 juV EP, KP B 1.6 1.6 D . O 5.7 4.4 1.2 1.0 o . y C 2.2 2.2 17 1 0.1 0.1 c c 0 . D D 1.3 1.3 5.4 4.7 4.7 6.9 3.0 3.0 4.0 EN, TN E 1.4 1.4 5.9 0.4 0.3 0.8 F 4.8 3.8 8.0 2.1 2.1 6.8 G 1.2 0.8 7.4 4.0 2.8 7.3 1.0 1.0 *w7.6

KN H 1.0 1.0 6.6 1.3 1.3 9.8 0.7 0.7 10.0

I 3.3 3.3 9.7 1.4 1.4 12.3

1 Kinks were formed by forming a loop in the wire and applying tension; 6 kinks were made on each wire.

2 The wires were strained by a 2% elongation.

3 The "undamaged" results given here are for one particular sample from each company, while the corresponding "short length" tests in table 4 represent the maximum

values from several spools from each company.

percent in the "strain" test. Results of these "kink"

and "strain" tests are given in table 6, along with

similar tests performed before the wire was damaged.

These tests were not performed on each wire sample

from each manufacturer; however, the general effect of abusing thermocouple wire is evident. The samples

used in these tests should represent the outer limit

of damage to wires in ordinary assemblies from acci- dental cold working.

Experimental methods described above allowed us

to select materials that were most homogeneous and

therefore had the smallest amount of spurious volt- ages. The tests also provided data necessary for making

realistic error analyses.

4. Apparatus

A schematic of the cryostat used to determine the

thermal voltage for temperatures between 4 and 280 K

is shown in figure 2. The principal parts are labelled UPPER CHAMBER and LOWER CHAMBER. The

two chambers are connected by a thermal stand-off tube which serves as a wire duct and allows gas con- duction from the lower to the upper chambers. During

operation, the lower chamber contains the cryogen. The cryogenic liquid serves as the reference junction

for the thermocouples, provides a source of refrigera- tion for the upper chamber, and serves as a heat sink

for all wires that are in the upper chamber. The upper

chamber contains a heavy (~10 kg) copper block. The variable junctions of the thermocouples are thermally anchored to this block. A stable temperature

gradient is established between the reference junctions and variable junctions by balancing the refrigera- tor power from the boiling reference cryogen with

the power supplied to a heater coil wound on the

copper block. A manually controlled heater coil is wrapped on the lower cryostat so that the rate of

boiling in the lower chamber may be increased;

refrigeration from the liquid to the upper copper

block is sufficient without applying external power

except for the lowest temperature intervals. The upper and lower cryostats are completely

contained in a vacuum chamber. The vacuum chamber is, in turn, totally immersed in liquid nitrogen.

THERMOMETER

TEMPERING

FOR LEADS

UPPER TEMPERING

BLOCK

-PLATINUM AND GERMANIUM THERMOMETERS

-COPPER

BLOCK

-COPPER THERMAL

BY - PASS

RADIATION SHIELD —LOWER CHAMBER

- LOWER

TEMPERING

RING

Figure 2. Schematic of thermocouple calibration cryostat.

6
In addition to the vacuum insulation and liquid

nitrogen shield, radiation shields have been wrapped on the upper and lower chambers and on the inner

surface of the vacuum chamber. The radiation shields consist of layers of aluminum foil separated by balsa wood strips. The insulating vacuum is maintained

at approximately 5X10-6 torr by a 20 t/s. diffusion pump. All vacuum seals are made using a low melting

point solder in the flange and trough arrangement

shown in figure 3. The outer vacuum chamber seal is effective at ~76 K, while the seals on the two inner

cryostats are used down to 4 K. Seals of this sort require no heavy flange and are made at low enough

temperatures that there is little danger of overheating

nearby primary thermometers. Care must be taken,

however, to center the cup and lip. If either the cup

or lip is out of round, differential contraction can

cause cracks in the seals at low temperatures.

\3

Figure 3. Flange and trough arrangement for using low melting

point solder to make cryogenic vacuum seals.

It is imperative that the upper chamber is iso- thermal; temperature fluctuations of the variable

junction of the thermocouples have to be minimized,

since approximately one hour is required to make the necessary measurements at each temperature gradient. Energy flow into the upper chamber is controlled

as follows: (1) All wires coming into the system are

first brought to 76 K by thermal attachment to the

liquid nitrogen shield. They are then thermally an- chored in the reference liquid before going into the

upper chamber. (2) The gas vent line for the inner

chambers is in the proximity of the upper chamber.

Since the vent line is in contact with the liquid nitro- gen shield, it could be warm relative to the temperature of the upper chamber. A heavy copper thermal

bypass was installed to transfer any excess energy to

the reference liquid in the lower chamber without

coming near the upper chamber. (3) Radiative heat

transfer to the copper block is essentially eliminated

by placing a concentric thermal shield between the block and the walls of the upper cryostat. The temperature of the shield is regulated by supplying current

to a heater coil on the upper chamber walls. The temperature difference between the block and shield was

never greater than 0.01 K while taking the data re- ported in this monograph.

The temperatures of the variable junction block

and of the thermal shield surrounding the block are controlled automatically. The controllers used are

solid state devices designed specifically for low power

(10 watts maximum), high stability applications. For

the block heater, either a platinum or germanium

resistance thermometer is used as a sensor. A bucking

voltage corresponding to the desired thermometer

resistance is set on a potentiometer; the controller senses the misbalance between the potentiometer

setting and the thermometer voltage and supplies

power to the block heater until a null situation is achieved. The temperature drift of the block during

a one hour run is nominally between 3 and 5 milli- kelvin (mK). A separate power supply is used for the

shield heater; its control sensor is a four-junction

differential thermopile between the block and the

shield.

The pressure above the reference cryogen is manostatically controlled [3] when using liquid hydrogen or

liquid nitrogen. Pressure control is such that the temperature drift of the reference liquid is less than 3

mK/h, as determined from readings of a calibrated platinum resistance thermometer in the reference

liquid. This temperature stability corresponds to less than 0.5 mm pressure drift during the one hour runs. When liquid helium is used as the reference liquid,

the system is opened to atmospheric pressure and the

temperature is determined by reading the barometric

pressure. The maximum pressure variations observed

during a single testing period of one hour are usually

less than 0.9 mm, which corresponds to a temperature

change of 1.4 mK in the liquid helium reference

bath [4].

Two types of resistance thermometers are used to determine the temperature of the variable junctions of

the thermocouples. Capsule type platinum resistance

thermometers are used between 20 and 280 K: ger- manium resistance thermometers are used below 20 K. Three thermometers of each type are usually inserted

in the copper block. The thermal resistance between

the thermometers and the block is reduced by wrapping

7
Electrically shielded wires to Instrument System INSULATED

JUNCTION BOX

THERMAL ANCHORING

at Liquid Nitrogen Temperatures VARIABLE TEMPERATURE BLOCK

for Thermocouples and Thermometers 7^

Thermocouple

test wires

2^ Leads to primary Thermometers

Multiple coils Copper extension wires -

REFERENCE

TEMPERATURE BATH

for Thermocouples

Figure 4. Schematic of thermal and electrical placement of

thermometers in the calibration system.

each thermometer with 0.025 mm aluminum foil and

then removing layers of foil one at a time until a snug

fit is obtained between the thermometers and the

thermometer wells. For this research, one thermometer

of each type was calibrated at NBS-Washington. The

ice-point resistance, Ro, for the platinum thermometer

was carefully determined by measurement at the triple

point of water [5, 6, 7]. The NBS-Washington calibra- tion was then adjusted to account for the precise value

of Ro, as measured with our bridge [8]. The two re- maining thermometers of each type are used as sensors

for the heater control system and as checks on the

primary thermometers

The schematic given in figure 4 illustrates the electrical and thermal placement of the thermocouple test wires. The room temperature segments of the copper

wires enter the system through a wax seal. The temperature of the wires is subsequently reduced to liquid

nitrogen temperature by wrapping on an 11 mm di- ameter copper rod which is in intimate contact with

the liquid nitrogen shield. The wires are then drawn

into the reference liquid in the lower chamber. Approximately one meter of each wire is wrapped on the

copper cylinder below the reference cryogen level in the lower chamber. This is done to ensure that the

wires are at the temperature of the reference liquid

before being taken into the upper chamber. The wires

are then taken into the upper chamber via the thermal

stand-off tube connecting the chambers. Approximately one meter of each wire is wrapped on the upper

tempering block. The thermocouple test wires are

similarly anchored to the variable temperature block

and to a short cylinder in the reference liquid. The

thermocouple reference junctions are made by spot

welding the copper extension wires to the thermocouple test wires. It is important to note that thermal

gradients across the junctions (both variable and refer- ence) are minimized by carefully bringing all wires to the same temperature before the junctions are made.

As mentioned above, a fixed length of one meter of

wire was used to thermally anchor the wires at various

temperatures. A thermal analysis based on Hust's [9] method indicates that this length is more than should

be necessary even under more unfavorable conditions.

However, since our thermocouple test wires had

various diameters, thermal conductivities, and insulations, we used a conservatively calculated length.

As shown in figure 4, all of the thermocouple test wires come together to form a single junction in the

variable temperature chamber. This junction is ther- mally tied to the copper block, but is electrically

insulated from it. The reference junctions in the lower

chamber are electrically insulated from one another

and are in thermal contact with the reference liquid.

There are actually 19 thermocouple test wires in the

system during the calibration. A block diagram of our measurement system is given

in figure 5. The output of the various thermometers in the cryostat is fed into a bank of switches labeled THERMOMETER SELECTOR SWITCH in this dia- gram. The signal from the thermometer or thermometers we wish to monitor is transferred from the

thermometer selector switch to another bank of

switches labeled INSTRUMENT SELECTOR SWITCH.

These switches allow the thermometer signal to be

measured on the appropriate instrument. Both the

THERMOMETER SELECTOR SWITCHES and the

INSTRUMENT SELECTOR SWITCHES are multichanneled, i.e., more than one incoming thermometer

signal can be directed to the proper instrument at any

THERM

REFERENCE

JUNCTION

THERMOMETER

SELECTOR

SWITCH

BLOCK TEMPERATURE CONTROLLER

SHIELD TEMPERATURE

CONTROLLER

POTENTIAL RECORDER

INSTRUMENT SELECTOR

SWITCH RESISTANCE RECORDER

POTENTIOMETER BRIDGE

AMPLIFIER GALVANOMETER

Figure 5. Block diagram of thermocouple calibration instru- mentation.

8
one time. The switches used in the sensitive circuits are of the low-thermal, rotary type. All switch banks

utilize solder which matches copper thermoelectrically

and are shielded by ~0.6 cm thick iron boxes packed

with glass fibers. These procedures substantially reduce

the spurious thermal voltage effects at the switches.

The instruments indicated in figure 5 are as follows:

(1) The potentiometer is a six dial device with a resolution of 0.01 jtiV. The limit of error for this instrument is 0.01 percent of reading, plus 0.02 ^V.

The potentiometer was calibrated at NBS-Boulder

prior to the tests. The unsaturated cadmium sulfate standard cell used with this potentiometer was also calibrated in Boulder prior to the tests. The potentiometer is used to measure the thermocouple output,

germanium resistance thermometer voltage, and

standard resistor voltages.

(2) The bridge is a type G-2 Mueller bridge. The

bridge reads directly to 0.0001 and interpolation on

the galvanometer allows two additional figures in precision. The bridge was calibrated in our laboratory

[10] prior to the tests. We found it necessary to pro- vide thermal isolat ion for 1

m 1 » / i < 1 ^r< ; in order to achieve the precision mentioned above. The thermal

isolation consists of encasing the entire bridge in a metal box with about 2.5 cm plastic foam completely

surrounding the bridge; remote dial manipulations are accomplished by plastic extensions from the bridge

dials. (3) An electronic amplifier galvanometer is used

with both the Mueller bridge and with the potenti- ometer.

(4) The potential and resistance recorders shown

are used to monitor the system during cooldown and

to roughly indicate when a stable temperature gradient

has been established between the upper and lower

thermocouple junctions.

5. Experimental Design and Technique

Our method of data acquisition is designed to take advantage of the large amount of partially redundant

information available. The common junction allows many different combinations to be measured. Concepts

derived by analogy from the connectivity of paths in graph theory are used to determine optimum experimental procedures [11, 12, 13]. As a simple illustration of how graph theory is applied, consider the situation

where one is to intercompare some property of two

different objects where two other intermediate objects are also available. Graphically this situation can be

represented as in figure 6. In this figure, the objects

B

D

Figure 6. Four object measurement graph.

are represented by the vertices and the comparison of some property between objects is represented by the

connecting lines. For example, the comparison a might

represent the difference in weight between objects A

and B. In applying graph theory to thermoelectric

measurements, the vertices represent the thermocouple test wires and the connecting lines represent

the thermal voltages generated by a given temperature

gradient. The thermoelectric voltage between A and C

in figure 6 would be determined by (1) measuring c, that is, a direct measurement of the desired voltage,

(2) measuring the thermal voltages a and b and combining these data algebraically, and (3) measuring the

thermal voltages d and e and similarly combining these

data. The algebraic combination of a-\-b and d-\-e

yield two independent determinations of the desired

voltage, equivalent to c. The final determination of the

voltage (A-C) is given by

eC aic= (A-C) = [2c+ (a+b) + (d+e)]/4. (1) The measurement c is given a weight of 2, since it in- volves only one experimental determination, whereas

the other two measurement paths both require two

readings. The estimate of the standard deviation for (A-C) is given by

5

2 ={2(ecalc -c) 2 +[eca ,c-(a+6)] 2 + [ecaic-(e+rf)] 2 }/3. (2) The advantages of taking data in this way are that it randomizes potentiometer dial errors, eliminates any

subconscious operator prejudice, and randomizes

spurious voltages in the lead wires. The magnitudes of

a, b, c, d, and e usually vary considerably; this means

that the potentiometer dial settings are also considerably different. Any dial errors which exist are randomized by this method. These random errors would then

appear as scatter in the data and would be accounted

for in the variance calculated from eq. (2). Since the potentiometer dial readings vary a great deal and the order of readings may be random, the

chance for subconscious operator prejudice is minimized. In order to influence the readings in a sys- tematic way, the operator would have to algebraically

combine very different numbers which are not necessarily taken in adjacent readings. This is not done

subconsciously, even on the simple four object system

being considered here. On the other hand, it multiple

readings are taken of the same quantity, there is a strong tendency to produce data which are biased in a systematic way.

9
Spurious voltages in the extension wires are also randomized by using the graph theory method. Consider a three wire system such as that which would

result if the D wire were eliminated from figure 6. Assume the number we actually want is (B-C). This

is the thermoelectric voltage generated by the thermocouple made from materials B and C when a thermal

gradient, AT=Ti — T2 , exists. The number which is actually measured is b which includes the spurious

voltages generated in the extension wires to both B

and C. If the spurious voltages hB i and bci are zero or

are at least known, then the true value of (B-C) may be

determined. The voltages 8 Bi and 5ci can be deter- mined by an isothermal test where T\ = Tz. When

Ti = T2, (5-0=0 and b = (B-C) +dBi+dci = 8Bi +&ci.

However, this determination of the spurious voltages

is valid only when the thermal gradients in the system

are the same as when the isothermal test was made. In many experimental situations this approach to the

spurious voltage problem is not practical. The only

other solution is to randomize these voltages so that they appear as scatter in the experimental data and

are therefore included in the estimate of the variance,

S

2

. The graph theory approach does allow these volt- ages to be randomized. Suppose, for instance, that we

wish to determine (B-C) in figure 6. The voltages a,

b, and c would then be measured.

a = (B-A) + 5ai+ Sbi

b = (B-C) +

B2 +5C i C=(A-C) + 5a2+&C2

&caic=[&+Ma+c)]/3/2 = 2b+a+c

bc&\c

[2(B-C)+(B-A) + (A-C)]

+

If the spurious conditions are stable, i.e., the measure- ments are made rapidly enough that the system

gradients haven't changed,

then 5a = 8ai = <>b = 5bi = 5j3 2, and 5c = <5ci = 5c2

[2(B-C) + (B-A) + (A-Q]

and 6ca ic =

If the more common procedure of multiple readings of

b were used, b would be measured, say, 3 times:

b 1 =(B-C) 1 +5B +dc,

b 2 = (B-C) 2 +5B1 +8Ch

b 3 = (B-C) 3 +5B2 +dc2, and

^calc [(B-C) 1 +(B-C) 2 +(B-C) 3 ]

+

8B -\- 5c+ 5bi+ 5ci+ 5^2+ 5c2

Again, assume stable spurious conditions for the time

required to determine b three times. Then 8B = 8 B i =

$B2, 5c=5ci = 5c2, and bca.\ c = (B-C)i, 2 ,3~\-8 B -\-8c- The

tendency to randomize dial errors and to eliminate

operator prejudice is illustrated by comparing 6ca ic from

the graph theory method and from the multiple readings method. More dials are probably changed in de- termining (B-C), (B-A), and (A-C) than are changed

in determining (B-C) three times. The subconscious

operator prejudice is reduced by having to combine

the two readings (B-A) and (A-C) to get the inde- pendent determination of (B-C).

The third and perhaps the most important advantage

of the graph theory approach to the measurement of

thermocouple outputs is the randomization of spurious

voltages in the extension wires. These errors would not

be accounted for, i.e., they would be systematic, if the

multiple reading approach is utilized. This is shown in the calculation of the estimate of variance for the two

methods:

Graph theory:

[2(B-Q + (B-A) + (A-Q]

bc&ic

+

5ai+5a2+5bi+25b2+25ci+5c2

5

26calc = { 2 (6CB lc - b) 2 + [fecalo ~ (a +c) ] 2

} /2j now assume that the only cause of variation is the

spurious voltages

S

26calc =l/3(5^ + 5^-5c0 2

where 8a' = 8ai+8A2,

8B' = 5B i— d B2, and

<>c" = 5a— 5c2.

If spurious conditions are constant, 8B> =0, 5c =0 and

5

2

6oaIc = l/35^ 2

.

Multiple measurements:

bcalc [(B-C) 1 +(B-C) 2 +(B-C) 3 ]

+

5b+5c+5bi+5ci+5b2+5c2

5

26cal0 = { (6ealc-6 1)

2 + (6c.lo- b2)

2 + (be&ia -b3y}/2

10
PLATINUM

Ag0.37 ot%Au

Figure 7. Measurement graph used for calibration of thermocouple materials TP, KP (or EP), KN, TN (or EN), Pt, Ag-0.37

at% Au, and Ag-28 at% Au.

again assuming all scatter is due to spurious voltages,

i.e.,

(B-C) 1 = (B-C) 2 = (B-Ch, then

18 S

26calc = [- 2(6B + 5 C) + 8 B1 + 5 Ci+

B2 + 5 C2] 2 + [-2(5b1 +5ci) + 5 b +5c+5b2 +5C2 ] 2 + [-2(5B2 +5c2+Sb+5c+Sb1 +Sci] 2

. Now if the spurious conditions are constant 8b =

8bi = 8b2, 8c = Sci = 8c2, and S

2&cal(! = 0. The spurious voltages do not appear in the estimate

of the standard deviation when the multiple measure- ment method is used. They are present but unac- counted for until some estimate of systematic error is introduced.

The graph used to represent the measurements

made on thermocouple materials TP, TN(EN),

KP(EP), KN, Pt, Ag-0.37 at% Au, and Ag-28 at% Au

is given in figure 7. The terminology discussed earlier in this section applies to this figure, i.e., materials are represented by the vertices and thermovoltage meas- urements are represented by lines. The dashed line connecting platinum and Ag-28 at% Au indicates that

comparison was made in a separate calibration. This was necessary because the optimum Ag-Au alloy

had not been received at the time the original calibra- tion was done. A detailed discussion of how these data were treated is contained in the DATA ANALYSIS

section of this report.

Each of the measurements indicated in li»ure 7 was made at sixty-eight different temperature interval-. L9 in the liquid helium range (4 K to 25 K), 17 in the

liquid hydrogen range (19 K to 90 K), and 32 in the

liquid nitrogen range (75 K to 290 K). The number of temperature intervals in each range was as above for the Pt versus Ag-28 at% Au combination also, even though the individual intervals were not exactly the same. During the course of making the measurements, the

current of the potentiometer was checked before each

set of thermocouple readings, e.g., prior to reading

thermocouples 1, 8, 15, etc. This was done to minimize

the effect of changing potentiometer standard current due to battery drift. The bridge zero of the Mueller

bridge was determined before and after each temperature gradient sequence. When operating with liquid nitrogen and liquid

hydrogen, the temperature of the variable junction was measured three times during each run. These

determinations were made at the beginning, near the

middle, and at the conclusion of each run. The 3 to 5 mK drift during each run was sufficiently small and

linear to allow the true variable temperature of each

thermocouple to be approximated. The reference

temperature was determined six times during the course of each run. The bath temperature was ad- justed to be very near 20 K and 75 K for liquid hydrogen and liquid nitrogen, respectively, by controlling the pressure over the bath liquid. The actual reference

temperature for the individual thermocouples was

determined by linear interpolation.

The exact time of each of the primary temperature

determinations was recorded during each run. Periodically, the time for each step of a run was recorded. After several of these runs, it was clear that the

variation of time between a given thermocouple volt- age determination and the primary temperature de- termination was very nearly constant. This information

and the chronological data for the primary temperature

measurements from all tests allowed the variable and

reference temperatures to be determined for each particular thermocouple. The temperatures determined in this way minimized the effect of junction temperature

drift.

6. Data Analysis

Two major steps were needed to transform the ex- perimental data from its original form into its final form. The first operation involved making minor ad- justments to the data and forming the desired thermocouple combinations using graph theory considerations.

The second step consisted of finding the best analytical

representation of the adjusted data and calculating

statistical quantities such as precision, skewness and

elongation.

The first operation on the data was to apply potenti- ometer dial corrections to all voltage data and to apply

Mueller bridge dial corrections to all resistance data. The corrected resistances were used to determine the

temperature of the primary platinum thermometer by

linear interpolation in the resistance versus temperature tables. The tables used have temperature incre- ments of 1 K from 90 K to 300 K and 0.1 K from 14 K

to 90 K. The error introduced by linear interpolation

U
in these tables is less than 0.1 mK above 28 K and less than 0.4 mK below 28 K. The platinum thermometers

had been calibrated by members of the Temperature

Section, NBS-Washington, using the IPTS-48 and

NBS-55 scales; we later updated the calibrations to the

IPTS-68 scale [14]. A calibrated germanium resistance thermometer was

used to determine variable junction temperatures in the range from 4 K to 20 K. The thermometer current was determined by measuring the voltage across a standard resistor which was in series with the ther- mometer. Corrected voltages from the thermometer

and from the standard resistor were used to determine

the resistance of the thermometer. A power series representation of T=f(R) for our thermometer was

used to determine the temperature. The germanium

thermometer had been calibrated by members of the

Cryogenic Physics Section in NBS-Washington, using

the NBS P 2-20 (1965) scale [14]. As discussed in the previous section the time se- quence of primary temperature determinations and

thermocouple readings was known. Using this in- formation, it was possible to determine the variable

and reference temperatures which actually existed at the time the thermocouple voltages were measured.

However, in order to take advantage of the graph

theory approach to data acquisition, it was necessary

that all combinations have the same reference temperature and the same variable junction temperature.

Linear interpolation in the Ei versus Ti data for each

thermocouple combination was used to adjust the

variable junction temperature of each thermocouple

to the average of the values which are taken for each

gradient. An analytic fit of the data near the reference

temperature is used to determine the dEi/dT, neces- sary to make the small correction which adjusts all reference voltages to the voltage equivalent of 4 K,

20 K, or 75 K reference temperatures.

HeH2 N, 1 4 8 12 16 20 Order of Polynomial Coefficients

Figi ke 8. Graph of | A„ | versus number of coefficients for

thermocouple Type T.

After these corrections and adjustments have been

made, the data represent the thermoelectric voltages of the desired thermocouple combinations with identical reference temperatures and identical variable temperatures. Graph theory manipulations were then per- formed with these data to obtain multiple indirect determinations of a given thermal voltage. The general

procedure for calculation of thermal voltages is similar

to that given in the previous discussion of graph theory.

The next major step in the data analysis is to fit the

experimental data in order to provide a continuous

E=f(T) relationship for each thermocouple combination. The method used to represent the data is a modified Gram-Schmidt approximation [15, 16]. The

calculated values for the voltages of each thermocouple

combination were approximated by a series of ortho- normal polynomials in the Li norm (least squares),

that is,

L

- E(T) = £ An Fn (T)

n=l

where

E(T) = thermocouple potential in microvolts;

T = temperature in degrees Kelvin;

L =the highest order fit—an order high

enough to represent the data with no

loss of precision, but not so high as to introduce mathematical oscillations; A n = constants to be determined by the fitting

approximations; and

Fn (T) = orthonormal polynomials, orthonormal on

the data points over the range of variation of the independent variable, T.

The orthonormal polynomials are taken to be the

truncated power series

Fn (T)=tcnjTJ

where the Cn j are determined from the orthonormality

conditions at the measured temperatures. It should be

stressed that the Fn are determined by the values of

the independent variable T only. The Fn (T) are therefore the same for all thermocouple combinations

which are based on the same set of temperatures. All of the data for the solid line measurements in figure 7

are based on the same set of temperatures. The dashed

line measurement, being from a second set of calibra- tions, is based on another set of temperatures. Rather

than provide two sets of orthonormal polynomials,

interpolations in the second set of data were done to provide the Ei, Ti data for Pt versus Ag-28 at% Au at the temperatures used in the first calibration. Third

and fourth order interpolations were sufficient to convert the second calibration data to the temperatures of

the first calibration within the precision of the data.

12
There is, therefore, a single set of orthonormal polynomials for all of the data being reported here. The

coefficients An are determined by minimizing the sum

of the squared deviations in E and are different for each thermocouple combination. The highest order, L,

also differs from combination to combination.

A common problem in the numerical analysis of

data fitting by polynomials is selection of the proper

order—an order high enough to represent the data with no loss of precision, but not so high as to intro- duce mathematical oscillations. This problem is well solved by the method of fitting with orthonormal polynomials. The absolute values of the coefficients An decrease with increasing n as long as they are larger

than the noise level. However, when the noise level is reached the coefficients are random valued. An in- spection of a graph of | An \ versus number of terms

(n) shows the noise level and the probable maximum

value of n that is significant. In figure 8, | An | versus n

is shown for thermocouple Type T. The coefficient for order 11 is accidentally below the noise level of 2X10-1

. The first three points in the figure are called the range shift constants. As mentioned previously, our data are taken using three different reference

temperatures; the range shift constants plotted in

figure 8 are used to adjust these reference temperatures to a common value. Figure 9 shows a least squares approximation to the experimental data for thermocouple Type T before the range shift constants

are applied. The necessary shifts are determined by

using the principle of successive temperatures [17]. This principle may be illustrated by considering two

dissimilar homogeneous metals which produce a thermal voltage of E\ when the junctions are at temperatures T\ and T2 and a thermal voltage of E2 when

the junctions are at temperatures T2 and 7Y The

thermal voltage generated when the junctions are at temperatures T\ and Tz will be E\-\-E%.

Another advantage of the orthonormal polynomial

representation is that the function may be simplified

by lowering the order of the fit without having to de- termine new An . A quantitative discussion of errors as- sociated with reduced order fits and with reduced num4 20 76 280 TEMPERATURE,

Figure 9. Least squares approximations to typical data before the range shift constants are applied.

ber of significant figures is given in the STANDARD

TABLES AND FUNCTIONS section. As a convenience to users who wish to use the

highest order, and therefore highest precision, fit for

a particular thermocouple combination, the ortho- normal polynomials and coefficients have been combined to give simple power series coefficients. The

power series method of generating the standard data

is more straight forward to program for a computer,

since it involves only one summation. Using the power

series coefficients, the E=f{T) relationships are given by

E= E BjT>

;'=o

It should be stressed that the full array of coefficients must be used in the power series method, whereas in the orthogonal representation each order is inde- pendent.

7. Error Analysis

The estimate of variance used in the first stage of our data analysis was arrived at by using the direct measurement and the various indirect measurements:

a (Ec&lc -Edireet) ^~\~ (Ecalc ^indireotf 1) )

^

ale — £'indirect(2))

2

where a is a weighting factor. The direct and indirect measurements were weighted to account for the actual number of experimental determinations used to make

up each indirect voltage. In the curve fitting part of the analysis, the precision

of the analytical approximation of the data was needed.

Again, precision is determined by the estimate of the

variance. The coefficients, A„, and the standard deviao

o

4 280 TEMPERATURE, K

Figure 10. Characteristic propagated standard deviation {aB) in voltage for the thermocouple calibrations.

L3
Table 7. Average values of the standard deviations for

the main thermocouple combinations

Thermocouple material

Type E

Type K

Type T

Pt versus Ag-28 at% Au..

Pt versus TN

Ag-28 at% Au versus TN.

<r*G*V)

Table 8. Average values of the standard deviation of

the thermocouple combinations, average values for the standard deviation of the adjustment constant, and the overall standard deviation resulting from the combined

effect of these uncertainties

0.12

0.08

0.06

0.06

0.12

0.13

tions, aAn, are available from the orthonormal fit E(T) =f(An , Fn (T)). The estimate of the standard

deviation of a predicted point [18, 19] is then given by

Thermocouple material 0»V) <^adi(MV) "E. totalOuV)

KP versus Pt_ 0 .10 0.06 0 12

Pt versus TP 0 .10 0.07 0 12

Pt versus KN . . 0 .10 0.08 0 13 KP versus Ag-28 at% Au 0 .12 0.06 0 13 TP versus Ag-28 at% Au 0 .11 0.07 0 13

Ag-28 at% Au versus KN 0 .12 0.08 0 14

1=1 \OAi

1/2

where n = number of coefficients. The <?e obtained in this way is an indication of both

the scatter in the experimental data for a particular

thermocouple pair and of the closeness of the fitting

approximation to the experimental data. A typical ex- ample of a (7e versus temperature curve is shown in

figure 10. It should be noted that the propagated

standard deviation increases radically at both ends of

the graph. This is partially because our input data are

less precise near 4 and 280 K. However, the upturns

are caused primarily by the lack of constraints near

the extremes, a typical characteristic encountered in curve fitting "to data. The standard deviation for each of the main thermocouple combinations is given in tables 7 and 8. The

tabular values represent averages for the entire curves; values near the extremes will usually be

about twice as large.

Thermoelectric data for the thermocouple combinations listed in table 8 were obtained by the addition of

shift adjustment constants to the analytical repre- sentation of the experimental data. Therefore, their

total imprecision must include the imprecision of the

adjustment. The total standard deviation for these

combinations is calculated from

<*E, total = [o-2?

2 +0-adj.2

] 1/2

.

Table 9. Estimates of systematic errors in temperature measurements

Estimated bias (in millikelvin) for each temperature range (Kelvin)

Source of error 4 to 20 K 20 to 75 K 75 to 280 K

Reference Variable Reference Variable Reference Variable block block block block block block

Nonlinear temperature drift.. . _ 0.6 2.0 1.0 1.1 ; 0.6

Nonuniform time intervals _ 0.1 0.1 0.1 0.1 0.1 0.1

Mueller bridge uncertainty- 1.3 • 0.4 0.4 0.9

Potentiometer uncertainty .. _ _ 0.8

Helium vapor pressure manometer correction 0.2

Thermal gradients in variable block _ 0.1 0.2 0.5 Germanium R. T. uncertainty ______ 2.0

Platinum R. T. uncertainty 2.0 2.0 2.0 3.0

Estimate of total uncertainty in temperature dif- ference.. ... 3.0 3.5 3.9

14
Table 10. Estimated systematic errors in thermocouple

voltage readings

Thermocouple material Estimated systematic error (//V)

4-20 K 20-75 K 75-280 K

Type E 0 .03 0.13 1 .04

Type K 0 .02 0 .08 0 .70

TvDe T 0.03 0 .09 0 .67

Pt versus KN 0.02 0.07 0 .30 KP versus Pt _ _ 0.02 0 .04 0.42

Pt versus TN 0.03 0.11 0 .64

Pt versus TP 0.02 0 .04 0.04

Pt versus Ag-28 at% Au 0 .02 0 .05 0 .06

Ag-28 at% Au versus KN.. 0.02 0.03 0.28 KP versus Ag-28 at% Au . . 0.02 0.07 0.44

Ag-28 at% Au versus TN_ _ 0.03 0.04 0.62 TP versus Ag-28 at% Au. . 0.03 0.03 0.07

Values for the initial (o\e), adjustment (o-adj.), and

total (o\e, total) standard deviations for these combinations are given in table 8. The systematic errors, unlike the random errors or

imprecision, can only be estimated from a knowledge

of the system. The main possible sources of systematic

error in the determination of the independent variable,

T, are as follows: (1) deviation from linear temperature

drift during the course of a single run, (2) nonuniform

time intervals between thermocouple voltage readings,

(3) Mueller bridge bias that remains or occurs after the calibration, (4) similar potentiometer errors, (5) platinum resistance thermometer calibration errors,

(6) similar germanium resistance thermometer errors, and (7) thermal gradients in the variable temperature

block. Our estimates of these errors are given in table

9. The quoted uncertainties do not include the

systematic errors caused by disagreement between the

International Practical Temperature Scale and the true thermodynamic scale. These errors are estimated to be

about 2 mK.

There are three main sources of systematic error in

Table 11. Total uncertainties in thermocouple

calibrations These data include all random and systematic uncertainties.

Thermocouple

material

Total uncertainty

4-20 K 20-75 K 75-280 K

Type E . 29.9 mK 10.8 mK 25 .1 mK

Type K_ 38.1 12.0 25.9 Type T_ _ _ O C A lb .4 10.5 24 .7

Pt versus KN .. 112.3 21.7 27.7 KP versus Pt . __ 132.9 40.2 28.1

Pt versus TN 40 .

12 .3 24 .8

Pt versus TP 529.6 39.8 141.2

Pt versus Ag-28

at% Au~ 153.2 18.3 57.3

Ag-28 at% Au

versus KN ZD / . U

CO H bo. I 29.9 KP versus Ag-28

at% Au. 89.1 19.9 27.2

Ag-28 at% Au

versus TN 52.5 16.2 25.4 TP versus Ag-28

at% Au . . 597.9 112.7 61 .2

our measurement of thermocouple voltages: (1) potentiometer uncertainty, (2) uncertainty in the

standard reference cells used with the potentiometer,

and (3) adjustment of the actual reference temperatures to a fixed value at 4.0, 20.0, and 75.0 K, using

calculated values of dE/dT for each of the thermocouple combinations. Estimates of these systematic

errors are given in table 10. The total uncertainties in the thermoelectric volt- ages expressed in millikelvin, are given in table 11. The

values in the table are obtained by taking the square

root of the sum of the squares of the corresponding

values in tables 7, 8, 9 and 10. The voltage uncertainties are converted to temperature uncertainties bv

dividing them by the Seebeck coefficient, dE/dT,

appropriate for each thermocouple combination in each temperature range.

8. Standard Tables and Functions

Units for the thermocouple tables and functions are based on the "NBS as-maintained volt" [20]; the

International Practical Temperature Scale, IPTS-68

[21, 22, 23] for temperature above 20 K; and the NBS

acoustical scale, P 2-20 (1965) [24, 25] for temperatures between 4 and 20 K. The tabular values of

thermovoltages for Types E, K, and T are slightly different from those reported informally by us earlier

[26, 27]. The earlier values were based on a pre- liminary IPTS-68 scale; the preliminarv and final IPTS-68 scales differed slightly.

The thermovoltages for the other thermocouple

combinations (Pt and Ag-28 at% Au versus KP, KN,

TP, TN) are also different from those reported earlier; they have been adjusted in two ways. The temperature

scale modification discussed above was required to

L5
O

A,

0 5 TEMPERATURE, Kelvin

Figure 1 1 . Illustration of the nonzero thermoelectric voltage at T = 0K which results when experimental data are extrapolated from 5 K to 0 K.

base these values on the final IPTS-68 and the NBS

P 2-20 (1965) scales. The second modification was re- quired to establish internal consistency between the

tables referenced to platinum and Ag-28 at% Au and

those tables based on the E, K, and T combinations. For example,

Type £ = EP-£7V=(£'.P-Pt) + (Pt-£/V).

The algebraic combination of the values for (EP —Pt)

and (Pt-EN) must yield (EP-EN). The reason for the earlier inconsistency in the absolute numbers

(there was no inconsistency if temperature differences were used) was that our data were extrapolated to 0 K

from about 5 K. Each resulting table was then shifted by a constant A, (see figure 11) so that £"=0 pV at r=0 K. Since each table was shifted by a constant,

A,, the sensitivity or slope was not affected. The

difference in thermal voltage between any two temperatures has not been changed. It must be emphasized

that the adjustments made for these reasons do not devalue the data significantly; the need for the shifts was created by requiring that E = 0 pV at T=0 K when

the extrapolation from the lowest data point would not

otherwise pass through E=0 pV at T=0 K. The method used to insure additive consistency

among all of the tables was to solve three simultaneous

equations for the materials referenced to platinum.

Equations for those materials are as follows:

(1) Type E=(EP-Pt+AEP) + (?t-EN +AEN),

(2) Type K=(KP-Pt+AKP) + (Pt-KN+AKN),

and

(3) Type T= (Pt — TN+AT??) — (Pt — TP+ATp).

Note that EP = KPand that 77V

EN so that AEp = AKp and Atn = Aen- Let Aen = 0 arbitrarily, then

(1) Type£=(EP-Pt +Ai? p) + (Pt-£/V),

(2) Type K=(EP-Pt+AEP) + {P\-KN+AKN),

and

(3) Type T= (Pt-EN) - (Pt- TP+ATP).

The required shifts are then determined by eqs. (4),

(5), and (6) below.

(4) AEP = Type E-(EP-Pt)- (Pt-EN),

(5) ATM = Type A-Type E— (Pt -KN) +(Pt -EN),

and

(6) Arp = (Pt-£W)-(Pt-rP)-Type T.

The tables referenced to Ag-28 at% Au are calculated by eqs. (7) through (10).

(7) EP-Ag-28 at% Au = (Pt -Ag-28 at% Au) + (£P-Pt),

(8) Ag-28 at% Au-AW

= (Pt- KN) - (Pt- Ag-28 at% Au),

(9) Ag-28 at% Au- TN

= (Pt - TN) - (Pt -Ag-28 at% Au),

and

(10) TP- Ag-28 at% Au = (Pt - Ag-28 at% Au) - (Pt - TP).

The platinum-referenced tables used in these equations

include the adjustments discussed previously.

Tabular data for thermocouple types E, K, and T

are presented in three different forms. The first form,

given in tables 12, 13, and 14, is the full-precision

representations of E(T), S(T), and dS(T). The second

and third forms of the same data are reduced precision

tables for both E(T) (tables 15, 16, and 17) and T(E)

(tables 18, 19, and 20). Tables 12 through 17 are referenced to 0 K while tables 18 through 20 are referenced to 0° C (273.15 K). The reduced precision

formats are especially .useful for field applications.

The remaining thermocouple combinations consist of platinum and Ag-28 at% Au versus the materials in thermocouple types E, K, and T. These tabular data

are presented in tables 21 through 29 as E(T), S(T),

and dS(T) in full precision. Other tabular formats for these data are not given.

Graphic representation of E, dE/dT=S and

d'2E/dT2 =dS/dT versus T are given in figures 12

through 14 for thermocouple types E, K, and T. Graphs of E and S versus T are given in figures 15

through 18 for the remaining thermocouple combinations.

16
Modern methods of data analysis require that functional representations of thermocouple data also be

available. As mentioned previously, the full precision

tables presented in this report were generated with

orthonormal polynomials and coefficients. Our primary reason for using this approach, rather than the more common power series, was that we could select the optimum order for the fit and then examine lower

and higher orders without having to redetermine new

coefficients. In the final analysis, this functional ap- proach presents the user with an often needed alternative not available when power series alone are used. Since each fit in the orthonormal polynomial scheme

represents a best fit for that order, the user can deter- mine his own accuracy requirements and choose the

lowest order fit that fills these particular needs. Computer economy benefits greatly from this freedom. In

situations where all of the precision inherent in the

experimental data is required, a power series using the

highest order of fit may be used, using the recombined

coefficients from the orthogonal expansion.

The thermal voltages given in tables 12 through 14

and 21 through 29 are given by

L E(T)=A0 +j:AnFn (T)

71=1

where the orthogonal polynomials Fn (T) are given by

Fn {T)= t CnjT>\

The F„(T) (up to rc = 14) for our data are given in

table 30 to 12 significant figures. For computer

economy and round-off considerations, the table is given in the product-factored form. The orthogonal

polynomial coefficients, An, for each of the thermocouple combinations are given in tables 31 and 32. The numbers are given with a sufficient number of

significant digits so that no precision is lost in the

final calculation. Since many computers cannot handle

12 significant figures in single precision, double precision constants and software are usually required if the computed values are to retain all of the precision

inherent in the experimental data. If the full array of

functions and constants (Xmax)i are used with a double precision program, the resultant precision of

the data fits are those given in tables 7 and 8. The thermocouple calibration data given in tables 12 through 14 and 21 through 29 were computed using

26 digits (84 binary bits) and the highest order fit (Lt ) for each thermocouple combination, as given in tables 31 and 32. However, the functional representation can be

simplified at the cost of increasing the standard

deviation of the fit. One simplifying step is to reduce

the order of the fit. This may be done without having

to redetermine the constants due to the orthogonal

representation, i.e., the lower order function uses the same An and represents the best fit for that order. The

standard deviation of the fit increases as the order is reduced, as is shown in tables 33 and 34. A second

method of simplifying the computation is to reduce

the number of digits carried in the calculations. Table

35 shows the limits of error to be expected when using

decreasing numbers of digits. When reducing either

the number of coefficients used or the number of

digits carried, one must consider both the errors found in tables 33 and 34 and table 35. For example, if one wishes to generate the data for Type T with a pre- cision of 1 jliV, table 33 shows that L = 6. Table 35

shows that to achieve this precision 10 decimal digits

(32 binary bits) should be carried. The full precision data may be generated using the more common power series formulation:

E(T)=B0 + £ Bn T»

71=1

for each of the thermocouple combinations being re- ported. Tables 36 and 37 contain the Bn needed; again,

the Bn are given with a sufficient number of digits so

that no significant precision is lost. The resultant pre- cision is the same as for the highest order orthogonal fit.

17
Table

T E

K MV

o 0.00

1 0.09

2 0.76

3 1.97

4 3.69

5 5.92

6 8.61

7 11.77

8 15.38

9 19.41

10 23.87 U 28.74

12 34.01

13 39.68

14 45.74

15 52.18

16 59.01

17 66.22

18 73.80

19 81.75

20 90 . 07

2i 98 • 76

22 107.81

23 117.23

24 127.01

25 137.15

26 147.65

27 158.51

28 169.73

29 181.30

30 193.22

31 205. 50 32 218.12

33 231.09

34 244.41

35 258.08

36 272.09

37 286.43

38 301.12

39 316.14

40 331.50

41 347.19

42 363.20

43 379.55

44 396.21

45 413.20

46 430.51

47 448. 14 48 466.07

49 484.32

5g 502.88

51 5 2 1 . 74

52 540.91

53 560.38

54 580.14

55 600.20

56 620.55

57 641.19

58 662.12

59 683.33

60 704.83

Type E—thermoelectric

S dS/dT

jiV/K nV/K2 -0.203 604.4 0.384 571.8

0.941 543.0

1.472 517.7

1.978 495.6

2.464 476.2

2.931 459.4

3.383 444.7

3.821 432.1 4.248 421.1 4.664 411.7

5.072 403.6

5.472 396.7

5.865 390.8 6.254 385.8 6.637 381.5 7.017 377.8

7.393 374.6 7.766 371.9 8.137 369.5 8.505 367.4

8.872 365.6 9.237 363.9 9.600 362.3 9.961 360.8

10.321 359.3 10.680 357.9 11.037 356.4

11.393 354.9

11.747 353.4

12.099 351.8 12.450 350.1 12.800 348.4 13.147 346.5

13.493 344.6

13.836 342.7

14.178 340.6 14.517 338.4

14.855 336.2 15.190 333.9

15.523 331.5 15.853 329.1

16.181 326.6

16.506 324.1 16.829 321.5 17.149 318.9

17.467 316.3

17.782 313.6 18.094 311.0

18.404 308.3

18.711 305.6

19.015 303.0

19.317 300.3

19.616 297.7

19.912 295.1 20.206 292.5 20.497 289.9 20.786 287.4

21.072 284.9 21.355 282.5 21.637 280.0

;e, E(T), Seebeck

JK *v

60 704.83

61 726.61

62 74 8.66

63 770.99

64 793.59

65 816.47

66 839.61

67 863 .02

68 886.69

69 910.63

70 934.82

71 959.28

72 983.99

73 1008.96

74 1034.18

75 1059.65

76 1085 .37 77 1111.35

78 1137.56

79 1164.03

80 1 190 . 73

81 1217.68

82 1244.87

83 1272.30

84 1299.97

85 1327.88

86 1356.02

87 1384.40

88 1413.01

89 1441.85

90 1470.92

91 1500.22

92 1529.75

93 1559.51

94 1589.49

95 1619. 70 96 1650 .13 97 1680 . 79 98 1711.67

99 1742.77

100 1774.09

101 1805.63

102 1837.38

103 1869.36

104 1901.54

105 1933.95

106 1966.57

107 1999.40

108 2032.44

109 2065.69

110 2099. 16 HI 2132.83

112 2166 .71 113 2200.80

114 2235.09

115 2269.59

116 2304.29

117 2339.20

118 2374.31

119 2409.62

120 2445.13

•fjicient , S(T), and

S dS/dT

jtV/K BV/K2 21.637 280.0

21.915 277.7

22.192 275.4

22.466 273.1 22.738 270.9 23.008 268.8 23.276 266.7

23.541 264.6 23.805 262.6 24.067 260.7

24.326 258.8 24.584 256.9 24.840 255.1 25.094 253.4 25.347 251.7

25.598 250.0 25.847 248.4

26.095 246.9

26.341 245.4

26.585 243.9 26.829 242.4

27.070 241.0

27.311 239.7 27.550 238.3 27.787 237.0 28.024 235.7 28.259 234.5 28.493 233.2

28.725 232.0 28.957 230.9 29.187 229.7 29.416 228.6 29.644 227.4

29.871 226.3 30.097 225.2

30.321 224.1 30.545 223.1 30.768 222.0 30.989 221.0

31.210 219.9

31.429 218.9

31.647 217.9

31.865 216.9

32.081 215.9 32.297 214.9

32.511 213.9 32.724 212.9 32.937 211.9

33.148 210.9 33.359 210.0 33.568 209.0

33.777 208.1 33.984 207.1 34.191 206.2 34.397 205.2 34.601 204.3 34.805 203.4

35.008 202.4

35.210 201.5

35.411 200.6

35.611 199.7

of the Seebeck coeffi<

T

K

EMV

120

121

122 123 124

2445.13 2480.84

2516.75

2552.86 2589.17

125

126 127

128 129

2625.67

2662.36

2699.25 2736.34

2773.62

130

131

132 133

134

2811.09

2848.75

2886.60 2924.64

2962.87

135

136 137

138 139

3001.29

3039.89

3078.69 3117.66

3156.83

140

141

142

143 144

3196.17

3235.70

3275.42

3315.31 3355.39

145 146

147

148 149

3395.65

3436.09

3476.71

3517.51 3558.48

150

151

152 153 154

3599.64 3640.97

3682.47

3724.16

3766.02

155

156

157

158 159

3808.05

3850.26 3892.64

3935.19

3977.91

160

161 162

163 164

4020.81

4063.88

4107.11 4150.52

4194.10

165

166

167

168 169

4237.84

4281.76

4325.84

4370.08

4414.50

170

171

172

173

174

4459.07

4503.82

4548.73 4593.80

4639.03

175 176 177

178 179

4684.43

4729.99

4775.71

. 4821.59

4867.63

180 4913.83

!, dS(T)

S dS/dT

pV/K nV/K2

35.611 199.7 35.811 198.8 36.009 198.0 36.207 197.1 36.403 196.2 36.599 195.4 36.794 194.5 36.988 193.7 37.181 192.9 37.374 192.0 37.565 191.2 37.756 190.4 37.946 189.6 38.136 188.9 38.324 183.1 38.512 187.3 38.699 186.6 38.885 185.9 39.070 185.1 39.255 184.4 39.439 183.7 39.623 183.0 39.805 182.3 39.987 181.6 40.169 180.9 40.349 180.3 40.529 179.6 40.708 179.0 40.887 178.3 41.065 177.7 41.242 177.0 41.419 176.4 41.595 175.8 41.771 175.2 41.946 174.6 42.120 173.9 42.293 173.3 42.466 172.7 42.639 172.1 42.811 171.5 42.982 170.9 43.153 170.3 43.323 169.7 43.492 169.1 43.661 168.5 43.829 167.9 43.997 167.3 44.164 166.7 44.330 166.1 44.496 165.5 44.661 164.9 44.826 164.3 44.990 163.7 45.153 163.1 45.316 162.5 45.478 161.8 45.640 161.2 45.800 160.6 45.961 160.0 46.120 159.4 46.279 158.7

18
Table 12. Type E—thermoelectric voltage, E(T), Seebeck coefficient , S(T), and derivative of the Seebeck coefficient, dS(T) —Continued

T

K

180

181

182

183 184

185

186 187

188 189

190

191

192 193 194

195

196

197

198 199 200

201

202 203

204

205

206 207

208

209 210

211 212

213 214

215

216 217

218 219

220

221 222 223 224

E

4913.83 4960.19

5006.70 5053.38

5100.21

5147.20 5194.34

5241.64

5289.09

5336.70 5384.46 5432.37

5480.43

5528.65

5577.01 5625.53

5674.19

5723.00

5771.97

5821.08

5870.33 5919.74

5969.28 6018.98

6068.82

6118.80 6168.93

6219.20

6269.61

6320.16

6370.86 6421.69

6472.67 6523.79

6575.04

6626.44 6677.97

6729.64

6781.45 6833.39

6885.47

6937.69

6990.04

7042.53

7095.15

s

46.279

46.438 46.596

46.753 46.909

47.065

47.221

47.375 47.529

47.683 47.835

47.988 48.139

48.290

48.440

48.590

48.739

48.888 49.036

49.183 49.330

49.476

49.622

49.767

49.911

50.055

50.198

50.341 50.483

50.625 50.766

50.907

51.047

51.186

51.325 51.464

51.602 51.739 51.876

52.013

52.149 52.284

52.419 52.554

52.688

dS/dT

nV/K2

158.7

158.1 157.5 156.9

156.2 155.6

155.0 154.4

153.7

153.1 152.5 151.9

151.2 150.6

150.0 149.4

148.8

148.2 147.6

147.0

146.4

145.9

145.3 144.7

144.1 143.6

143.0

142.5 141.9

141.4

140.9

140.3

139.8

139.3

138.8

138.3

137.8 137.3

136.8

136.3 135.8

135.3 134.8

134.3

133.8

T E s dS/dT

K Mv nV/K*

240 7954.95 54.767 126.1

241 8009.78 54.893 125.7

242 8064.74 55.018 125.2 243 8119.82 55.143 124.8

244 8175.02 55.268 124.3

245 8230.35 55.392 123.9

246 8285.81 55.516 123.5

247 8341.38 55.639 123.1

248 8397.09 55.762 122.7

249 8452.91 55.884 122.3

250 8508.85 56.006 121.9

251 8564.92 56.128 121.5

252 8621.11 56.250 121.2

253 8677.42 56.371 120.8 254 8733.85 56.491 120.5

255 8790.40 56.611 120.1

256 8847.07 56.731 119.8 257 8903.86 56.851 119.4

258 8960.78 56.970 119.1

259 9017.81 57.089 118.7

260 9074.95 57.208 118.3

261 9132.22 57.326 117.9

262 9189.61 57.444 117.4

263 9247.11 57.561 116.9

264 9304.73 57.677 116.3

265 9362.46 57.793 115.6

266 9420.31 57.908 114.8

267 9478.28 58.023 113.9

268 9536.36 58.136 112.8

269 9594.55 58.248 111.5

270 9652.85 58.359 110.

271 9711.27 58.468 108.2

272 9769.79 58.575 106.2 273 9828.42 58.680 103.7

274 9887.15 58.783 100.9

275 9945.98 58.882 97.6

276 10004.91 58.978 93.8 277 10063.94 59.069 89.3

278 10123.05 59.156 84.2 279 10182.25 59.237 78.2

280 10241.52 59.312 71.4

E s dS/dT

nV/K2

225

226 227

228

229

7147.90 7200.79

7253.81 7306.97

7360.25

52.821 52.955

53.087

53.219

53.351

133.3

132.8

132.3 131.9 131.4

230

231

232

233 234

7413.67

7467.22 7520.89

7574.70 7628.64

53.482

53.613

53.743 53.872

54.002

130.9 130.4

129.9 129.4

129.0

235

236

237

238 239

7682.70

7736.90

7791.22 7845.67

7900.25

54.130

54.259

54.386 54.514

54.641

128.5 128.0

127.5

127.1 126.6

240 7954.95 54.767 126.1

19
Table 13. Type K—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T)

T E K MV

0 0.00

1 0.32

2 0.78

3 1.42

4 2.21

5 3.19

6 4.34

7 5.67

8 7.20

9 8.92

10 10.83

11 12.95

12 15.27

13 17.80

14 20.53

15 23.48

16 26.65

17 30.03

18 33.63

19 37.45

20 41.48

21 45.75

22 50.23

23 54.94

24 59.87

25 65.02

26 70.40

27 76.01

28 81.84

29 87.89

30 94.17

31 100.68

32 107.40

33 114.36

34 121.53

35 128.93

36 136.54

37 144-.38 38 152.44

39 160.72

*0 169.22

41 177.94

42 186.87

43 196.02

44 205.38

45 214.95

46 224.74

47 234.75

48 244.96

49 255.38

50 266.01

51 276.85

52 287.89

53 299.14

54 310.60

55 322.26

56 334.12

57 346.18

58 358.44

59 370.90

60 383.56

S dS/dT

H.V/K nV/K2

0.241 146.9

0.391 154.3 0.549 161.3 0.714 167.7 0.884 173.7

I. 061 179.2 1.243 184.3

1.429 189.0

1.621 193.4 1.816 197.3 2.015 200.9

2.218 204.2 2.424 207.2 2.632 209.9

2.843 212.3 3.057 214.5

3.272 216.4

3.489 218.1

3.708 219.5

3.928 220.8 4.150 221.9

4.372 222.8 4.595 223.5

4.819 224.0

5.043 224.4

5.268 224.7

5.493 224.9

5.718 224.9

5.942 224.8 6.167 224.6

6.392 224.3 6.616 224.0

6.840 223.5

7.063 223.0 7.285 222.4

7.508 221.7

7.729 221.0

7.950 220.3

8.169 219.4

8.388 218.6

8.607 217.7

8.824 216.8 9.040 215.8 9.256 214.9 9.470 213.9

9.683 212.9

9.896 211.8

10.107 210.8

10.317 209.7

10.526 208.7

10.735 207.6

10.942 206.5

11.148 205.5

11.353 204.4

11.556 203.3

11.759 202.3

11.961 201.2

12.162 200.1

12.361 199.1 12.560 198.1 12.757 197.0

T E

K Mv

60 383.56

61 396.41

62 409.47

63 422.71

64 436.15

65 449.79

66 463.61

67 477.63

68 491.84

69 506.23

70 520.82

71 535.59

72 550.55

73 565.69

74 581.02

75 596.53

76 612.23

77 628.11

78 644.17

79 660.41

80 676.83

81 693.43

82 710.20

83 727.16

84 744.29

85 761.60

86 779.08

87 796.74

88 814.57

89 832.58

90 850.75

91 869.10

92 887.62

93 906.31

94 925.18

95 944.21

96 963.40

97 982.77

98 1002.31

99 1022.01

100 1041.87

101 1061.91

102 1082.11

103 1102.47

104 1122.99

105 1143.68

106 1164.53

107 1185.55

108 1206.72

109 1228.06

110 1249.55

111 1271.21

112 1293.02

113 1315.00

114 1337.13

115 1359.42

116 1381.86

117 1404.46

118 1427.22

119 1450.13

120 1473.20

S dS/dT

pV/K nV/K2

12.757 197.0 12.954 196.0 13.149 195.0 13.344 194.0 13.537 193.0

13.730 192.1 13.922 191.1 14.112 190.2 14.302 189.2

14.491 188.3 14.678 187.4

14.865 186.5

15.051 185.6

15.237 184.8

15.421 183.9 15.604 183.1 15.787 182.2 15.969 181.4

16.150 180.6 16.330 179.8 16.510 179.1 16.688 178.3 16.866 177.5

17.043 176.8 17.220 176.1 17.396 175.3

17.571 174.6 17.745 173.9 17.918 173.2 18.091 172.6 18.264 171.9

18.435 171.2 18.606 170.6 18.776 169.9 18.946 169.3

19.115 168.6

19.283 168.0

19.451 167.4 19.618 166.8 19.784 166.2 19.950 165.5 20.115 164.9 20.280 164.3 20.444 163.7 20.608 163.2 20.770 162.6 20.933 162.0 21.094 161.4 21.255 160.8 21.416 160.2 21.576 159.7 21.735 159.1 21.894 158.5 22.052 157.9 22.210 157.4 22.367 156.8 22.524 156.2 22.679 155.6 22.835 155.1 22.990 154.5 23.144 153.9

T E K MV

120 1473.20

121 1496.42

122 1519.80

123 1543.32

124 1567.00

125 1590.83

126 1614.81

127 1638.95

128 1663.23

129 1687.66

130 1712.24

131 1736.97

132 1761.84

133 1786.87

134 1812.04

135 1837.35

136 1862.81

137 1888.42

138 1914.17

139 1940.06

140 1966.10

141 1992,28

142 2018.60

143 2045.06

144 2071.66

145 2098.40

146 2125.28

147 2152.30

148 2179.46

149 2206.75

150 2234.19

151 2261.76

152 2289.46

153 2317.30

154 2345.27

155 2373.38

156 2401.62

157 2430.00

158 2458.50

159 2487.14

160 2515.91

161 2544.81

162 2573.84

163 2603.00

164 2632.28

165 2661.70

166 2691.24

167 2720.90

168 2750.70

169 2780.62

170 2810.66

171 2840.83

172 2871.12

173 2901.53

174 2932.07

175 2962.73

176 2993.51

177 3024.41

178 3055.42

179 ' 3086.56

180 3117.82

S dS/dT

fiV/K nV/K*

23.144 153.9 23.297 153.4 23.451 152.8

23.603 152.2 23.755 151.6 23.906 151.1 24.057 150.5 24.207 149.9 24.357 149.3 24.506 148.8 24.654 148.2 24.802 147.6 24.950 147.0 25.096 146.4 25.243 145.9 25.388 145.3 25.533 144.7 25.678 144.1 25.821 143.5 25.965 142.9 26.107 142.3 26.249 141.7 26.391 141.1 26.532 140.6 26.672 140.0 26.811 139.4

26.950 138.8 27.089 138.2 27.227 137.6 27.364 137.0

27.501 136.4 27.637 135.7 27.772 135.1 27.907 134.5

28.041 133.9

28.175 133.3 28.308 132.7 28.440 132.1 28.572 131.5 28.703 130.9 28.834 130.3 28.964 129.7 29.093 129.0 29.222 128.4

29.350 127.8 29.478 127.2 29.604 126.6 29.731 126.0 29.856 125.3 29.981 124.7 30.106 124.1 30.230 123.5 30.353 122.9 30.475 122.2 30.597 121.6 30.718 121.0 30.839 120.4 30.959 119.7 31.079 119.1 31.197 118.5 31.316 117.9

20
Table 13. Type K—thermoelectric voltage, E(T) , Seebech coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) —Continued

T

K

180

181

182 183 184

185

186 187

188 189

190

191

192 193 194

195 196

197

198 199 200

201

202 203 204

205 206

207

208 209 210

211

212 213 214

215

216

217

218

219

220

221

222 223 224

225

226

227

228

229

EMV

3117.82 3149.19

3180.68 3212.29

3244.02 3275.86

3307.81

3339.88

3372.06 3404.36

3436.76 3469.28

3501.91 3534.65

3567.50

3600.46

3633.52

3666.70 3699.98

3733.36

3766.86

3800.46

3834.16

3867.96 3901.87

3935.89

3970.00 4004.22

4038.53

4072.95 4107.46

4142.08 4176.79

4211.60

4246.50

4281.51

4316.60 4351.79

4387.08 4422.46

4457.93

4493.49

4529.15

4564.90

4600.73 4636.66

4672.67

4708.77

4744.96 4781.24

S /iV/K 31.316

31.433

31.550 31.666

31.782 31.897

32.011 32.125

32.238

32.351

32.463 32.574

32.684

32.794

32.904

33.012 33.120

33.228 33.334

33.440

33.546

33.651 33.755

33.858

33.961 34.063 34.165

34.266

34.366

34.466 34.565

34.663

34.761 34.857 34.954

35.049

35.144

35.239

35.333 35.426

35.518 35.610

35.701

35.791 35.881 35.970

36.059

36.146

36.233 36.320

dS/dT

BV/K2

117.9

117.2 116.6

116.0

115.3 114.7

114.1 113.4

112.8

112.2 111.5 110.9

110.3

109.6

109.0

108.3 107.7

107.1 106.4

105.8

105.1 104.5

103.8

103.2 102.5 101.9

101.2 100.6 99.9

99.3 98.6 98.0

97.3

96.7

96.0 95.3

94.7

94.0 93.4

92.7

92.1 91.4

90.7

90.1 89.4

88.8

88.1

87.5 86.8

86.2

T

K

240

241

242

243 244

245

246 247

248 249

250

251 252

253 254

255

256 257

258 259

260

261

262

263 264

265 266 267

268 269

270

271 272

273 274

275 276 277

278 279

280

EMV

5185.83

5223.10

5260.44

5297.87 5335.37

5372.94

5410.60

5448.32

5486.13

5524.00

5561.95

5599.98 5638.07

5676.23 5714.47

5752.78

5791.15

5829.59

5868.10

5906.68

5945.33 5984.04

6022.81 6061.65 6100.56

6139.52

6178.55 6217.64

6256.79

6296.00 6335.27

6374.60

6413.98

6453.42

6492.91 6532.46

6572.06

6611.72

6651.42

6691.18

s

fi.V/% 37.228

37.307

37.385

37.462 37.539

37.615

37.691 37.765 37.840

37.913

37.986

38.058

38.130

38.201

38.271 38.340

38.409 38.477

38.545

38.612

38.678 38.743

38.808

38.872

38.935

38.998 39.059

39.120

39.180 39.239

39.298

39.355 39.412 39.467

39.522

39.575 39.628

39.679

39.729

39.778 6730.98 39.826

dS/dT

nV/K*

79.0

78.4 77.7

77.1 76.4

75.8

75.1 74.5

73.8

73.2

72.5 71.9

71.2 70.6 69.9

69.2 68.5 67.9

67.2

66.5 65.8

65.1

64.3 63.6

62.8

62.1 61.3

60.5

59.6

58.8 57.9

57.0

56.1

55.1

54.1 53.0 51.9

50.8 49.6

48.4

47.1

E s dS/dT

nV/K*

230

231

232

233 234

4817.60

4854.05 4890.59

4927.20

4963.90

36.406

36.491

36.575

36.659

36.743

85.5 84.8

84.2 83.5

82.9

235

236 237

238

239

5000.69

5037.55

5074.50

5111.53 5148.64

36.825

36.907

36.988

37.069

37.149

82.2

81.6 80.9

80.3

79.6

240 5185.83 37.228 79.0

21
Table 14. Type r

thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T)

T E s dS/dT T E s dS/dT T E s dS/dT

K uV/K oV/K* K Mv pV/K nV/K2 K nV/K2

0 0.00 -0.400 526.6 60 461.11 13.826 154.6 120 1540.74 21.931 126. 0

1 -0.15 0.099 473.2 61 475.01 13.980 152.9 121 1562.73 22.057 125,,8 0*18 428.0 62 489 • 0 7 14.132 151.3 122 1584.85 22.182 1 £. -> 6

3 0.94 0^958 390.1 63 503.28 14.283 149.8 123 1607. 10 22.308 125 4

4 2.09 1.332 358.4 64 517.64 14.432 148.4 124 1629.47 22.433 125..3

5 3.59 1.677 332.3 65 532.14 14.580 147.1 125 1651.96 22.558 125 ,1 6 5.43 1.998 310.9 66 546.79 14.726 146.0 126 1674.58 22.683 125 .0 7

7 9 q ft ft 6 7 561 . 59 14.872 144.9 127 1697.33 22.808 124 8

8 10.03 2.586 279.7 68 576.54 15.016 143.9 128 1720.20 22.933 124 ,7 9 12.75 2.860 268.8 69 591.62 15.159 142.9 129 1743.20 23.058 124 >5

10 15.74 3.124 260.3 70 606.86 15 . 302 142 .

130 1766.31 23. 182 124 >4 11 19.00 3.381 254.0 71 622.23 15.444 141.3 131 1789.56 23.306 124 .3 12 22. 50 3.633 249 . 3 72 637.74 15.584 140.6 132 1812.93 23.431 124 ,2 13 26.26 3.880 246.0 73 653.40 15.725 139.9 133 1836.42 23.555 124 • 0 14 30.26 4.125 243.8 74 669.19 15.864 139.3 134 1860.04 23.679 123 .9

15 34.51 4.368 242.5 75 685.13 16.003 138.8 135 1883.78 23. 803 123 >8 16 39.00 4.610 241.8 76 701.20 16.142 138.3 136 1907.64 23.926 123 ,7 17 43. 73 4.852 241.5 77 717.41 16.280 137.8 137 1931.63 24.050 123 ,5 18 48.70 5.094 241.6 78 733.76 16.417 137.4 138 1955.74 24.173 123 .4 19 53.92 5.335 241.8 79 750.24 16.555 137.0 139 1979.98 24.297 123 • 3

20 59.37 5.577 242.2 80 766.87 16.691 136.6 140 2004. 33 24. 420 123 ,2 21 65.07 5.820 242.5 81 783.63 16.828 136.? 141 2028.82 24.543 123 .0 99 71.01 A ftA 9 242 . 7 82 Oftft *i 9 16.964 135.9 142 2053.42 24.666 122 , 9 23 77.20 6.305 242.7 83 817.55 17.100 135.6 143 2078.15 24.789 122 ,7 24 83.62 6.5*8 242.6 84 834.72 17.235 135.3 144 2103.00 24.911 122 >6

25 90.29 6.790 242.2 85 852.02 17. 370 135.0 145 2127.97 25.034 122 • 4

26 97.20 7.032 241.6 86 869.46 17.505 134.7 146 2153.07 25.156 122 ,3 97 1 04 • 36 7 • 273 240 • 8 87 887.03 17.640 134.5 147 2178.28 25.279 122 ,1 28 111.75 7.513 239.7 88 904.74 17.774 134.2 148 2203.62 25.401 121 9 29 119.38 7.752 238.3 89 922.58 17.908 133.9 149 2229.08 25.522 121 .8

30 127.25 7.990 236.7 90 940.56 18.042 133.7 150 2254.67 25.644 121 ,6 31 135.36 8.226 234.8 91 958.66 18.175 133.4 151 2280.37 25.766 121 • 4

32 1 43 <• TO 8 .459 232.7 097£ 976 .91 18.309 133.1 152 2306.20 25.887 121 ,2 33 152.28 8.691 230.4 93 995.28 18.442 132.9 153 2332.15 26.008 121 • 0 34 161.08 8.920 227.9 94 1013.79 18.574 132.6 154 2358.21 26.129 120 ,7

35 170.12 9.147 225.2 95 1032.43 18.707 132.3 155 2384.40 26.249 120 ,5 36 179.38 9.371 222.4 96 1051.20 18.839 132.1 156 2410.71 26.370 120 .3

9.7 inn. loot aaOO 9 • 592 219.4 97 1 ft 7rv 1 1 18.971 131.8 157 2437.14 26.490 120 1 38 198.56 9.809 216.4 98 1089.14 19.102 131.5 158 2463.69 26.610 119 8 39 208.48 10.024 213.2 99 1108.31 19.234 131.2 159 2490.36 26.730 119, 6

40 218.61 10.236 210.0 100 1127.61 19 , 365 131.0 160 2517.15 26.849 119. 3 41 228.95 10.444 206.7 101 1147.04 19.496 130.7 161 2544.06 26.968 119, 0 239 . 49 1 0 • 649 203*4 1 ft 9 1 1 AA Aft 1 1 DO • DU 19.626 130.4 162 2571.09 27.087 118, 8 43 250.24 10.851 200.1 103 1186.29 19.757 130.1 163 2598.24 27.206 118 5 44 261.19 11.049 196.8 104 1206.12 19.886 129.8 164 2625.50 27.324 118 ,2

45 272.34 11.245 193.5 105 1226.07 20.016 129.6 165 2652 .88 27.442 118 0 46 283.68 11.437 190.3 106 1246.15 20.146 129.3 166 2680.39 27.560 117 7 295*21 i i A9t; 1 P7 1 1 A7 1 266 • 36 20.275 129.0 167 2708.00 27.678 117 ,4 48 306.93 11.811 184.0 108 1286.70 20.404 128.7 168 2735.74 27.795 117, 1 49 318.83 11.993 181.0 109 1307.17 20.532 128.5 169 2763.59 27.912 116. 8

50 330.92 12.173 178.0 110 1327.76 20.661 128.2 170 2791 . 56 28.029 116. 6 51 343.18 12.349 175.2 111 1348.49 20.789 128.0 171 2819.65 28.145 116. 3

t»9 3"»3»62 1 7 ^9^ 1 72 • 5 112 1 369 #34 20.916 127.7 172 2847.85 28.261 116 o 53 368.23 12.694 169.8 113 1390.32 21.044 127.5 173 2876.17 28.377 115 7 54 381.00 12.863 167.3 114 1411.43 21.171 127.2 174 2904.61 28.493 115 5

55 393.95 13.029 164.9 115 1432.66 21 .298 127.0 175 2933 .16 28 . 608 115. 2 56 407.06 13.193 162.6 116 1454.02 21.425 126.8 176 2961.82 28.723 114, 9 57 420.33 13.354 160.4 117 1475 .51 21.552 126.6 177 2990.60 28.838 114. 7 58 433.77 13.514 158.4 118 1497.13 21.678 126.3 178 , 3019.50 28.952 114, 4

59 447.36 13.671 156.4 119 1518.87 21.805 126.1 179 3048.51 29.067 114, 2

60 461.11 13.826 154.6 120 1540.74 21.931 126.0 180 3077.63 29.181 113.9

22
Table 14. Type T—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) —Continued

T

K 180

181 182

183 184

185

186

187

188

189

190

191 192

193 194

195

196

197

198 199

EMV

3077.63 3106.87

3136.22

3165.63

3195.26 3224.95

3254.76 3284.67

3314.70 3344.84

3375.09

3405.46

3435.93

3466.52 3497.22

3528.03 3558.95

3589.98

3621.12

3652.37

S

fiV/K 29.181 29.294

29.408

29.521 29.634

29.747

29.860

29.972 30.085

30.197

30.308 30.420

30.531

30.643 30.754

30.865

30.975

31.086 31.196

31.306

dS/dT

nV/K*

113.9 113.7

113.4

113.2

113.0

112.8

112.5

112.3 112.1 111.9 111.7

111.5 111.3

111.1 111.0

110.8

110.6 110.4

110.2 110.0

T

K

240 241

242

243 244

245

246 247

248

249

250

251

252

253 254

255 256 257

258

259

EMV

5025.40 5061.04

5096.78

5132.62 5168.56 5204.60

5240.73 5276.97

5313.30

5349.73 5386.26

5422.89

5459.62 5496.44

5533.37

5570.39 5607,50

5644.72

5682.03 5719.44

s pV/K

35.591 35.690

35.789

35.888 35.987 36.086

36.185 36.284

36.382

36.481 36.579

36.678

36.776

36.874

36.972 37.069

37.166

37.263 37.359

37.455

dS/dT

BV/K2

99.3

99.2

99.1 99.0 98.9

98.8

98.8 98.7

98.6

98.5 98.4

98.3

98.1 97.9

97.6

97.3

97.0 96.6

96.1 95.6

E s dS/dT

nV/K2

200

201 202

203 204

205 206

207

208 209

210

211 212 213 214

215

216 217

218

219

220

221

222

223 224

225

226 227

228

229

3683.73 3715.20

3746.78

3778.47

3810.27

3842.18

3874.30 3906.32

3938.55

3970.90 4003.34

4035.90 4068.56

4101.34

4134.21

4167.20 4200.29

4233.48

4266.78 4300.19

4333.70 4367.31

4401.03

4434.85

4468.78

4502.81 4536.94 4571.17

4605.51

4639.94

31.416

31.526 31.635

31.744

31.853 31.962

32.071 32.179 32.287

32.395

32.503 32.610

32.717 32.824

32.930

33.036

33.142 33.248

33.353 33.458

33.562 33.667

33.770

33.874

33.977

34.080

34.1B3 34.285

34.387

34.488

109.8

109.6

109.4

109.2

108.9 108.7

108.5

108.2 108.0 107.7

107.4

107.2 106.9

106.6

106.3

106.0 105.7 105.4

105.0

104.7 104.4

104.0 103.7

103.4

103.1 102.7

102.4

102.1 101.8 101.5

260

261 262

263 264

265 266 267

268

269 270

271

272

273 274

275

276 277

278 279

280

5756.94

5794.54

5832.23

5870.02 5907.90 5945.87

5983.93 6022.08

6060.32 6098.66

6137.08

6175.58

6214.18

6252.86 6291.64

6330.50

6369.45

640 8.49 6447.63 6486.87

37.551 37.645 37.739

37.833

37.925 38.017

38.108

38. 198 38.287

38.376 38.464

38.552 38.640

38.728

38.816 38.906

38.997

39.091

39.189

39.291

95.0

94.3

93.6 92.9

92.1 91.3

90.5

89.8

89.0 88.4

88.0 87.7

87.8

88.2

89.0 90.5 92.6

95.6

99.7

105.0 6526.22 39.399 111.8

230

231 232

233 234

4674.46

4709.12 4743.87

4778.71 4813.65

34.590

34.691 34.792

34.892

34.993

101.2 101.0

100.7

100.5

100.2

235 236

237

238 239

4848.69

4883.84

4919.08 4954.42

4989.86

35.093

35.193 35.293

35.392

35.492

100.0 99.9

99.7

99.5

99.4

240 5025.40 35.591 99.3

23
Table 15. Type E—reduced precision tables, E(T)

K 0 1 2 3 4 5 6 THERMOELECTRIC VOLTAGE IN ABSOLUTE

0 0.0 0.1 0.8 2.0 3.7 5.9 8.6

10 23.9 28.7 34.0 39.7 45.7 52.2 59.0

20 90.1 98.8 107.8 117.2 127.0 137.2 147.7

30 193.2 205.5 218.1 23 1 • 1 244 . 4 258.

272 .

40 331.5 347.2 363.2 379. 5 396 . 2 413.2 430 . 5

50 502.9 521.7 540 9 560.4 ?OU| 1 600 . 2 620.6

60 704.8 726.6 748.7 771.0 793.6 816.5 839.6

70 934.8 959.3 984.0 1009.0 1034.2 1059.7 1085.4

80 1190.7 1217.7 1 ?Ai Q 1 C **** . 7

1 17? Q

s i 1 c. • J 1300.0 1 5 it / • 7 1356.0

90 1470.9 1500.2 1529.8 1559.

1589 . 5 1619.7 1650.

100 1774.1 1805.6 1 837. 4 1 869 •

1901 .

1933 .

1 966.

110 2099.2 2132.8 2166.7 2200.8 2235.1 2269.6 2304.3

120 2445.1 2480.8 2516.8 2552.9 2589.2 2625.7 2662.4

130 2811.1 2848.7 2 8 86.

2924.

2962 •

3 00 1 •

140 3196.2 3235.7 DC 3315*3 3355.4 3395 .

3436.

150 3599.6 3641.0 3682 .

3724 .

3766 .

5 O U O '. U 3850 . 3 160 4020.8 4063.9 4107.1 4150.5 4194.1 4237.8 4281.8

170 4459.1 4503.8 4548.7 4593.8 4639.0 4684.4 4730.0

180 4913.8 4960.2 5006.5053.4 5100.2 5147.2 5 194.

190 5384.5 5432.4 5480.4 5528.6 5577.0 5625.5 5674 .

200 5870.3 5919.7 5969.3 6019.0 6068.8 6118.8 6168.9

210 6370.9 6421.7 6472.7 6523.8 6575.0 6626.4 6678.0

220 6885.5 6937.7 6990.0 7042 .7095.

7147.9 7200.8

230 7413.7 7467.2 7520.9 7574.7 7628.6 7682.7 7736.9

240 7955.0 8009 •8064.7 8119.8 8175.0 8230.4 8285.8

250 8508.9 8564.9 8621.1 8677.4 8733.9 8790.4 8847.

260 9075.0 9132.2 9189.6 9247.1 9304.7 9362.5 9420.3

270 9652.9 9711.3 9769.8 9828.4 9887.1 9946.0 10004.9

280 10241.5

K 0 1 2 3 4 5 6

11.8 66.2

158.5 286.4

448.1

641.2

863.0

1111.3 1384.4

1680.8 1999.4

2339.2 2699.3

3078.7

3476.7

3892.6

4325,8 4775.7

5241.6 5723.0

6219.2 6729.6

7253.8

7791.2 8341.4 8903.9

9478.3

10063.9

8 9 10 K

15.4 19.4 23.9 0 73.8 81.7 90.1 10 169.7 181.3 193.2 20 301.1 316.1 331.5 30 466.1 484.3 502.9 40 662.1 683.3 704.8 50 886.7 910.6 934.8 60 1137.6 1164.0 1190.7 70 1413.0 1441.8 1470.9 80 1711.7 1742.8 1774.1 90 2032.4 2065.7 2099.2 100 2374.3 2409.6 2445.1 110 2736.3 2773.6 2811.1 120 3117.7 3156.8 3196.2 130 3517.5 3558.5 3599.6 140 3935.2 3977.9 4020.8 150 4370.1 4414.5 4459.1 160 4821.6 4867.6 4913.8 170 5289.1 5336.7 5384.5 180 5772.0 5821.1 5870.3 190 6269.6 6320.2 6370.9 200 6781.4 6833.4 6885.5 210 7307.0 7360.3 7413.7 220 7845.7 7900.2 7955.0 230 8397.

8452 .

8508 . 9 240 8960.8 9017.8 9075.0 250 9536.4 9594.6 9652.9 260 10123.0 10182.2 10241.5 270

280

8 9 10 K

Table 16. Type K—reduced precision tables, E(T)

THERMOELECTRIC VOLTAGE IN ABSOLUTE fi\j

10

01020

3040

5060

7080

90

100

110

120

130

140

0.0

10.8 41.5

94.2

169.2 266.0

383.6

520.8 676.8

850.8 1041.9

1249.6

1473.2

1712.2

1966.1

0.3 12.9 45.7

100.7

177.9

276.8 396.4

535.6 693.4

869. 1 1061.9

1271.2 1496.4

1737.0

1992.3

0.8

15.3 50.2 107.4

186.9 287.9

409.5

550.5 710.2 887.6

1082.1 1293.0

1519.8

1761.8 2018.6

1.4

17.8 54.9 114.4

196.0 299.1 422.7

565.7

727.2 906.3

1102.5

1315.0

1543.3

1786.9

2045.1

2.2 20.5 59.9

121.5 205.4

310.6 436.2

581.0 744.3

925.2

1123.0

1337.1 1567.0 1812.0 2071.7

3.2 23.5

65.0 128.9

215.0

322.3 449.8

596.5

761.6 944.2

1143.7

1359.4

1590.8

1837.4 2098.4

4.3 26.6

70.4

136.5 224.7

334.1 463.6

612.2

779.1 963.4

1164.5 1381.9

1614.8

1862.8 2125.3

5.7 30.0

76.0 144.4 234.7

346.2 477.6

628.1 796.7 982.8

1185.5 1404.5

1638.9

1888.4 2152.3

7.2 33.6 81.8 152.4 245.0

358.4

491.8 644.2 814.6

1002.3 1206.7

1427.2

1663.2

1914.2 2179.5

8.9 37.4

87.9

160.7 255.4

370.9

506.2 660.4

832.6 1022.0

1228.1

1450.1 1687.7

1940.1 2206.8

10.8 41.5

94.2

169.2 266.0

383.6

520.8 676.8

850.8

1041.9

1249.6

1473.2

1712.2

1966.1 2234.2

01020

30

40

5060

7080

90

100

110 120

130

140

150

160 170

180 190

2234.2

2515.9

2810.7

3117.8

3436.8

2261.8 2544.8

2840.8

3149.2 3469.3

2289.5

2573.8

2871.1 3180.7

3501.9

2317.3

2603.0

2901.5

3212.3 3534.6

2345.3

2632.3

2932.1 3244.0

3567.5

2373.4

2661.7

2962.7

3275.9

3600.5

2401.6

2691.2 2993.5

3307.8

3633.5

2430.0 2720.9

3024.4

3339.9

3666.7

2458.5 2750.7

3055.4

3372.1 3700.0

2487.1

2780.6

3086.6 3404.4

3733.4

2515.9

2810.7

3117.8

3436.8

3766.9

150

160

170

180 190 200

210 220

230

240

3766.9 4107.5 4457.9

4817.6

5185.8

3800.5 4142.1 4493.5

4854.1

5223.1

3834.2 4176.8

4529.2 4890.6

5260.4

3868.0 4211.6

4564.9

4927.2

5297.9

3901.9

4246.5 4600.7

4963.9

5335.4

3935.9 4281.5 4636.7

5000.7

5372.9

3970.0

4316.6 4672.7

5037.6 5410.6

4004.2 4351.8

4708.8

5074.5

5448.3

4038.5

4387.1 4745.0

5111.5

5486.1

4072.9

4422.5

4781.2

5148.6

5524.0

4107.5 4457.9

4817.6

5185.8

5562.0

200

210

220

230

240

250

260 270

280

5562.0 5945.3 6335.3

6731.0

5600.0

5984.0 6374.6

5638.1 6022.8

6414.0

5676.2 6061.7 6453.45714.5 6100.6 6492.95752.8 6139.5

6532.5

5791.2 6178.6

6572.1

5829.6 6217.6 6611.7

5868.1 6256.8 6651.45906.7 6296.0

6691.2

5945.3 6335.3 6731.0

250

260

270

280

10

24
Table 17. Type T—reduced precision tables, E(T)

10 THERMOELECTRIC VOLTAGE IN ABSOLUTE /iV

0 10

20

30

40

5060

70

80

90

0.0 15.7 59.4

127.3 218.6

330.9 461.1

606.9 766.9

940.6

-0.1

19.0 65.1 135.4

228.9

343.2 475.0

622.2 783.6

958.7

0.2 22.5 71.0

143.7 239.5 355.6

489.1 637.7

800.5

976.9

0.9 26.3

77.2 152.3

250.2 368.2

503.3 653.4

817.6

995.3

2.1 30.3

83.6

161.1 261.2

381.0

517.6 669.2

834.7 1013.8

3.6 34.5

90.3 170.1 272.3

394.0

532.1 685.1

852.0 1032.4

5.4 39.0

97.2

179.4 283.7 407.1

546.8

701.2 869.5

1051.2

7.6 43.7

104,4

188.9 295.2 420.3

561.6

717.4

887.0

1070.1

10.0 48.7

111.7

198.6 306.9

433.8

576.5 733.8 904.7

1089.1

12.7 53.9

119.4

208.5 318.8 447.4

591.6

750.2 922.6

1108.3

15.7 59.4

127.3 218.6 330.9

461.1 606.9

766.9

940.6

1127.6

0

1020

30

to

50

6070

BO

90

100

110 120

130

140

1127.6

1327.8 1540.7

1766.3 2004.3

1147.0

1348»5 1562.7

1789.6 2C28.8

1166.6

1369.3 1584.9

1812.9 2053.4

1186.3 1390.3

1607.1 1836.4

2078.1

1206.1 1411.4

1629.5 1860.0

2103.0

1226.1 1432.7

1652.0

1883.8 2128.0

1246.1 1454.0

1674.6

1907.6 2153.1

1266.4

1475.5

1697.3 1931.6 2178.3

1286.7

1497.1 1720.2

1955.7 2203.6

1307.2 1518.9

1743.2 1980.0

2229.1

1327.8 1540.7

1766.3 2004.3

2254.7

100

110

120

130

140

150

160 170

180

190

2254.7

2517.2 2791.6

3077.6

3375.1

2280.4

2544.

2819.7

3106.9

3405.5

2306.2

2571.1

2847.9

3136.2 3435.9

2332.1

2598.2 2876.2

3165.7

3466.5

2358.2

2625.5 2904.6

3195.3

3497.2

2384.4

2652.9

2933.2

3225.0 3528.0

2410.7 2680.4

2961.8

3254.8

3558.9

2437.1

2708.0

2990.6 3284.7

3590,0

2463.7

2735.7

3019.5

3314.7

3621.1

2490.4

2763.6

3048.5 3344.8

3652.4

2517.2 2791.6

3077.6

3375.1 3683.7

150

160

170

180 190

200

210

220 230

240

3683.7

4003.3 4333.7

4674.5

5025.4

3715.2 4035.9

4367.3 4709.1

5061.0

3746.8 4068.6 4401.0

4743.9

5096.8

3778.5 4101.3

4434.9

4778.7

5132.6

3810.3

4134.2

4468.

4813.7

5168.6

3842.2 4167.2

4502.8

4848.7

5204.6

3874.2 4200.3 4536.9

4883.8

5240.7

3906.3 4233.5

4571.2 4919.1

5277,0

3938.6 4266.8

4605.5 4954,4

5313.3

3970.9

4300.2 4639.9

4989.9

5349.7

4003.3 4333.7

4674.5

5025.4

5386.3

200

210

220

230

240

250

260

270

280

5386.3 5756.9

6137.1

6526.2

5422.9

5794.5 6175.6

5459.6

5832.2 6214.2

5496.4

5870.0 6252.9

5533.4

5907.9

6291.6

5570.4

5945.9 6330.5

5607.5 5983.9 6369.45644.7

6022.1 6408.5

5682.0 6060.3

6447.6

5719.4 6098.7

6486.9

5756.9

6137.1

6526.2

250

260

270

280

10

25
1.2x10'

80 160 240 TEMPERATURE, K

320 80 160 240 TEMPERATURE, K

320

Figure 12. Thermoelectric voltage for primary thermocouple

types, E, K, and T. Figure 14. Derivative of the Seebeck coefficient for primary

thermocouple types E, K, and T.

80 160 240 TEMPERATURE, K

320

Figure 13. Seebeck coefficient for primary thermocouple types E, K, and T.

26
Table 18. Type E—reduced precision tables, T(E)

mV .00 .01 .02 .03 • 04

T CUDCO

-9.80

-9.70

-9.60

-9.50

12.58 25.01

33.46 40.37

10.70

24.02 32.70

39.72

8.47

23.00

31.93

39.07

5.51 21.94

31.14

38.41

1 LMKLKA

20.83 30.33

37.74 -9.40

-9.30

-9.20

-9.10 -9.00

46.3 8 51.81

56.81 61.48 65.90

45.81 51.29

56.32 61.03

65.47

45.23

50.76 55.84

60. 57 65.03

44.65

50.23 55.35

60.11 64.60

44.06 49.70

54.85

59.65 64.16

-8.90

-8.80

-8.70

-8.60 -8.50

70.10

74.12

77.99

81.72

85.33

69.69

73.73

77.61

81.35 84.98

69.27

73.33

77.22 80.98

84.62

68.86

72.93 76.84

80.61 84.26

68.44

72.53 76.46

80.24

83.90

• 05 .06 .07 .08 .09 .10 mV

ES IN K -9.80

19.66 18.44 17.14 15.74 14.24 12.58 -9.70

29.50 28.65 27.78 26.88 25.96 25.01 -9.60

37.05 36.36 35.66 34.94 34.21 33.46 -9.50 43.46 42.86 42.25 41.63 41.00 40.37 -9.40

49.16 48.61 48.06 47.51 46.95 46.38 -9.30

54.35 53.85 53.35 52.84 52.33 51.81 -9.20

59.18 58.71 58.24 57.77 57.29 56.81 -9.10

63.72 63.28 62.83 62.38 61.94 61.48 -9.00

68.02 67.60 67.18 66.75 66.33 65.90 -8.90

72.13 71.73 71.32 70.92 70.51 70.10 -8.80 76.07 75.68 75.30 74.90 74.51 74.12 -8.70

79.87 79.50 79.12 78.74 78.37 77.99 -8.60

83.54 83.18 82.82 82.45 82.09 81.72 -8.50

-8,40 88.84 88.49 88.15 87.80 87.45 87.10 86.75 86.40 86.04 85.69 85.33 -8.40

-8.30 92.25 91.91 91.58 91.24 90.90 90.56 90.22 89.87 89.53 89.19 88.84 -8.30

-8.20 95.58 95.25 94.92 94.59 94.26 93.92 93.59 93.26 92.92 92.59 92.25 -8.20

-8,10 98.82 98.50 98.18 97.86 97.53 97.21 96.88 96.56 96.23 95.90 95.58 -8.10

-8.00 101.99 101.68 101.37 101.05 100.73 100.42 100.10 99.78 99.46 99.14 98.82 -8.00

-7.90 105.10 104.79 104.48 104.18 103.87 103.56 103.24 102.93 102.62 102.31 101.99 -7.90

-7.80 108.14 107.84 107.54 107.24 106.93 106.63 106.33 106.02 105.71 105.41 105.10 -7.80

-7.70 111.13 110.83 110.54 110.24 109.94 109.64 109.35 109.05 108.75 108.45 108.14 -7.70

-7.60 114.06 113.77 113.48 113.19 112.90 112.60 112.31 112.02 111.72 111.43 111.13 -7.60

-7.50 116.94 116.66 116.37 116.08 115.80 115.51 115.22 114.93 114.64 114.35 114.06 -7.50

-7.40 119.78 119.50 119.21 118.93 118.65 118.37 118.08 117.80 117.51 117.23 116.94 -7.40

-7.30 122.57 122.29 122.01 121.74 121.46 121.18 120.90 120.62 120.34 120.06 119.78 -7.30

-7.20 125.32 125.04 124.77 124.50 124.22 123.95 123.67 123.40 123.12 122.84 122.57 -7.20

-7.10 128.02 127.75 127.49 127.22 126.95 126.67 126.40 126.13 125.86 125.59 125.32 -7.10

-7.00 130.69 130.43 130.16 129.90 129.63 129.36 129.10 128.83 128.56 128.29 128.02 -7.00

-6.90 133.33 133.07 132.81 132.54 132.28 132.02 131.75 131.49 131.22 130.96 130.69 -6.90

-6.80 135.93 135.67 135.41 135.15 134.89 134.63 134.37 134.11 133.85 133.59 133.33 -6.80

-6.70 138.50 138.24 137.99 137.73 137.48 137.22 136.96 136.70 136.45 136.19 135.93 -6.70

-6.60 141.04 140.79 140.53 140.28 140.03 139.77 139.52 139.26 139.01 138.76 138.50 -6.60

-6.50 143.55 143.30 143.05 142.80 142.55 142.30 142.05 141.79 141.54 141.29 141.04 -6.50

-6.40 146.03 145.78 145.53 145.29 145.04 144.79 144.54 144.29 144.05 143.80 143.55 -6.40

-6.30 148.48 148.24 147.99 147.75 147,50 147.26 147.01 146.77 146.52 146.27 146.03 -6.30

-6.20 150.91 150.67 150.43 150.18 149.94 149.70 149.46 149.21 148.97 148.73 148.48 -6.20

-6.10 153.31 153.07 152.83 152.59 152.35 152.11 151.87 151.63 151.39 151.15 150.91 -6.10

-6.00 155.69 155.45 155.22 154.98 154.74 154.51 154.27 154.03 153.79 153.55 153.31 -6.00

n>V ,00 ,01 .02 .03 .04 .05 .06 .07 .08 .09 .10 mV

27
Table 18. Type E—reduced precision tables, T(E) —Continued

mV .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .10 mV

TEMPERATURES IN K

-6.00 155.69 155.45 155.22 154.98 154.74 154.51 154.27 154.03 153.79 153.55 153.31 -6.00

-5.90 158.05 157.81 157.58 157.34 157.11 156.87 156.64 156.40 156.16 155.93 155.69 -5.90

-5.80 160.38 160.15 159.92 159.68 159.45 159.22 158.98 158.75 158.52 158.28 158.05 -5.80

-5.70 162.69 162.46 162.23 162.00 161.77 161.54 161.31 161.08 160.85 160.61 160.38 -5.70

-5.60 164.99 164.76 164.53 164.30 164.07 163.84 163.61 163.38 163.15 162.92 162.69 -5.60

-5.50 167.26 167.03 166.80 166.58 166.35 166.12 165.90 165.67 165.44 165.21 164.99 -5.50

-5.40 169.51 169.29 169.06 168.84 168.61 168.39 168.16 167.94 167.71 167.48 167.26 -5.40

-5.30 171.74 171.52 171.30 171.08 170.85 170.63 170.41 170.18 169.96 169.73 169.51 -5.30

-5.20 173.96 173.74 173.52 173.30 173.08 172.85 172.63 172.41 172.19 171.97 171.74 -5.20

-5.10 176.16 175.94 175.72 175.50 175.28 175.06 174.84 174.62 174.40 174.18 173.96 -5.10

-5.00 178.34 178.12 177.90 177.69 177.47 177.25 177.03 176.81 176.60 176.38 176.16 -5.00

-4.90 180.51 180.29 180.07 179.86 179.64 179.42 179.21 178.99 178.77 178.56 178.34 -4.90

-4.80 182.65 182.44 182.23 182.01 181.80 181.58 181.37 181.15 180.94 180-72 180.51 -4.80

-4.70 184.79 184.58 184.36 184.15 183.94 183.72 183.51 183.30 183.08 182.87 182.65 -4.70

-4.60 186.91 186.70 186.48 186.27 186.06 185.85 185.64 185.43 185.21 185.00 184.79 -4.60

-4.50 189.01 188.80 188.59 188.38 188.17 187.96 187.75 187.54 187.33 187.12 186.91 -4.50

-4.40 191.10 190.89 190.68 190.48 190.27 190.06 189.85 189.64 189.43 189.22 189.01 -4.40

-4.30 193.18 192.97 192.76 192.56 192.35 192.14 191.93 191.73 191.52 191.31 191.10 -4.30

-4.20 195.24 195.03 194.83 194.62 194.42 194.21 194.00 193.80 193.59 193.38 193.18 -4.20

-4.10 197.29 197.09 196.88 196.68 196.47 196.27 196.06 195.86 195.65 195.45 195.24 -4.10

-4.00 199.33 199.12 198.92 198.72 198.51 198.31 198.11 197.90 197.70 197.49 197.29 -4.00

-3.90 201.35 201.15 200.95 200.75 200.54 200.34 200.14 199.94 199.73 199.53 199.33 -3.90

-3.80 203.37 203.17 202.96 202.76 202.56 202.36 202.16 201.96 201.76 201.56 201.35 -3.80

-3.70 205.37 205.17 204.97 204.77 204.57 204.37 204.17 203.97 203.77 203.57 203.37 -3.70

-3.60 207.36 207.16 206.96 206.76 206.56 206.36 206.17 205.97 205.77 205.57 205.37 -3.60

-3,50 209.34 209.14 208.94 208.74 208.55 208.35 208.15 207.95 207.75 207.56 207.36 -3.50

-3 .40 211.30 211.11 210.91 210.72 210.52 210.32 210.13 209.93 209.73 209.53 209.34 -3.40

-3 .30 213.26 213.07 212.87 212.68 212.48 212.28 212.09 211.89 211.70 211.50 211.30 -3.30

-3 .20 215.21 215.02 214.82 214.63 214.43 214.24 214.04 213.85 213.65 213.46 213.26 -3.20

-3 . 10 217.15 216.95 216.76 216.57 216.37 216.18 215.99 215.79 215.60 215.40 215.21 -3.10

-3 .00 219.07 218.88 218.69 218.50 218.30 218.11 217.92 217.73 217. 53 217.34 217. 15 -3.00

-2 .90 220.99 220.80 220.61 220.42 220.23 220.03 219.84 219.65 219.46 219.27 219.07 -2.90

-2 .80 222.90 222.71 222. 52 222.33 222.14 221.95 221.76 221.56 221.37 221.18 220.99 -2.80

-2 .70 224.80 224.61 224.42 224.23 224.04 223.85 223.66 223.47 223.28 223.09 222.90 -2.70

-2 .60 226.69 226.50 226.31 226.12 225.93 225.74 225.55 225.37 225. 18 224.99 224.80 -2.60

-2 .50 228.57 228.38 228. 19 228.00 227.82 227.63 227.44 227.25 227.06 226.88 226.69 -2.50

-2.40 230.44 230.25 230.07 229.88 229.69 229.51 229.32 229.13 228.94 228.76 228.57 -2.40

-2.30 232.30 232.12 231.93 231.75 231.56 231.37 231.19 231.00 230.81 230.63 230.44 -2.30

-2.20 234.16 233.97 233.79 233.60 233.42 233.23 233.05 232.86 232.68 232.49 232.30 -2.20

-2.10 236.01 235.82 235.64 235.45 235.27 235.08 234.90 234.71 234.53 234.34 234.16 -2.10

-2.00 237.84 237.66 237.48 237.29 237.11 236.93 236.74 236.56 236.37 236.19 236.01 -2.00

-1.90 239.68 239.49 239.31 239.13 238.94 238.76 238.58 238.40 238.21 238.03 237.84 -1.90

-1.80 241.50 241.32 241.14 240.95 240.77 240.59 240.41 240.22 240.04 239.86 239.68 -1.80

-1.70 243.32 243.13 242.95 242.77 242.59 242.41 242.23 242.05 241.86 241.68 241.50 -1.70

-1.60 245.12 244.94 244.76 244.58 244.40 244.22 244.04 243.86 243.68 243.50 243.32 -1.60

-1.50 246.93 246.75 246.57 246.39 246.21 246.03 245.85 245.67 245.48 245.30 245.12 -1.50

-1.40 248.72 248.54 248.36 248.18 248.00 247.82 247.64 247.46 247.28 247.10 246.93 -1.40

-1.30 250.51 250.33 250.15 249.97 249.79 249.61 249.43 249.26 249.08 248.90 248.72 -1.30

-1.20 252.29 252.11 251.93 251.75 251.58 251.40 251.22 251.04 250.86 250.68 250.51 -1.20

-1.10 254.06 253.88 253.71 253.53 253.35 253.17 253.00 252.82 252.64 252.46 252.29 -1.10

-1.00 255.83 255.65 255.47 255.30 255.12 254.94 254.77 254.59 254.41 254.24 254.06 -1.00 -0.90 257.59 257.41 257.23 257.06 256.88 256.71 256.53 256.36 256.18 256.00 255.83 -0.90 -0.80 259.34 259.16 258.99 258.81 258.64 258.46 258.29 258.11 257.94 257.76 257.59 -0.80

-0.70 261.09 260.91 260.74 260.56 260.39 260.21 260.04 259.86 259.69 259.51 259.34 -0.70 -0.60 262.83 262.65 262.48 262.31 262.13 261.96 261.78 261.61 261.44 261.26 261.09 -0.60

-0. 50 264.56 264.39 264.22 264.04 263.87 263.70 263.52 263.35 263. 18 263.00 262.83 -0.50 -0.40 266.29 266. 12 265.95 265.77 265.60 265.43 265.26 265.08 264.91 264. 74 264. 56 -0.40 -0.30 268.01 267.84 267.67 267.50 267.33 267.15 266.98 266.81 266.64 266.46 266.29 -0.30 -0.20 269.73 269.56 269. 39 269.22 269.05 268.87 268.70 268.53 268.36 268. 19 268.01 -0.20

-0.10 271.44 271.27 271.10 270.93 270.76 270.59 270.42 270.25 270.07 269.90 269.73 -0.10

0.00 273,15 272.98 272.81 272.64 272.47 272.30 272.13 271.96 271.79 271.61 271.44 0.00

mV .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .10 mV

28
Table 19. Type K—reduced precision tables, T(E)

mV .00 .01 .02

— 6 23.90 21.81 19.48

TM6 38.83 37.62 36.36

-6 .20 49.37 48.42 47.45

-6 10 58.07 57.26 56.44

-6 00 65.69 64.97 64.24

_5 90 72.58 71.92 71.25

_5 80 78.93 78.32 77.70

-5 70 84.87 84.29 83.71

-5 60 90.47 89.92 89.37

_5 50 95.79 95.27 94.75

— 5 40 100.87 100.37 99.87

_5 J u 105.75 105.27 104.79

-5 .20 110.45 109.99 109.53

-5 10 115.00 114.55 114. 10 _5 i00 119.40 118.97 118.53

—4 90 123.68 123.25 122.83

—4 1 80 127.84 127.43 127.02

-4 .70 131.90 131.50 131.10

-4 .60 135.86 135.47 135.08

—4 i 50 139.74 139.36 138.97

—4 .40 143.54 143. 16 142.78

_^ 3 0 147.26 146.89 146.52

-4 20 150.91 150.55 150. 19 -4 .10 154.50 154. 14 153.79

00 158.03 157.68 157.33

_3 90 161.50 161.16 160.81

_3 80 164.92 164.58 164.24

-3 70 168.29 167.95 167.62

-3 60 171.61 171.28 170.95

^3 50 174.89 174. 56 174.24

"3 178.13 177.80 177.48

_3 30 181.32 181.00 180.69

-3 20 184.48 184.17 183.85

-3 10 187.61 187.29 186.98

_3 00 190.69 190.39 190.08

_2 90 193.75 193.45 193. 14

_2 80 196.78 196.46 196. 18 -2 70 199.78 199.48 199. 18 -2 60 202.75 202.45 202.15

_ 2 50 205.69 205.39 205.10

_2 40 208.60 208.31 208.02

_2 30 211.50 211.21 210.92

-2 20 214.37 214.08 213.80

-2 10 217.21 216.93 216.65

__2 i00 220.04 219.76 219.48

_ ^ 90 222.84 222.57 222.29

_1 80 225.63 225.35 225.07

-1 .70 228.40 228.12 227.84

-1 60 231.14 230.87 230.60

_1 i 50 233.88 233.60 233.33

_1 1 40 236.59 236.32 236.05

_1 30 239.29 239.02 238.75

-1 .20 241.97 241.70 241.44

-1 .10 244.64 244.37 244. 11 _1 1 00 247.29 247.03 246.76

—0 » 90 249.93 249.67 249.40

—0 . 80 252.56 252.30 252.03

-0 .70 255.17 254.91 254.65

—0 257.77 257.51 257.25

-0 .50 260.36 260.10 259.85

-0 .40 262.94 262.68 262.43

-0 .30 265.51 265.25 265.00

-0 .20 268.07 267.81 267. 55 -0 .10 270.61 270.36 270. 10

0 .00 273.15 272.90 272.64

m V .00 .01 .02

.03 .04 .05 .06 .07 .08 .09 .10 mV

TEMPERATURES IN K 16.80 13.57 9.23 -6.40 35.06 33.70 32.28 30.80 29.23 27.58 25.81 23.90 -6.30

46.46 45.45 44.42 43.36 42.27 41.16 40.01 38.83 -6.20

55.60 54.75 53.89 53.02 52.13 51.23 50.31 49.37 -6.10 63.49 62.75 61.99 61.23 60.45 59.67 58.88 58.07 -6.00

70.58 69.90 69.21 68.52 67.83 67.12 66.41 65.69 -5.90 77.08 76.45 75.82 75.18 74.54 73.89 73.24 72.58 -5.80 83.13 82.54 81.95 81.35 80.75 80.15 79.55 78.93 -5.70

88.82 88.27 87.71 87.15 86.58 86.01 85.44 84.87 -5.60

94.22 93.69 93.16 92.63 92.09 91.55 91.01 90.47 -5.50

99.37 98. e7 98.36 97.85 97.34 96.82 96.31 95.79 -5.40

104.31 103.82 103.34 102.85 102.36 101.86 101.37 100.87 -5.30

109.06 108.59 108.12 107.65 107.18 106.71 106.23 105.75 -3.20

113.65 113.20 112.74 112.29 111.83 111.37 110.91 110.45 -5.10

118.09 117.65 117.21 116.77 116.33 115.89 115.44 115.00 -5.00

122.41 121.98 121.55 121.13 120.70 120.27 119.83 119.40 -4.90

126.60 126.19 125.77 125.36 124.94 124.52 124.10 123.68 -4.80

130.69 130.29 129.88 129.48 129.07 128.66 128.25 127.84 -4.70

134.68 134.29 133.89 133.50 133.10 132.70 132.30 131.90 -4.60

138.59 138.20 137.81 137.42 137.04 136.65 136.26 135.86 -4.50

142.41 142.03 141.65 141.27 140.89 140.51 140.12 139.74 -4.40

145.15 145.78 145.41 145.04 144.66 144.29 143.91 143.54 -4.30

149.82 149.46 149.09 148.73 148.36 148.00 147.63 147.26 -4.20

153.43 153.07 152.71 152.36 152.00 151.64 151.27 150.91 -4.10

156.98 156.62 156.27 155.92 155.57 155.21 154.86 154.50 -4.00

160.47 160.12 159.77 159.42 159.08 158.73 158.38 158.03 -3.90

163.90 163.56 163.22 162.87 162.53 162.19 161.85 161.50 -3.80

167.28 166.95 166.61 166.27 165.94 165.60 165.26 164.92 -3.70

170.62 170.29 169.96 169.62 169.29 168.96 168.62 168.29 -3.60

173.91 173.58 173.26 172.93 172.60 172.27 171.94 171.61 -3.50

177.16 176.84 176.51 176.19 175.86 175.54 175.22 174.89 -3.40

180.37 180.05 179.73 179.41 179.09 178.77 178.45 178.13 -3.30 183.54 183.22 182.91 182.59 182.27 181.96 181.64 181.32 -3.20

186.67 186.36 186.05 185.74 185.42 185.11 184.80 184.48 -3.10

189.77 189.46 139.15 188.84 188.54 188.23 187.92 187.61 -3.00

192.84 192.53 192.23 191.92 191.62 191.31 191.00 190.69 -2.90

195.87 195.57 195.27 194.97 194.66 194.36 194.06 193.75 -2.80

198.88 198.58 198.28 197.98 197.68 197.38 197.08 196.78 -2.70 201.86 201.56 201.26 200.97 200.67 200.37 200.07 199.78 -2.60 204.81 204.51 204.22 203.93 203.63 203.34 203.04 202.75 -2.50

207.73 207.44 207.15 206.86 206.57 206.27 205.98 205.69 -2.40

210.63 210.34 210.05 209.76 209.48 209.19 208.90 208.60 -2.30

213.51 213.22 212.94 212.65 212.36 212.0"? 211.79 211.50 -2.20 216.36 216.08 215.79 215.51 215.22 214.94 214.65 214.37 -2.10 219.19 218.91 218.63 218.35 218.06 217.78 217.50 217.21 -2.00

222.01 221.73 221.44 221.16 220.88 220.60 220.32 220.04 -1.90 224.80 224.52 224.24 223.96 223.68 223.40 223.12 222.84 -1.80 227.57 227.29 227.02 226.74 226.46 226.18 225.91 225.63 -1.70 230.32 230.05 229.77 229.50 229.22 228.95 228.67 228.40 -1.60 233.06 232.79 232.51 232.24 231.97 231.69 231.42 231.14 -1.50 235.78 235.51 235.23 234.96 234.69 234.42 234.15 233.88 -1.40

238.48 238.21 237.94 237.67 237.40 237.13 236.86 236.59 -1.30 241.17 240.90 240.63 240.36 240.09 239.83 239.56 239.29 -1.20 243.84 243.57 243.31 243.04 242.77 242.51 242.24 241.97 -l.lo 246.50 246.23 245.97 245.70 245.44 245.17 244.90 244.64 -1.00

249.14 248.88 248.61 248.35 248.08 247.82 247.56 247.29 -0.90 251.77 251.51 251.25 250.98 250.72 250.46 250.19 249.93 -0.80

254.39 254.13 253.87 253.60 253.34 253.08 252.82 252.56 -0.70 256.99 256.73 256.47 256.21 255.95 255.69 255.43 255.17 -0.60 259.59 259.33 259.07 258.81 258.55 258.29 258.03 257.77 -0.50

262.17 261.91 261.65 261.39 261.14 260.88 260.62 260.36 -0.40 264.74 264.48 264.23 263.97 263.71 263.45 263.20 262.94 -0.30

267.30 267.04 266.79 266.53 266.28 266.02 265.76 265.51 -0.20

269.85 269.59 269.34 269.09 268.83 268.58 268.32 268.07 -0.10

272.39 272.14 271.88 271.63 271.37 271.12 270.87 270.61 0.00

.03 .04 .05 .06 .07 .08 .09 .10 mV

29
Table 20. Type T—reduced precision tables, T(E)

mV .00 .01 .02 .03 .OA .05 .06 .07 .08 .09 .10 mV

TEMPERATURES IN K 6.20 19.87 17.99 15.93 13.61 10.90 7.46 -6.20

6.10 33.73 32.58 31.40 30.18 28.91 27.59 26.21 24.76 23.23 21.61 19.87 -6.10

6.00 43.77 42.85 41.92 40.97 40.01 39.02 38.01 36.98 35.92 34.84 33.73 -6.00

5.90 52.24 51.44 50.63 49.82 48.99 48.15 47.30 46.43 45.56 44.67 43.77 -5.90

5.80 59.82 59.10 58.36 57.62 56.88 56.12 55.36 54.59 53.82 53.04 52.24 -5.80

5.70 66.80 66.13 65.45 64.76 64.07 63.38 62.68 61.97 61.26 60.55 59.82 -5.70

5.60 73.34 72.70 72.06 71.42 70.77 70.12 69.46 68.81 68.14 67.47 66.80 -5.60

5.50 79.51 78.91 78.30 77.69 77.08 76.46 75.84 75.22 74.60 73.97 73.34 -5.50

5.40 85.38 84.81 84.23 83.65 83.07 82.48 81.89 81.30 80.71 80.11 79.51 -5.40

5.30 91.00 90.45 89.90 89.34 88.78 88.22 87.66 87.09 86.53 85.95 85.38 -5.30

5.20 96.40 95.87 95.33 94.80 94.26 93.72 93.18 92.64 92.10 91.55 91.00 -5.20

5.10 101.60 101.08 100.57 100.05 99.54 99.02 98.50 97.98 97.45 96.92 96.40 -5.10

5.00 106.62 106.13 105.63 105,13 104.63 104.13 103.63 103.12 102.61 102.11 101.60 -5.00

4.90 111.49 111.01 110.53 110.04 109.56 109.07 108.59 108.10 107.61 107.11 106.62 -4.90

4.80 116.22 115.75 115.28 114.81 114.34 113.87 113.40 112.92 112.45 111.97 111.49 -4.80

4.70 120.82 120.36 119.91 119.45 118.99 118.53 118.07 117.61 117.15 116.68 116.22 -4.70

4.60 125.30 124.85 124.41 123.96 123.52 123.07 122.62 122.17 121.72 121.27 120.82 -4.60

4.50 129.67 129.24 128.80 128.37 127.93 127.50 127.06 126.62 126.18 125.74 125.30 -4.50

4.40 133.94 133.52 133.10 132.67 132.25 131.82 131.39 130.96 130.53 130.10 129.67 -4.40

4.30 138.12 137.71 137.29 136.88 136.46 136.04 135.62 .135. 21 134.79 134.36 133.94 -4.30

4.20 142.21 141.81 141.40 140.99 140.59 140.18 139.77 139.36 138.95 138.53 138.12 -4.20

4.10 146.22 145.83 145.43 145.03 144.63 144.23 143.83 143.42 143.02 142.62 142.21 -4.10

4.00 150.16 149.77 149.38 148.96 148.59 148.20 147.81 147.41 147.02 146.62 146.22 -4.00

3.90 154.02 153.63 153.25 152.87 152.48 152.10 151.71 151.32 150.93 150.55 150.16 -3.90

3.80 157.81 157.43 157.06 156.68 156.30 155.92 155.54 155.16 154.78 154.40 154.02 -3.80

3.70 161.54 161.17 160.80 160.43 160.06 159.68 159.31 158.94 158.56 158.19 157.81 -3.70

3.60 165.21 164.85 164.48 164.12 163.75 163.38 163.02 162.65 162.28 161.91 161.54 -3.60

3.50 168.82 168.46 168.11 167.75 167.39 167.02 166.66 166.30 165.94 165.57 165.21 -3.50

3.40 172.38 172.03 171.67 171.32 170.97 170.61 170.25 169.90 169.54 169.18 168.82 -3.40

3.30 175.89 175.54 175.19 174.84 174.49 174.14 173.79 173.44 173.09 172.74 172.38 -3.30

3.20 179.35 179.01 178.66 178.32 177.97 177.63 177.28 176.93 176.59 176.24 175.89 -3.20

3.10 182.76 182.42 182.08 181.74 181.40 181.06 180.72 180.38 180.04 179.69 179.35 -3.10

3.00 186.13 185.80 185.46 185.13 184.79 184.45 184.12 183.78 183.44 183.10 182.76 -3.00

2.90 189.46 189.13 188.80 188.46 188.13 187.80 187.47 187.13 186.80 186.47 186.13 -2.9o

2.80 192.74 192.42 192.09 191.76 191.43 191.11 190.78 190.45 190.12 189.79 189.46 -2.80

2.70 195.99 195.67 195.34 195.02 194.70 194.37 194.05 193.72 193.40 193.07 192.74 -2.70

2.60 199.20 198.88 198.56 198.24 197.92 197.60 197.28 196.96 196.64 196.31 195.99 -2.60

2.50 202.38 202.06 201.74 201.43 201.11 200.79 200.48 200.16 199.84 199.52 199.20 -2.50

2.40 205.52 205.20 204.89 204.58 204.26 203.95 203.64 203.32 203.01 202.69 202.38 -2.40

2.30 208.62 208.31 208.00 207.69 207.38 207.07 206.76 206.45 206.14 205.83 205.52 -2.30

2.20 211.70 211.39 211.09 210.78 210.47 210.16 209.86 209.55 209.24 208.93 208.62 -2.20

2.10 214.74 214.44 214.14 213.83 213.53 213.22 212.92 212.61 212.31 212.00 211.70 -2.10

2.00 217.76 217.46 217.16 216.86 216.55 216.25 215.95 215.65 215.35 215.04 214.74 -2.00

1.90 220.74 220.45 220.15 219.85 219.55 219.25 218.95 218.66 218.36 218.06 217.76 -1.90

1.80 223.70 223.41 223.11 222.82 222.52 222.23 221.93 221.63 221.34 221.04 220.74 -1.80

1.70 226.64 226.34 226.05 225.76 225.47 225.17 224.88 224.59 224.29 224.00 223.70 -1.70

1.60 229.54 229.25 228.96 228.67 228.38 228.09 227.80 227. .51 227.22 226.93 226.64 -1.60

1.50 232.43 232.14 231.85 231.56 231.28 230.99 230.70 230.41 230.12 229.83 229.54 -1.50

1.40 235.28 235.00 234.71 234.43 234.14 233.86 233.57 233.29 233.00 232.71 232.43 -1.40

1.30 238.12 237.84 237.55 237.27 236.99 236.71 236.42 236.14 235.85 235.57 235.28 -1.30

1.20 240.93 240.65 240.37 240.09 239.81 239.53 239.25 238.97 238.68 238.40 238.12 -1.20

1.10 243.73 243.45 243.17 242.89 242.61 242.33 242.05 241.77 241.49 241.21 240.93 -1.10

1.00 246.50 246.22 245.94 245.67 245.39 245.11 244.84 244.56 244.28 244.00 243.73 -1.00 247.05 246.77 246.50 -0-90 249.79 249.52 249.24 -0.80 252.52 252.25 251.97 -0.70

255". 22 254.95 254.68 -0.60

257.91 257.64 257.37 -0.50 260.58 260.31 260.05 -0.40 263.23 262.96 262.70 -0.30 265.86 265.60 265.34 -0.20

268.48 268.22 267.96 -0.10 271.08 270.82 270.56 0.00

mV .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .10 mV

0.90 249.24 248.97 248.70 248.42 248.15 247.87 247.60 247. 32 0.80 251.97 251.70 251.43 251.16 250.88 250.61 250.34 250. 07 0.70 254.68 254.41 254. 14 253.87 253.60 253.33 253.06 252. 79 0.60 257.37 257.11 256.84 256.57 256.30 256.03 255.76 255. 49 0.50 260.05 259.78 259.51 259.25 258.98 258.71 258.45 258. 18 0.40 262.70 262.44 262. 17 261.91 261 .64 261.38 261.11 260. 84 0.30 265.34 265.07 264.81 264.55 264.28 264.02 263.76 263. 49 0.20 267.96 267.70 267.43 267.17 266.91 266.65 266.39 266. 12 0.10 270.56 270.30 270.04 269.78 269.52 269.26 269.00 268. 74 0.00 273.15 272.89 272.63 272.37 272.12 271.86 271.60 271. 34

30
Table 21. Type KP (or EP) versus Pt

thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, <JS(T)

T E

K /iV

0 0.79

1 1.66

2 2.52

3 3.38

4 4.22

5 5.07

6 5.92

7 6.77

8 7.63

9 8.50

10 9.38

11 10. -6

12 11.15

13 12.06

14 12.97

15 13.89

16 14.83

17 15.77

18 16.73

19 17.70

20 18.69

21 19.68

22 20.70

23 21.72

24 22.77

25 23.83

26 24.91

27 26.01

28 27.13

29 28.28

30 29.45

31 30.66

32 31.89

33 33.16

34 34.46

35 35. do 36 37.18

37 38.61

38 40.08

39 41.60

40 43.17

41 44.80

42 46.49

43 48.24

44 50.05

45 51.94

46 53.89

47 55.92

48 58.03

49 60.21

50 62.48

51 64.84

52 67.29

53 69.83

54 72.47

55 75.20

56 78.04

57 80.98

58 84.03

59 87.19

60 90.46

S dS/dT

/iV/K nV/K«

0.882 -18 »8 0.866 -12 >9 0.855 -8 > 0 0.850 -3 ,9 0.847 -0 .6 0.848 2 ,1 0.851 4 .2 0*856 5 8 0.863 7 ,1 0.871 8 ,1 0.879 8 9 0.888 9 5 0.898 9 9 0.908 10 >3 0.919 10 ,7 0.929 11 0 0.941 11 ,4 0.952 1

8 0.964 12 ,3 0.977 12 ,9 0.990 13 6 1.004 14,,4

1 .019 15 4 1.035 16 5 1.052 17 8

1.071 19. 2 1.091 20, 8 1.112 22

C

-> 1.136 24,.3 1.161 26 3 1.188 28. 4 1.218 30 ,7 1.250 33 > 1 1.284 35 • 6 1.321 38 ,2 1.360 40 9 1.403 43 7

1 . 448 46 6 1.496 49. 5 1.547 52 5 1.601 55. 6 1.658 58. 7 1.718 61 g 1.782 65 0 1.848 68 2

1.918 71. 3 1.991 74, 5 2.067 77

7 2.146 80, 8 2.229 83, 9 2.314 87, 0 2.403 90, 1 2.494 93, 1 2.589 96, 0 2.686 98, 9 2.786 101, 7 2.890 104, 5 2.995 107, 1 3.104 109. 7 3.215 112. 3 3.328 114. 7

T E

K MV

60 90.46

61 93.85

62 97.35

63 100.98

64 104.72

65 108.59

66 112.58

67 116.70

68 120.95

69 125.33

70 129.84

71 134.49

72 139.27

73 144.19

74 149.25

75 154.44

76 159.78

77 165.26

78 170.88

79 176.64

80 182.54

81 188.59

82 194.79

83 201.13

84 207.61

85 214.24

86 221.02

87 227.94

88 235.01

89 242.23

90 249.59

91 257.10

92 264.76

93 272.56

94 280.51

95 288.61

96 296.85

97 305.24

98 313.78

99 322.46

100 331.28

101 340.25

102 349.36

103 358.62

104 368.02

105 377.56

106 387.25

107 397.07

108 407.04

109 417.15

110 427.40

111 437.79

112 448.32

113 458.99

114 469.80

115 480.74

116 491.82

117 503.04

118 514.40

119 525.89

120 537.51

S d3/dT

/iV/K nV/K*

3.328 114.7 3.444 117.0 3.562 119.3 3.683 121.5 3.805 123.5 3.930 125.5 4.056 127.4

4.185 129.2 4.315 130.9 4.446 132.5 4.580 134.0 4.714 135.4 4.850 136.7 4.988 138.0

5.126 139.1 5.266 140.1 5.406 141.1 5.548 142.0 5.690 142.8 5.834 143.5 5.977 144.1 6.122 144.7 6.267 145.2 6.412 145.6 6.558 145.9 6.704 146.2 6.850 146.4 6.997 146.6 7.143 146.7 7.290 146.8 7.437 146.8 7.584 146.7

7.730 146.6 7.877 146.5 8.023 146.3 8.170 146.1 8.316 145.9

8.461 145.6 8.607 145.3 8.752 144.9 8.897 144.6

9.041 144.2 9.185 143.8 9.328 143.3 9.472 142.9 9.614 142.4 9.756 141.9 9.898 141.5 10,039 140.9 10.180 140.4

10.320 139.9 10.460 139.4 10.599 138.8 10.738 138.3 10.876 137.8 11.013 137.2 11.150 136.6 11.286 136.1 11.422 135.5 11.557 135.0

11.692 134.4

T

K

E

/*V 120

121 122 123 124

537.51 549.27 561.16

573.19

585.35

125

126

127

128 129

597.64

610.06

622.61 635.30

648.11

130

131 132

133 134

661.05

674.13

687.33

700.65

714.11

135

136 137

138

139

727.69 741.39

755.23

769.18

783.26

140

141

142 143 144

797.47

811.79 826.24

840.81 855.50

145

146 147

148 149

870.32

885.25 900.30

915.47

930.75

150

151 152

153 154

946.16

961.68

977.32 993.07

1008.94

155

156 157

158 159

1024.92

1041.02

1057.23

1073.55 1089.98

160

161

162

163 164

1106.52 1123.18

1139.94

1156.81 1173.80

165

166 167

168

169

1190.88

1208.08

1225.38 1242.79

1260.30

170

171 172

173 174

1277.92 1295.65 1313.47

1331.40

1349.43

175 176

177

178

179

1367.56

1385.79

1404.13 1422.56

1441.09

180 1459.72

S dS/dT

/iV/K nV/K*

11.692 134.4 11.826 133.8 11.960 133.3 12.093 132.7 12.225 132.1 12.357 131.5

12.488 131.0 12.619 130.4 12.749 129.8 12.878 129.3 13.007 128.7 13.136 128.1 13.264 127.5 13.391 126.9 13.518 126.4 13.644 125.8 13.769 125.2 13.894 124.6 14.018 124.0 14.142 123.4

14.265 122.8 14.388 122.2 14.510 121.6

14.631 121.0 14.752 120.4

14.872 119.8

14.991 119.2 15.110 118.6 15.229 118.0

15.346 117.4

15.463 116.7

15.580 116.1 15.696 115.5

15.811 114.8 15.925 114.2 16.039 113.6 16.152 112.9

16.265 112.3 16.377 111.6 16.488 111.0 16.599 110.4 16.709 109.7 16.818 109.1 16.927 108.4

17.035 107.8 17.143 107.1 17.249 106.5 17.356 105.9 17.461 105.2 17.566 104.6 17.670 104.0 17.774 103.3 17.877 102.7 17.979 102.1 18.081 101.5 18.182 100.9 18.283 100.3 18.383 99.7 18.482 99.1 18.581 98.5 18.679 98.0

31
Table 21. Type KP (or EP) versus Pt—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) —Continued

T1 5 dS/dT

K /IV tiM fj.V/K nV/K 2

180 1459.72 18.679 98.0

181 1478.45 18.777 97.4

182 1497.27 18.874 96.8

183 1516.20 18.971 96.3

184 1535.22 19.067 95.8

j s dS/dT

K /XV /J.V/K nV/K 2

240 2739.43 23.698 69.2

241 2763.16 23.766 68.7

242 2786.96 23.835 68.3

243 2810.83 23.903 67.9

244 2834.76 23.971 67.5

T E S dS/dT

K fiV /iV/K nV/K 2

185 1554.33

186 1573.54

187 1592.84

188 1612.2.

189 1631.74

190 1651.32

191 1671.00

192 1690.77

193 1710.63

194 1730.58

19.162 95.2 19.257 94.7

19.352 94.2 19.446 93.7

19.539 93.2 19.632 92.7 19.724 92.2 19.816 91.7

19.908 91.3 19.999 90.8

245 2858.77

246 2882.84

247 2906.98

248 2931.18

249 2955.46

250 2979.79

251 3004.20

252 3028.67

253 3053.20

254 3077.80

24.038 67.2 24.105 66.8 24.172 66.5 24.238 66.3 24.304 66.0

24.370 65.8 24.436 65.6 24.502 65.5 24.567 65.3 24.632 65.2

195 1750.63

196 1770.76

197 1790.99

198 1811.30

199 1831.70

20.089 90.4 20.180 89.9 20.269 89.5 20.359 89.0 20.447 88.6255 3102.46

256 3127.19

257 3151.99

258 3176,85

259 3201.77

24.697 65.1 24.762 65.0 24.827 65.0 24.892 64.9 24.957 64.8

200 1852.20

201 1872.78

202 1893.44

203 1914.20

204 1935.04

205 1955.97

206 1976.98

207 1998.08

208 2019.27

209 2040.54

20.536 88.2 20.624 87.7

20.711 87.3 20.798 86.9 20.885 86.5 20.971 86.0 21.057 85.6 21.142 85.2 21.227 84.8 21.312 84.4

260 3226.76

261 3251.82

262 3276.94

263 3302.12

264 3327.37

265 3352.68

266 3378.06

267 3403.49

268 3429.00

269 3454.56

25.022 64.8 25.087 64.7

25.151 64.5 25.216 64.3 25.280 64.1 25.344 63.7 25.407 63.3 25.470 62.7 25.533 62.0 25.594 61.1

210 2061.89

211 2083.33

212 2104.85

213 2126.45

214 2148.14

215 2169.91

216 2191.76

217 2213.69

218 2235.71

219 2257. dC

21.396 83.9 21.480 83.5 21.563 83.1 21.646 82.6 21.728 82.2 21.810 81.7 21.892 81.3 21.973 80.8 22.053 80.3 22.133 79.8270 3480.18

271 3505.87

272 3531.61

273 3557.41

274 3583.27

275 3609.17

276 3635.13

277 3661.13

278 3687.18

279 3713.26

25.655 59.9 25.714 58.5 25.772 56.8 25.828 54.7 25.881 52.3 25.932 49.4 25.980 46.0 26.024 42.0 26.063 37.3 26.098 32.0

220 2279.97

221 2302.23

222 2324.56

223 2346.97

224 2369.46

225 2392.02

226 2414.66

227 2437.38

228 2460.18

229 2483.05

22.213 79.4 280 3739.37 26.127 25.8 22.292 78.9

22.371 78.4 22.449 77.9 22.527 77.4 22.604 76.8 22.680 76.3 22.756 75.8 22.832 75.3 22.907 74.7

230 2505.99

231 2529.01

232 2552.10

233 2575.27

234 2598.50

235 2621.81

236 2645.19

237 2668.65

238 2692.17

239 2715.76

22.981 74.2 23.055 73.7

23.129 73.2 23.202 72.6 23.274 72.1 23.346 71.6 23.417 71.1 23.488 70.6 23.558 70.1 23.628 69.6

240 2739.43 23.698 69.2

32
Table 22. Type Pt versus TN (or EN) —thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative oj the Seebeck coefficient, dS(T)

T E K

0 0.00

1 -1.02

2 -1.39

3 -1.17

4 -0.39

5 0.92

6 2.73

7 5.01

8 7.74

9 10.91

10 14.50

11 18.49

12 24.88

13 27.66

14 32.81

15 38.34

16 44.24

17 50.51

18 57.13

19 64.11

20 71.44

21 79.13

22 87.17

23 95.55

24 104.28

25 113.35

26 122.76

27 132.50

28 142.58

29 152.99

30 163.73

31 174.79

32 186.18

33 197.88

34 209.89

35 222.21

36 234.83

37 247.75

38 260.96

39 274.47

40 288.25

41 302.31

42 316.65

43 331424

44 346.10

45 361.22

46 376.58

47 392.18

48 408.02

49 424.09

50 440.38

51 456.90

52 473.62

53 490.56

54 507.69

55 525.02

56 542.54

57 560.24

58 578.13

59 596.19

60 614.42

S ds/dT

liV/K nv/K 2

-1.355 693.1 -0.688 642.1 -0.069 597.8 0.509 559.3

1.051 526.0

1.563 497.4

2.047 472.9

2.510 452.0

2.953 434.3

3.379 419.3

3.792 406.6

4.193 396.0 4.585 387.2 4.968 379.8

5.345 373.6

5.715 368.4

6.082 364.1 6.444 360.4

6.803 357.2

7.158 354.3

7.511 351.7

7.862 349.3 8.210 346.9 8.556 344.5 8.899 342.1 9.240 339.6 9.578 336.9

9.913 334.0

10.246 330.9 10.575 327.6

10.901 324.1

11.223 320.4

11.542 316.4

11.856 312.2 12.166 307.8

12.472 303.1 12.772 298.3

13.068 293.2 13.359 288.0

13.644 282.6

13.924 277.1 14.198 271.5

14.467 265.8

14.730 260.0 14.987 254.1

15.238 248.2

15.483 242.3

15.723 236.3 15.956 230.4

16.183 224.4

16.405 218.6

16.620 212.7

16.830 207.0

17.034 201.3 17.233 195.7 17.426 190.2 17.613 184.8 17.795 179.6 17.972 174.4 18.144 169.4

18.311 164.6

T E K fLV 60 614.42

61 632.81

62 651.36

63 670.07

64 688.93

65 707.93

66 727.08

67 746.37

68 765.79

69 785.34

70 805.02

71 824.82

72 844.75

73 864.79

74 884.95

75 905.22

76 925.60

77 946.09

78 966.68

79 987.38

80 1008.18

81 1029.07

82 1050.06

83 1071.15

84 1092.33

85 1113.60

86 1134.96

87 1156.41

88 1177.94

89 1199.57

90 1221.27

91 1243.06

92 1264.94

93 1286.89

94 1308.92

95 1331.04

96 1353.23

97 1375.50

98 1397.85

99 1420.27

100 1442.77

101 1465.34

102 1487.99

103 1510.71

104 1533.51

105 1556.37

106 1579.31

107 1602.32

108 1625.40

109 1648.55

110 1671.76

111 1695.05

112 1718.41

113 1741.83

114 1765.32

115 1788.88

116 1812.51

117 1836.20

118 1859.95

119 1883.78

120 1907.67

s ds/dT

yuV/K. flV/K 2

18.311 164.6 18.473 159.9

18.631 155.3 18.784 150.9 18.933 146.6 19.077 142.5 19.218 138.5 19.354 134.7 19.487 131.1 19.617 127.6 19.743 124.3 19.865 121.1 19.985 118.0 20.101 115.1 20.215 112.4 20.326 109.8 20.435 107.3 20.541 104.9 20.645 102.7 20.746 100.5 20.846 98.5 20.943 96.6 21.039 94.8 21.133 93.1 21.225 91.5 21.316 90.0

21.405 88.5 21.493 87.2 21.579 85.9

21.665 84.7 21.749 83.5 21.832 82.4 21.914 81J4 21.994 80.4 22.074 79.5 22.153 78.6 22.232 77.7 22.309 76.9 22.385 76.1 22.461 75.4

22.536 74.7

22.611 74.0 22.684 73.4 22.757 72.8 22.830 72.2 22.902 71.6

22.973 71.0 23.044 70.5 23.114 69.9 23.184 69.4

23.253 68.9

23.322 68.5 23.390 68.0 23.458 67.6

23.525 67.1 23.592 66.7 23.658 66.3 23.724 65.9

23.790 65.5 23.856 65.2 23.921 64.8

TK

E(IV

120

121

122

123 124

1907.67

1931.62 1955.64

1979.72 2003.86

125

126

127

128 129

2028.07 2052.34

2076.68 2101.08

2125.54

130

131

132 133 134

2150.06

2174.65

2199.30 2224.00

2248.78

135 136

137

138 139

2273.61

2298.50

2323.46 2348.47

2373.55

140

141 142

143 144

2398.69

2423.89

2449.15 2474.47

2499.85

145

146 147

148

149

2525.29

2550.79

2576.36 2601.98

2627.67

150 151

152

153 154

2653.41

2679.22 2705.09

2731.02 2757.00

155

156

157

158 159

2783.05 2809.17

2835.34

2861.57

2887.87

160

161 162 163 164

2914.22 2940.64

2967.12

2993.65 3020.25

165

166

167

168 169

3046.92 3073.64

3100.42 3127.27

3154.17

170

171 172 173

174

3181.14

3208.17

3235.26

3262.41

3289.62

175 176 177

178 179

3316.89

3344.22

3371.61 3399.07

3426.58

180 3454.16

s ds/dT

/xV/K nv/K 2

23.921 64.8 23.985 64.5 24.050 64.2 24.114 63.9 24.177 63.6

24.241 63.3

24.304 63.0 24.367 62.8 24.430 62.6

24.492 62.4 24.554 62.2 24.616 62.0 24.678 61.8

24.740 61.6

24.802 61.5 24.863 61.4 24.924 61.2

24.985 61.1 25.047 61.1 25.108 61.0 25.168 60.9

25.229 60.9

25.290 60.8 25.351 60.8 25.412 60.8 25.473 60.8 25.533 60.8 25.594 60.8 25.655 60.8 25.716 60.8 25.776 60.8 25.837 60.8 25.898 60.9 25.959 60.9

26.020 60.9

26.081 61.0 26.142 61.0

26.203 61.0 26.264 61.1

26.325 61.1 26.386 61.1 26.447 61.1 26.508 61.2 26.569 61.2

26.631 61.2 26.692 61.2 26.753 61.2 26.814 61.1 26.875 61.1 26.936 61.1 26.997 61.1 27.058 61.0 27.119 61.0 27.180 60.9

27.241 60.8 27.302 60.8

27.363 60.7

27.423 60.6 27.484 60.5 27.544 60.4

27.605 60.3

33
Table 22. Type Pt versus 77V (or EN) —thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) —Continued

T E K jtV 180 3454.16

181 3481.79

182 3509.49

183 3537.24

184 3565.06

S dS/dT

|iV/K nV/K* 27.605 60.3 27.665 60.2 27.725 60.0 27.785 59.9 27.845 59.8

T E

K mV

240 5215.64

241 5246.75

242 5277.91

243 5309.13

244 5340.40

S dS/dT T E S dS/dT

MV/K «V/K« K MV ft.WK nV/K*

31.080 55.8 31.135 55.6 31.191 55.5 31.246 55.3 31.301 55.1

185 3592.93

186 3620.86

187 3648.86

188 3676.91

189 3705.02

190 3733.20

191 3761.43

192 3789.72

193 3818.07

194 3846.47

195 3874.94

196 3903.46

197 3932.04

198 3960.69

199 3989.38

200 4018.14

201 4046.96

202 4075.83

203 4104.76

204 4133.75

205 4162.79

206 4191.90

207 4221.06

208 4250.28

209 4279.55

210 4308.89

211 4338.28

212 4367.73

213 4397.24

214 4426.80

215 4456.42

216 4486.10

217 4515.84

218 4545.63

219 4575.49

220 4605.40

221 4635.36

222 4665.39

223 4695.47

224 4725.61

225 4755.81

226 4786. Oo 227 4816. ?8

228 4846.75

229 4877.18

27.905 59.7 27.964 59.5 28.024 59.4 28.083 59.3 28.142 59.2 28.201 59,0 28.260 58.9 28.319 58.8 28.378 58.7 28.436 58.5 28.495 58.4 28.553 58.3 28.612 58.2 28.670 58.1 28.728 58.0 28.786 58.0 28.844 57.9 28.902 57.8 28.959 57.8 29.017 57.7 29.075 57.7 29.133 57.6 29.190 57.6 29.248 57.6 29.305 57.6 29.363 57.6 29.420 57.6 29.478 57.6 29.536 57.6 29.593 57.6 29.651 57.6 29.708 57.6 29.766 57.6 29.823 57.6 29.881 57.6 29.939 57.6 29.996 57.6 30.054 57.6

30.111 57.6 30.169 57.6 30.227 57.5 30.284 57.5 30.342 57.4 30.399 57.4 30.456 57.3

245 246

247

248

249

5371.73

5403.11

5434.55

5466.05 5497.59

250

251 252

253

254

5529.20

5560.85 5592.56

5624.33

5656.15

255

256 257

258

259

3688.02

5719.95

5751 . 93 5783.97

5816.06

260

261 262

263 264

5848.21

5880.41

5912. 66 5944.97

5977.34

265 266

267

268

269

6009.76

6042.24

6074. 77 6107.36 6140.00

270

271

272 273

274

6172.69 6205.44

6238.24

6271.08

6303.98

275

276 277

278 279

6336.92

6369.90

6402.92 6435.98 6469.05

280 6502.15

31.356 54.9 31.411 54.8 31.466 54.6 31.521 54.5 31.575 54.4 31.629 54.3 31.684 54.3 31.738 54.2 31.792 54.2 31.847 54.3 31.901 54.3 31.955 54.4 32.010 54.5 32.064 54.6 32.119 54.7 32.174 54.9 32.228 55.0 32.284 55.1 32.339 55.2 32.394 55.2 32.449 55.2 32.504 55.0 32.559 54.7 32.614 54,3 32.668 53.6 32.721 52.7 32.773 51.4 32.823 49.8 32.872 47.7

32.919 45.0

32.962 41.7

33.002 37.6 33.037 32.7

33.067 26.7 33.090 19.6 33.105 11.2

230 4907.66

231 4938.20

232 4968.80

233 4999.46

234 5030.17

235 5060.94

236 5091.77

237 5122.65

238 5153.59

239 5184.59

240 5215.64

30.514 57.2 30.571 57.1 30.628 57.0 30.685 56.9

30.742 56.8 30.798 56.6 30.855 56.5 30.911 56.3 30.968 56.2 31.024 56.0 31.080 55.8

34
Table 23. Type Pt versus KN—thermoelectric voltage, E(T), Seebeck coefficient. S(T), and derivative oj the Seebeck coefficient, dS(T)

T E K fjiM

0 -0.22

1 -0.93

2 -1.44

3 -1.76

4 -1.88

5 -1.81

6 -1.55

7 -1.09

8 -0.44

9 0.40

10 1.44

11 2.68

12 4.11

13 5.74

14 7.57

15 9.61

16 11.85

17 14.29

18 16.93

19 19.79

20 22.85

21 26.11

22 29.58

23 33.26

24 37.15

25 41.24

26 45.54

27 50.03

28 £4.73

29 5*. 63

30 64.73

31 70.02

32 75.51

33 81.19

34 87.05

35 93.10

36 99.33

37 105.74

38 112.32

39 119.08

*0 126.00

41 133.08

42 140.32

43 147.72

44 155.27

45 162.96

46 170.80

47 178.77

48 186.88

49 195.12

50 203.48

51 211.96

52 220.56

53 229.28

54 238.10

55 247.03

56 256.06

57 265.18

58 274.40

59 283.71

60 293.10

S dS/dT

ftV/K nV/K 2

-0.813 203.5

-0.611 199.4 -0.414 196.3 -0.218 194.3 -0.025 193.0 0.168 192.5 0.360 192.5 0.553 193.0 0.747 193.9 0.941 195.0 1.137 196.3

1.334 197.7

1.532 199.1

1.732 200.5

1.933 201.9

2.135 203.1 2.339 204.3 2.544 205.2 2.750 206.0

2.956 206.5

3.162 206.8

3.369 206.8

3.576 206.6

3.782 206.2

3.988 205.4

4.193 204.4

4.397 203.2 4.600 201.7

4.800 199.9 4.999 197.9 5.196 195.6

5.390 193.2

5.582 190.5

5.771 187.6 5.957 184.5 6.140 181.3 6.320 177.9 6.496 174.3 6.669 170.6 6.837 166.8 7.002 162.9 7.163 158.9 7.320 154.8 7.473 150.7

7.621 146.5 7.766 142.3 7.906 138.1 8.042 133.8 8.174 129.6

8.301 125.3 8.424 121.1 8.543 117.0

8.658 112.8 8.769 108.7

8.876 104.7

8.978 100.8 9.077 96.9 9.172 93.1 9.263 89.4 9.351 85.7 9.435 82.2

T E K

60 293.10

61 302.58

62 312.13

63 321.76

64 331.46

65 341.23

66 351.07

67 360.97

68 370.93

69 380.95

70 391.03

71 401.15

72 411.33

73 421.56

74 431.83

75 442.15

76 452.50

77 462.90

78 473.34

79 483.82

80 494.33

81 504.88

82 515.46

83 526.07

84 536.71

85 547.38

86 558.09

87 568.81

88 579.57

89 590.35

90 601.16

91 612.00

92 622.85

93 633.74

94 644.64

95 655.57

96 666.52

97 677.50

98 688.49

99 699.51

100 710.55

101 721.61

102 732.69

103 743.80

104 754.92

105 766.06

106 777.23

107 788.41

108 799.62

109 810.85

110 822.09

111 833.36

112 844.64

113 855.95

114 867.28

115 878.62

116 889.99

117 901.38

118 912.78

119 924.21

120 935.66

s ds/dT

fj.y/< nv/K. 2

9.435 82.2 9.515 78.8 9.593 75.5 9.666 72.3 9.737 69.2 9.805 66.2 9.869 63.3

9.931 60.5 9.991 57.8 10.047 55.3 10.101 52.9 10.153 50.6 10.202 48.4

10.250 46.3 10.295 44.3

10.338 42.4

10.380 40.6

10.419 38.9 10.458 37.4 10.494 35.9 10.529 34.5

10.563 33.2 10.596 32.0 10.627 30.9

10.658 29.8 10.687 28.9 10.715 28.0 10.743 27.2 10.770 26.4

10.796 25.7

10.821 25.1 10.846 24.5 10.870 24.0 10.894 23.5 10.917 23.1 10.940 22.7

10.963 22.4

10.985 22.1 11.007 21.8 11.029 21.5

11.050 21.3

11.071 21.1 11.092 21.0 11.113 20.8 11.134 20.7

11.155 20.6 11.175 20.5

11.196 20.4

11.216 20.3 11.236 20.2 11.256 20.2 11.277 20.1 11.297 20.1 11.317 20.0 11.337 20.0 11.357 20.0 11.377 19.9 11.397 19.9 11.416 19.9 11.436 19.8 11.456 19.8

TK

EMv

120

121 122

123 124

935.66

947.12

958.61

970.11 981.64

125

126

127

128

129

993.18

1004.75

1016.33 1027.94

1039.56

130 131

132 133 134

1051.20 1062.86

1074.55

1086.25 1097.97

135 136 137

138 139

1109.71 1121.46 1133.24

1145.04

1156.86

140

141 142

143 144

1168.69

1180.55

1192.42

1204.31 1216.22

145

146 147

148 149

1228.15

1240.11 1252.07

1264.06 1276.07

150

151

152 153 154

1288.10 1300.14

1312.21 1324.29

1336.40

155

156

157

158 159

1348.52 1360.66

1372.83

1385.01

1397.21

160

161

162 163 164

1409.43 1421.67

1433.93

1446.22

1458.52

165

166 167

168

169

1470.84

1483.18 1495.54

1507.92

1520.32

170

171 172 173 174

1532.74

1545.18

1557.65 1570.13 1582.63

175 176 177

178 179

1595.15

1607.70 1620.26

1632.85 1645.45

180 1658.08

S dS/dT

iiV/K nv/K 2

11.456 19.8 11.476 19.8 11.496 19.7

11.515 19.7 11.535 19.7 11.555 19.6 11.574 19.6 11.594 19.5 11.613 19.5 11.633 19.5 11.652 19.4 11.672 19.4 11.691 19.4 11.710 19.3 11.730 19.3 11.749 19.3 11.768 19.2 11.787 19.2 11.807 19.2 11.826 19.2 11.845 19.2 11.864 19.1 11.883 19.1 11.902 19.1 11.922 19.1 11.941 19.1 11.960 19.2 11.979 19.2 11.998 19.2 12.017 19.2 12.037 19.2 12.056 19.3 12.075 19.3 12.094 19.4 12.114 19.4 12.133 19.5 12.153 19.5 12.172 19.6 12.192 19.6 12.212 19.7 12.231 19.7 12.251 19.8 12.271 19.9

12.291 19.9 12.311 20.0

12.331 20.0 12.351 20.1 12.371 20.1 12.391 20.2 12.411 20.2 12.432 20.3

12.452 20.3 12.472 20.3 12.493 20.4

12.513 20.4

12.533 20.4

12.554 20.4 12.574 20.3 12.594 20.3

12.615 20.3 12.635 20.2

35
Table 23. Type Pt versus KN—thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) —Continued

T E

K /J.V 180 1658.08

181 1670.72

182 1683.39

183 1696.07

184 1708.78

185 1721.50

186 1734.25

187 1747.01

188 1759.80

189 1772.60

190 1785.42

191 1798.26

192 1811.13

193 1824.01

194 1836.90

195 1849.82

196 1862.76

197 1875.71

198 1888.68

199 1901.67

200 1914.67

201 1927.70

202 1940.73

203 1953.79

204 1966.86

205 1979.95

206 1993.05

207 2006.17

208 2019.30

209 2032.45

210 2045.62

211 2058.79

212 2071.99

213 2085.19

214 2098.41

215 2111.64

216 2124.89

217 2138.15

218 2151.42

219 2164.70

220 2178.00

221 2191.31

222 2204.63

223 2217.96

224 2231.31

225 2244.67

226 2258.04

227 2271.42

228 2284.81

229 2298.21

230 2311.62

231 2325.05

232 2338.49

233 2351.93

234 2365.39

235 2378.86

236 2392.34

237 2405.84

238 2419.34

239 2432.85

240 2446.37

S dS/dT

^.V/K nv/K2

12.635 20.2 12.655 20.2 12.675 20.1 12.695 20.0

12.715 19.9

12.735 19.8 12.755 19.7 12.775 19.6 12.794 19.4 12.813 19.3 12.833 19.1 12.852 19.0 12.871 18.8 12.889 18.6 12.908 18.4 12.926 18.1 12.944 17.9 12.962 17.7 12.979 17.5 12.997 17.2 13.014 17.0 13.031 16.7 13.047 16.4 13.064 16.2 13.080 15.9 13.095 15.7

13.111 15.4 13.126 15.1 13.141 14.9 13.156 14.6 13.170 14.4 13.185 14.1 13.199 13.9 13.212 13.7 13.226 13.4 13.239 13.2 13.252 13.0 13.265 12.8 13.278 12.6

13.291 12.5 13.303 12.3 13.315 12.1 13.327 12.0 13.339 11.9

13.351 11.8 13.363 11.7 13.374 11.6 13.386 11.5 13.397 11.4 13.409 11.3 13.420 11.2

13.431 11.2 13.442 11.1 13.453 11.0 13.464 10.9 13.475 10.9 13.486 10.8 13.497 10.7 13.507 10.6 13.518 10.4

13.528 10.3

T

K

EM

v 240

241

242

243 244

2446.37

2459.91 2473.45

2487.00 2500.57

245

246

247

248

249

2514.14

2527.72

2541.31

2554.91 2568.52

250

251

252 253

254

2582.13

2595.75

2609.38

2623.02

2636.66

255 256

257

258 259

2650.30

2663.95

2677.61 2691.26 2704.92

260

261

262 263

264

2718.58

2732.24

2745.90

2759.56

2773.22

265 266

267

268

269

2786.87

2800.52 2814.17

2827.82 2841.47

270

271

272

273 274

2855.11 2868.74

2882.38

2896.01 2909.65

275 276 277

278

279

2923.29

2936.93 2950.59

2964.25 2977.94

280 2991.64

S

fj.V/K dS/dT

nV/K 2

13.528

13.538

13.548

13.558

13.568

10.3

10.

9.9 9.7

9.5 13.577

13.586

13.595 13.603

13.611

9.2 8.9

8.5

8.1 7.7

13.619

13.626

13.632 13.638

13.643

7.2 6.7

6.1

5.5 4.9

13.648

13.652

13.655 13.657

13.659

4.2

3.5 2.8

2.1

1.3 13.660

13.660 13.659

13.658 13.657

0.6 -0.1 -0.8

-1.5

-2.1 13.654

13.651 13.648

13.645

13.642

-2.6

-2.9

-3.2

-3.2 -3.0

13.639

13.637

13.636

13.635 13.637

-2.6 -1.9

-0.8

0.8

2.8 13.641 13.648

13.659

13.673

13.693

5.4 8.6 12.5

17.2 22.9

13.720 29.6

E S dS/dT

^.V /iV/K nv/K2

36
Table 24. Type Pt versus TP—thermoelectric voltage, E(T), Seebech coefficient, S(T), and derivative of the Seebeck coefficient, <1S(T)

T E

K M

v

0 1.39

1 0.08

2 -0.95

3 -1.72

4 -2.25

5 -2.55

6 -2.64

7 -2.55

8 -2.27

9 -1.82

10 -1.22

11 -0.46

12 0.44

13 1.48

14 2.64

15 3.94

16 5.35

17 6.89

18 8.54

19 10.30

20 12.17

21 14.15

22 16.23

23 18.42

24 20.70

25 23.09

26 25.57

27 28.15

28 30.82

29 33.59

30 36.45

31 39.39

32 42.43

33 45.55

34 48.75

35 52.04

36 55.40

37 58.85

38 62.37

39 65.96

46 69.62

41 73.35

42 77.14

43 81.00

44 84.92

45 88.90

46 92.93

47 97.01

46 101.14

49 105.31

50 109.53

51 113.79

52 118.08

53 122.41

54 126.77

55 131.15

56 135.56

57 139.99

58 144.44

59 148.90

60 153.38

S dS/dT

fxV/K nv/K 2

-1.464 310.1 -1.167 284.4 -0.894 261.5 -0.643 241.1 -0.411 222.9 -0.197 206.8

0.003 192.6 0.189 180.1 0.363 169.0 0.528 159.3 0.682 150.8 0.829 143.3 0.969 136.8

1.103 131.2 1.232 126.2 1.356 121.9

1.476 118.1

1.592 114.8 1.706 111.9

1.816 109.3 1.924 106.9 2.030 104.8 2.134 102.9 2.236 101.1 2.336 99.3 2.435 97.7

2.531 96.0 2.627 94.4 2.720 92.8 2.812 91.1 2.902 89.4 2.991 87.6 3.078 85.8 3.162 83.8 3.245 81.8 3.326 79.7 3.405 77.6

3.481 75.3 3.555 73.0 3.627 70.5 3.696 68.0

3.763 65.4

3.827 62.8 3.889 60.0 3.947 57.2 4.003 54.4 4.056 51.5 4.106 48.5 4.153 45.5 4.197 42.5 4.238 39.5 4.276 36.4 4.311 33.3 4.343 30.3 4.372 27.2 4.397 24.1 4.420 21.1 4.439 18.0 4.456 15.0 4.469 12.0 4.480 9.1

T E K

60 153.38

61 157.86

62 162.35

63 166.84

64 171.34

65 175.83

66 180.32

67 184.80

68 189.26

69 193.72

70 198.16

71 202.59

72 206.99

73 211.37

74 215.73

75 220.06

76 224.37

77 228.64

78 232.88

79 237.09

80 241.26

81 245.40

82 249.49

83 253.55

84 257.56

85 261.54

86 265.46

87 269.35

88 273.18

89 276.97

90 280.71

91 284.39

92 288.03

93 291.62

94 295.15

95 298.63

96 302.06

97 305.43

98 308.75

99 312.01

100 315.22

101 318.37

102 321.46

103 324.49

104 327.47

105 330.39

106 333.25

107 336.05

108 338.79

109 341.47

110 344.09

111 346.65

112 349.15

113 351.59

114 353.97

115 356.29

116 358.54

117 360.74

118 362.87

119 364.95

120 366.96

S ds/dT

/J.V/K nv/K 2

4.480 9.1 4.488 6.2 4.492 3.3 4.494 0.5 4.493 -2.2 4.490 -4.9 4.484 -7.6

4.475 -10.1 4.463 -12.6

4.449 -15.1 4.433 -17.5

4,415 -19.8

4.394 -22.0

4.371 -24.1

4.345 -26.2 4.318 -28.2 4.289 -30.2

4.258 -32.0

4.225 -33.8

4.190 -35.5 4.154 -37.2

4.116 -38.7

4.077 -40.2 4.036 -41.6

3.993 -43.0

3.950 -44.3

3.905 -45.5

3.859 -46.7

3.811 -47.8

3.763 -48.8 3.714 -49.8

3.664 -50.7

3.612 -51.6

3.561 -52.4

3.508 -53.1 3.454 -53.8

3.400 -54.5

3.345 -55.1

3.290 -55.7

3.234 -56.3

3.177 -56.8

3.120 -57.2

3.063 -57.7

3.005 -58.1 2.947 -58.4

2.888 -58.8 2.829 -59.1 2.770 -59.4

2.710 -59.6

2.651 -59.9

2.591 -60.1

2.530 -60.3

2.470 -60.5

2.409 -60.7

2.349 -60.8

2.288 -61.0 2.227 -61.1 2.166 -61.2 2.104 -61.3

2.043 -61.4

1.982 -61.5

T

K

E

JJ.V 120

121

122

123 124

366.96

368.91 370.80

372.63

374.39

125

126

127

128 129

376.10 377.74

379.32 380.84 382.30

130

131

132

133 134

383.70 385.03

386.30

387.51 388.66

135

136 137

138 139

389.75 390.77

391.74

392.64

393.48

140

141

142 143 144

394.26

394.98

395.63

396.23 396.76

145

146

147

148 149

397.24

397.65 398.00

398.29

398.52

150

151

152

153 154

398.69

398.80

398.85 398.84

398.77

155

156

157

158 159

398.63 398.44

398.20 397.89

397.52

160

161

162 163 164

397.09

396.61 396.06

395.46 394.80

165

166

167

168 169

394.09

393.31 392.48 391.59

390.64

170

171 172

173 174

389.64

388.58

387.47

386.29

385.07

175

176 177

178 179

383.78

382.45 381.05

379.60

378.10

180 376.55

S ds/dT

/J.V/K nv/K 2

1.982 -61.5

1.920 -61.5

1.859 -61.6

1.797 -61.6

1.735 -61.7

1.674 -61.7

1.612 -61.7

1.550 -61.8

1.488 -61.8

1.427 -61.8

1.365 -61.8

1.303 -61.8

1.241 -61.7

1.180 -61.7

1.118 -61.7

1.056 -61.7

0.995 -61.6

0.933 -61.6

0.871 -61.5

0.810 -61.5

0.748 -61.4

0.687 -61.3

0.626 -61.2

0.565 -61.1 0.504 -61.0

0.443 -60.9

0.382 -60.8

0.321 -60.7

0.260 -60.6

0.200 -60.5 0.139 -60.3

0.079 -60.2

0.019 -60.0

-0.041 -59.9

-0.101 -59.7

-0.160 -59.5

-0.220 -59.4

-0.279 -59.2

-0.338 -59.0 -0.397 -58.8 -0.456 -58.6 -0.514 -58.4

-0.573 -58.2

-0.631 -58.0 -0.689 -57.8

-0.746 -57.6

-0.804 -57.3

-0.861 -57.1 -0.918 -56.9

-0.975 -56.7

-1.031 -56.4 -1.087 -56.2 -1.144 -56.0 -1.199 -55.7

-1.255 -55.5 -1.310 -55.3

-1.366 -55.1 -1.421 -54.8

-1.475 -54.6

-1.530 -54.4

-1.584 -54.2

37
Table 24. Type Pt versus TP—thermoelectric voltage, E(T). Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) —Continued

T E S ds/dT T E S ds/dT

K f±V/K nV/K 2 K fj.V fjN/K nV/K2

180 376.55 -1.584 -54.2 240 190.20 -4.523 -42 ,9 181 374.93 -1.638 -54.0 241 185.65 -4.566 -42 ,7 182 373.27 -1.692 -53.7 242 181.07 -4.609 —42 »5 183 371.55 -1.746 -53.5 243 176.44 -4.651 -42 3 184 369.78 -1.799 -53.3 244 171.77 -4.693 -42 .2 185 367.95 -1.852 -53.1 245 167.05 -4.735 -42 • 0 186 366.07 -1.905 -52.9 246 162.29 -4.777 -41 .9 187 364.14 -1.958 -52.7 247 157.50 -4.819 —41 ,7 188 362.16 -2.011 -52.6 248 152.66 -4.861 -41 • 6 189 360.12 -2.063 -52.4 249 147.77 -4.902 -41 .6 190 358.03 -2.116 -52.2 250 142.85 -4.944 -41 .5 191 355.89 -2.168 -52.0 251 137.89 -4.985 -41 .5 192 353.70 -2.220 -51.9 252 132.88 -5.027 —41 , 5 193 351.45 -2.271 -51.7 253 127.83 -5.068 -41 5 194 349.15 -2.323 -51.5 254 122.74 -5.110 -41 5

195 346.80 -2.374 -51.4 255 117.61 -5.151 -41 >6 196 344.40 -2.426 -51.2 256 112.44 -5.193 -41 .6 197 341.95 -2.477 -51.1 257 107.23 -5.235 -41 7 198 339.45 -2.528 -51.0 258 101.97 -5.276 -41 8 199 336.90 -2.579 -50.8 259 96.68 -5.318 -41 9 200 334.29 -2.630 -50.7 260 91.34 -5.360 -42 .0 201 331.64 -2.680 -50.5 261 85.96 -5.402 -42 ,1 202 328.93 -2.731 -50.4 262 80.53 -5.444 -42 ,2 203 326.18 -2.781 -50.3 263 75.07 -5.487 -42 .2 204 323.37 -2.831 -50.1 264 69.56 -5.529 -42 .2 205 320.51 -2.881 -50.0 265 64.01 -5.571 -42 .2 206 317.61 -2.931 -49.9 266 56.42 -5.613 -42 ,1 207 314.65 -2.981 -49.7 267 52.78 -5.655 -41 ,9 208 311.65 -3.031 -49.6 268 47.11 -5.697 -41 6 209 308.59 -3.080 -49.5 269 41.39 -5.738 -41 .1 210 305.49 -3.130 -49.3 270 35.63 -5.779 -40 >6 211 302.33 -3.179 -49.2 271 29.83 -5.819 -39 8 212 299.13 -3.228 -49.0 272 23.99 -5.859 -38. 8 213 295.87 -3.277 -48.9 273 18.11 -5.897 -37 .6 214 292.57 -3.326 -48.7 274 12.20 -5.934 -36 1

215 289.22 -3.375 -48.6 275 6.25 -5.969 -34 ,3 216 285.82 -3.423 -48.4 276 0.26 -6.002 -32 .0 217 282.38 -3.471 -48.2 277 -5.76 -6.033 -29 ,4 218 278.88 -3.520 -48.1 278 -11.80 -6.061 -26 .3 219 275.34 -3.568 -47.9 279 -17.88 -6.085 -22 .6

220 271.75 -3.615 -47.7 280 -23.97 -6.106 -18 i,3 221 268.11 -3.663 -47.5

222 264.42 -3.710 -47.3

223 260.69 -3.758 -47.1 224 256.91 -3.804 -46.9

225 253.08 -3.851 -46.6

226 249.20 -3.898 -46.4

227 245.28 -3.944 -46.2

228 241.32 -3.990 -45.9

229 237.30 -4.036 -45.7

230 233.24 -4.082 -45.4

231 229.14 -4.127 -45.2

232 224.99 -4.172 -44.9

233 220.80 -4.217 -44.7

234 216.56 -4.261 -44.4

235 212.27 -4.305 -44.2

236 207.95 -4.350 -43.9

237 203.57 -4.393 -43.7

238 199.16 -4.437 -43.4

239 194.70 -4.480 -43.2

240 190.20 -4.523 -42.9

E s

fj.V/K ds/dT

nv/K 2

38

Table 25. Type KP (or EP) versus Ag-28 at% Au

thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T)

T E

K

0 0.79

1 0.55

2 0.54

3 0.74

4 1.16

5 1.77

6 2.56

7 3.55

8 4.71

9 6.05

10 7.56

11 9.25

12 11.11

13 13.14

14 15.34

15 17.71

16 20.26

17 22.97

18 25.86

19 28.93

20 32.17

21 35.58

22 39.18

23 42.95

24 46.89

25 51.02

26 55.32

27 59.80

28 64.46

29 69.30

30 74.32

31 79.51

32 84.88

33 90.43

34 96.15

35 102.04

36 108.11

37 114.35

38 120.75

39 127.33

40 134.07

41 140.98

42 148.05

43 155.28

44 162.68

45 170.23

46 177.93

47 185.79

48 193.80

49 201.96

50 210.27

51 218.72

52 227.32

53 236.06

54 244.95

55 253.97

56 263.12

57 272.41

58 281.84

59 291.39

60 301.08

s ds/dT

/J.V/K nV/*2 -0.361 245.3 -0.123 229.7

0.099 216.6 0.311 205.8

0.512 197.0 0.705 189.8 0.892 184.2 1.074 179.8

1.252 176.6

1.427 174.2

1.601 172.6

1.773 171.6 1.944 171.2 2.115 171.2 2.287 171.4 2.458 172.0

2.631 172.6 2.804 173.4 2.977 174.2 3.152 175.1 3.327 175.9 3.504 176.6

3.681 177.2 3.858 177.7 4.036 178.1 4.214 178.4 4.393 178.4 4.571 178.4 4.749 178.2 4.927 177,8 5.105 177.3 5.282 176.6

5.458 175.8

5.633 174.8

5.808 173.7

5.981 172.5 6.153 171.2 6.323 169.8 6.492 168.2 6.660 166.6 6.825 165.0 6.990 163.2 7.152 161.4

7.312 159.6

7.471 157.7

7.628 155.8

7.782 153.8 7.935 151.9 8.086 149.9 8.235 148.0 8.382 146.0 8.527 144.1 8.670 142.2 8.812 140.3 8.951 138.4 9.088 136.6 9.224 134.8 9.358 133.0 9.490 131.3

9.621 129.6 9.749 127.9

T E K M

v

60 301.08

61 310.89

62 320.83

63 330.89

64 341.08

65 351.39

66 361.82

67 372.37

68 383.03

69 393.82

70 404.71

71 415.73

72 426.85

73 438.08

74 449.43

75 460.88

76 472.45

77 484.12

78 495.89

79 507.77

80 519.76

81 531.85

82 544.04

83 556.33

84 568.72

85 581.21

86 593.80

87 606.49

88 619.28

89 632.16

90 645.14

91 658.21

92 671.38

93 684.64

94 697.99

95 711.44

96 724.97

97 738.60

98 752.31

99 766.11

100 780.00

101 793.98

102 808.05

103 822.20

104 836.43

105 850.75

106 865.15

107 879.64

108 894.21

109 908.86

110 923.59

111 938.40

112 953.29

113 968.26

114 983.31

115 998.44

116 1013.64

117 1028.92

118 1044.27

119 1059.70

120 1075.21

S dS/dT pV/K nV/K2 9.749 127.9 9,876 126.3 10.002 124.8 10.126 123.2 10.248 121.8

10.369 120.3 10.489 118.9 10.607 117.6 10.724 116.3 10.840 115.0 10.954 113.8 11.067 112.6 11.179 111.4

11.290 110.3 11.400 109.2 11.509 108.1 11.616 107.1 11.723 106.1 11.829 105.1 11.933 104.1 12.037 103.2 12.140 102.3 12.241 101.4

12.342 100.5 12.443 99.7

12.542 98.8

12.640 98.0

12.738 97.1 12.834 96.3 12.930 95.5

13.025 94.7

13.120 94.0

13.213 93.2

13.306 92.4

13.398 91.6

13.489 90.9

13.580 90.1 13.670 89.4 13.759 88.7 13.847 87.9

13.935 87.2 14.021 86.5 14.108 85.7

14.193 85.0 14.278 84.3

14.362 83.6

14.445 82.9

14.527 82.3 14.609 81.6

14.691 80.9 14.771 80.2

14.851 79.6 14.930 78.9

15.009 78.3

15.087 77.7

15.164 77.1

15.241 76.5 15.317 75.9

15.393 75.3 15.468 74.7 15.542 74.1

T

K

E

120

121

122 123 124

1075.21 1090.79

1106.44

1122.17

1137.97

125 126 127

128 129

1153.84

1169.78

1185.79 1201.87

1218.03

130

131

132 133 134

1234.25 1250.54

1266.90

1283.33

1299.83

135 136

137

138 139

1316.39

1333.02

1349.72 1366.49

1383.32

140

141

142 143 144

1400.21 1417.17

1434.20 1451.29

1468.44

145

146 147

148

149

1485.66 1502.94

1520.28

1537.68

1555.15

150

151

152 153

154

1572.68 1590.27

1607.93 1625.64

1643,41

155

156 157

158 159

1661.25 1679.14

1697.09

1715.10

1733.17

160

161 162

163 164

1751.30 1769.49

1787.73

1806.03 1824.39

165 166

167

168 169

1842.81 1861.28

1879.80

1898.38

1917.02

170

171 172

173 174

1935.71 1954.46

1973.25

1992.11 2011.01

175 176

177

178

179

2029.97

2048.98

2068.04

2087.15

2106.31

180 2125.53

S dS/dT

fj.V/K nv/<2

15.542 74.1 15.616 73.6 15.689 73.0 15.762 72.5 15.835 72.0 15.906 71.5 15.978 71.0 16.048 70.5 16.119 70.0 16.188 69.6 16.258 69.1 16.327 68.7

16.395 68.2 16.463 67.8 16.531 67.4

16.598 67.0 16.665 66.6

16.731 66.2 16.797 65.8

16.863 65.4

16.928 65.1 16.993 64.7 17.057 64.3

17.121 64.0

17.185 63.6

17.249 63.2

17.312 62.9

17.374 62.5 17.437 62.2 17.499 61.8

17.560 61.5

17.622 61.1

17.683 60.8

17.743 60.4 17.804 60.1 17.863 59.7

17.923 59.4

17.982 59.0 18.041 58.7

18.100 58.3 18.158 57.9

18.215 57.5 18.273 57.2 18.330 56.8

18.386 56.4

18.443 56.0 18.498 55.6 18.554 55.3

18.609 54.9 18.664 54.5 18.718 54.1 18.772 53.7

18.825 53.3 18.878 52.9

18.931 52.5 18.983 52.1 19.035 51.8 19.087 51.4

19.138 51.0 19.189 50.6 19.239 50.3

40
25. Type KP (or EP) versus Ag-28 at% Au

thermoelectric voltage, E(T) , Seebeck coefficient, S(T), and derivative of the Scebeck coefficient, dS(T) —Continued

T E S ds/dT

K uV fj.y/K nv/<2

180 2125.53 19.239 50.3

181 2144.79 19.289 49.9

182 2164.11 19.339 49.5

183 2183.47 19.389 49.2 184 2202.88 19.438 48.9

T E s ds/dT

K /iV U.V/K 240 3360.75 21.783 33.0

241 3382.55 21.815 32.6

242 3404.38 21.848 32.2

243 3426.25 21.880 31.9 244 3448.14 21.912 31.6

T E s ds/dT

K fiM /J.V/K nv/K 2

185 2222.35

186 2241.86

187 2261.42

188 2281.02

189 2300.68

190 2320.38

191 2340.13

192 2359.92

193 2379.76

194 2399.65

19.486 48.5

19.535 48.2

19.583 47.9

19.630 47.6

19.678 47.3 19.725 47.0

19.772 46.7

19.818 46.4

19.865 46.2

19.911 45.9

245 3470.07

246 3492.03

247 3514.02

248 3536.04

249 3558.09

250 3580.18

251 3602.29

252 3624.43

253 3646.61

254 3668.82

21.943 31.4 21.974 31.2 22.005 31.0 22.036 30.9 22.067 30.8 22.098 30.8 22.129 30.9 22.160 31.0 22.191 31.2 22.222 31.4

195 2419.58

196 2439.56

197 2459.59

198 2479.66

199 2499.77

200 2519.93

201 2540.14

202 2560.39

203 2580.68

204 2601.02

205 2621.40

206 2641.82

207 2662.29

208 2682.80

209 2703.36

19.956 45. 7 20.002 45. 5 20.047 45. 2 20.093 45. 0 20.137 44. 8 20.182 44. 6 20.227 44. 4 20.271 44. 3 20.315 44. 1 20.359 43. 9 20.403 43. 7 20.447 43. 6 20.490 43. 4 20.534 43. 2 20.577 43.1255 3691.05

256 3713.32

257 3735.62

258 3757.96

259 3780.32

260 3802.72

261 3825.16

262 3847.63

263 3870.13

264 3892.66

265 3915.23

266 3937.84

267 3960.48

268 3983.15

269 4005.86

22.254 31.7 22.285 32.0 22.318 32.4 22.350 32.8 22.383 33.2 22.417 33.6 22.450 34.0 22.484 34.3 22.519 34.6 22.554 34.7 22.588 34.7 22.623 34.5 22.657 34.1 22.691 33.3 22.724 32.2

210 2723.96

211 2744.60

212 2765.28

213 2786.01

214 2806.78

215 2827.59

216 2848.44

217 2869.34

218 2890.27

219 2911.25

20.620 42.9 20.663 42.7 20.705 42.6 20.748 42.4 20.790 42.2 20.832 42.0 20.874 41.8 20.916 41.6 20.957 41.3 20.998 41.1

270 4028.60

271 4051.37

272 4074.17

273 4096.99

274 4119.84

275 4142.70

276 4165.58

277 4188.46

278 4211.34

279 4234.20

22.755 30.6 22.785 28.4 22.812 25.6 22.836 22.1 22.856 17.6 22.871 12.1 22.879 5.4 22.881 -2.7 22.874 -12.3 22.856 -23.7

220 2932. 27 21.039 40. 8 221 2953. 33 21.080 40. 5 222 2974. 43 21.120 40. 2 223 2995. 57 21.160 39. 9 224 3016. 75 21.200 39. 6 225 3037.97

226 3059.23

227 3080.52

228 3101.86

229 3123.24

21.240 39.3 21.279 38.9 21.317 38.5 21.356 38.1 21.394 37.7

230 3144.65

231 3166.10

232 3187.59

233 3209.11

234 3230.67

235 3252.26

236 3273.89

237 3295.56

238 3317.26

239 3338.99

240 3360.75

21.431 37.3 21.468 36.9 21.505 36.5 21.541 36.0 21.577 35.6 21.612 35.1 21.647 34.7 21.682 34.2 21.716 33.8 21.749 33.4 21.783 33.0

41
Table 26. Type Ag-28 at7o Au versus TN {or EN) —thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T)

T E K /J.V

o 0 00

1 0 10

2 0 59

3 1 46

4 2 68

5 4 23

6 6 09

7 8 24

8 10 67

9 13 36

10 16 31 11 19, 50

12 22. 92

13 26 57 14 30< 44

15 34, 52 16 38, 81 17 43, 31 18 48, 00

19 52, 88

20 57, 96

21 63 23

22 68, 69

23 74 33 24 80 15

25 86 16 26 92 34 27 98 71 28 105 25 29 111 97

30 118 87

31 125 91, 32 133 19 33 140 61 34 148 20

35 155 97 36 163 90 37 172 01 38 180 29 39 188 73

40 197 35 41 206 13 42 215, 08 43 224, 20 44 233 48

45 242 93 46 252 .54 47 262 31 48 272 ,25 49 282 > 34

50 292 , 60

51 303 ,01 52 313 59

53 324 32 54 335 .21

55 346 26 56 357 46

57 368 81 58 380 32 59 391 ,99

60 403.80

S dS/dT

-0.113 429.0

0.301 399.5 0.687 373.2 1.048 349.6

1.387 328.5 1.706 309.7 2.007 292.9

2.292 278.0 2.564 264.9

2.822 253.2 3.070 242.9

3.309 233.9

3.539 225.9

3.761 218.9

3.977 212.8 4.187 207.5 4.392 202.8 4.593 198.7 4.789 195.2 4.983 192.1 5.174 189.5

5.362 187.2 5.548 185.1 5.733 183.3 5.915 181.8 6.096 180.4 6.276 179.2 6.455 178.1 6.632 177.1 6.809 176.2 6.984 175.3 7.159 174.5 7.333 173.7 7.507 172.9 7.679 172.2 7.851 171.5

8.022 170.7 8.193 170.0

8.362 169.3

8.531 168.5 8.699 167.8 8.867 167.0 9.033 166.2 9.199 165.4 9.364 164.6

9.528 163.8 9.692 162.9 9.854 162.1 10.016 161.3 10.177 160.4 10.337 159.6 10.496 158.7 10.654 157.9

10.811 157.0

10.968 156.2 11.124 155.3 11.279 154.5

11.433 153.7 11.586 152.9

11.739 152.1 11.890 151.3

T E K

60 403.80

61 415.77

62 427.88

63 440.15

64 452.57

65 465.13

66 477.84

67 490.70

68 503.70

69 516.85

70 530. 15 71 543.59

72 557.17

73 570.90

74 584.77

75 598.78

76 612.94

77 627.23

78 641.67

79 656.25

80 670.96

81 685.82

82 700.81

83 715.95

84 731.22

85 746.63

86 762.17

87 777.86

88 793.68

89 809.63

90 825.73

91 841.95

92 858.32

93 874.82

94 891.45

95 908.21

96 925.12

97 942.15

98 959.32

99 976.62

100 994.05

101 1011.61

102 1029.31

103 1047.14

104 1065.09

105 1083.18

106 1101.40

107 1119.75

108 1138.23

109 1156.84

110 1 175.58

111 1194.44

112 1213.44

113 1232.56

114 1251.81

115 1271.19

116 1290.69

117 1310.32

118 1330.08

119 1349.96

120 1369.97

s ds/dT

fxV/K nV/K2 11.890 151.3

12.041 150.6

12.191 149.8

12.341 149.1 12.490 148.4

12.638 147.7 12.785 147.0 12.932 146.4 13.078 145.7

13.223 145.1 13.368 144.5

13.512 143.9 13.656 143.4 13.799 142.8

13.941 142.3 14.083 141.8

14.225 141.3 14.366 140.8 14.506 140.3 14.647 139.9 14.786 139.4

14.925 139.0 15.064 138.6

15.203 138.2

15.341 137.8 15.478 137.4

15.615 137.0

15.752 136.6 15.889 136.3 16.025 135.9 16.160 135.5

16.296 135.2 16.431 13A.8 16.565 134.5 16.700 134.1 16.834 133.8 16.967 133.4 17.100 133.1 17.233 132.8 17.366 132.4

17.498 132.1 17.630 131.7 17.762 131.4 17.893 131.1 18.024 130.7 18.154 130.4 18.285 130.0 18.414 129.7 18.544 129.3 18.673 129.0

18.802 128.6

18.930 1.28.3 19.058 127.9

19.186 127.6

19.313 127.2 19.440 126.8 19.567 126.5 19.693 126.1 19.819 125.8 19.945 125.4 20.070 125.1

T

K

E

120

121 122

123 124

1369.97

1390.10

1410.36 1430.74

1451.25

125

126 127

128 129

1471.87

1492.63 1513.50

1534.50

1555.62

130

131 132

133 134

1576.87

1598.23

1619.72 1641.33

1663.05

135

136 137

138 139

1684.90

1706.87

1728.96

1751.17

1773.50

140

141 142

143 144

1795.94

1818.51 1841.19

1863.99

1886.91

145

146 147

148 149

1909.95

1933.10

1956.38

1979.76 2003.27

150

151

152

153 154

2026.89

2050.63 2074.48

2098.45

2122.53

155

156 157

158 159

2146.73

2171.05 2195.47

2220.02 2244.67

160

161

162

163 164

2269.44

2294.33

2319.32 2344.44

2369.66

165

166 167

168 169

2394.99 2420.44

2446.00 2471.67

2497.46

170

171 172

173 174

2523.35

2549.36 2575.47

2601.70

2628.03

175 176

177

178

179

2654.48

2681.04

2707.70

2734.47

2761.36

180 2788.35

s ds/dT

/aV/K nv/K2

20.070 125.1 20.195 124.7 20.320 124.4 20.444 124.1 20.568 123.7 20.691 123.4 20.815 123.0 20.937 122.7 21.060 122.4 21.182 122.0 21.304 121.7 21.426 121.4 21.547 121.1 21.668 120.8 21.788 120.5 21.909 120.2 22.029 119.9 22.148 119.6 22.268 119.3 22.387 119.0 22.506 118.7 22.624 118.4 22.743 118.1 22.861 117.9 22.978 117.6 23.096 117.3 23.213 117.1 23,330 116.8 23.447 116.6 23.563 116.3 23.679 116.0 23.795 115.8 23.911 115.5 24.026 115.3 24.141 115.0 24.256 114.8

24.371 114.5 24.485 114.3 24.600 114.0 24.714 113.8 24.827 113.5 24.941 113.3 25.054 113.0 25.167 112.8 25.279 112.5 25.392 112.3 25.504 112.0 25.616 111.7 25.727 111.5 25.839 111.2 25.950 110.9

26.061 110.6 26.171 110.4 26.281 110.1 26.391 109.8 26.501 109.5 26.610 109.2 26.719 108.9 26.828 108.6 26.936 108.3 27.045 108.0

42
Table 26. Type Ag-28 at% Au versus 77V (or EN) —thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative oj the Seebeck coefficient, dS(T) —Conlinuud

TK

180

181

182 183 184

E

2788.35

2815.45

2842.65

2869.97 2897.39

S tlV/K 27.045

27. 152 27.260 27.367 27.474

ds/dT

nv/<2 108.0

107.7

107.3

107.0

106.7

T

K 240

241

242

243

244

E

4594.31 4627.35

4660.48

4693.71 4727.02

S iiV/K 32.995 33.086

33.178 33.269

33.361

dS/dT

92.0

91.8

91.5

91.3

91.0

E ds/dT

n v/k2

185 186 187

188 189

2924.91

2952.55 2980.29

3008. 13 3036.08

27.581 27.687

27.793 27.898

28.003

106.4

106. 1 105.7 105.4

105.1

245 246 247

248

249

4760.43

4793.92

4827.51 4861.19

4894.96

33.451 33.542

33.632 33.722

33.812

90.7

90.5

90.2 89.9

89.6

190

191

192 193 194

3064.14

3092.30 3120.57

3148.93

3177.41

28.108

28.213

28.317

28.421 28.525

104.7

104.4

104.1 103.8

103.4

250

251 252

253 254

4928.81 4962.76

4996.80

5030.92 5065.13

33.902

33.991 34.080

34.168

34.257

89.3 89.0

88.7

88.4

88.1

195 196

197

198 199

3205.98

3234.66

3263.45 3292.33

3321.32

28.628

28.731 28.834

28.936

29.038

103.1 102.8

102.4

102.1

101.8

255 256 257

258

2 59

5099.43

5133.82 5168.30

5202.86

5237.51

34.344

34.432 34.519

34.606

34.693

87.8 87.4

87.1 86.7

86.4

200

201 202

203 204

3350.41 3379.60 3408.89

3438.28

3467.77

29.139

29.241

29.342

29.442

29.543

101.5

101.2

100.9 100.6

100.3

260

261

262 263

264

5272.24

5307.07

5341 .97 5376.97

5412.05

34.779

34.865

34.950

35.036

35.120

86.0 85.7

85.3 85.0

84.6

205

206 207

208 209

3497.36

3527.06

3556.85 3586.74

3616.73

29.643

29.743 29.842 29.942

30.041

100.0 99.7

99.4

99.1

98.8

265 266 267

268

269

5447.21 5482.45 5517.79

5553.20

5588.70

35.205 35.289

35.372

35.455

35.538

84.2 83.8

83.4 82.9

82.5

210

211

212

213 214

3646.82

3677.01 3707.30 3737.68

3768.17

30.139

30.238 30.336 30.434

30.532

98.6

98.3 98.0

97.8

97.5

270

271 272

273 274

5624.28 5659.94

5695.68

5731.50

5767.41

35.620

35.702

35.783

35.864

35.944

82.0

81.5

80.9

80.3

79.7

215 216

217

218 219

3798.75

3829.42 3860.20 3891.07

3922.04

30.629 30.726

30.823 30.920

31.016

97.3

97.1 96.8 96.6

96.4

275 276

277 278

279

5803.39

5839.45 5875.59

5911.81

5948. 11

36.023

36.102

36.180

36.257

36.332

79.0 78.2

77.3

76.4

75.3

220

221

222 223

224

3953.10

3984.26 4015.52 4046.87

4078.32

31.113

31.209 31.304

31.400

31.495

96.2 95.9 95.7

95.5 95.3

280 5984.48 36.407 74.0

225 226

227

228

229

4109.86

4141.50

4173.23

4205.06 4236.98

31.591 31.686

31.781 31.875

31.970

95.1 94.9 94.7

94.5

94.3

230

231

232 233

234

4269.00

4301.11 4333.32

4365.62

4398.01

32.064

32.158

32.252

32.345 32.439

94.1 93.9 93.7

93.5

93.3

235 236

237

238

239

4430.49

4463.07 4495.74

4528.51 4561.36

32.532 32.625

32.718 32.810

32.902

93.1 92.9 92.7

92.4

92.2 240 4594.31 32.995 92.0

43
Table 27. Type Ag-28 at% Au versus KN—thermoelectric voltage, E(T) . Seebeck coefficient, S(T) , and derivative of the Seebeck coefficient, dS(T)

T E

K Mv

o -0 22

I 0 18

2 0

3 0 87

4 1 .19

5 1 50

6 1 81

7 2 14

8 2, 48

9 2 86

10 3 25

11 3 69

12 2 5 13 4 66

14 5. 20

15 5 79

16 6 .42 17 7 0 9 18 7 80 19 8 56

20 9 36

21 10 21 22 1 0 23 12 04 24 13 02

25 14 05 26 15. 12 27 16. 24 28 17, 40

29 18. 61

30 19. 87

31 21. 17

32 22 1 33 23 92 34 25 37

35 26 86 36 28 41 37 iin 3U > 00

38 31 65

39 33 35

40 35 10 41 36 90 42 38

76 43 40. 67

44 42. 64

45 44 67 46 46 ,76 47 48 90 48 51 10 49 53 37

50 55 69

51 58 08 52 60. 53 53 63. 04

54 65 62

55 68 27 56 70 98 57 73 75 58 76 60

59 79 51

60 82.49

S ds/dT

(jlV/K nV/K 2

0.430 -60.6

0.378 -43.2

0.342 -28.3

0.321 -15.4

0.311 -4.5

0.311 4.7 0.320 12.5 0.336 19.0 0.358 24.5 0.384 28.9 0.415 32.6 0.449 35.5 0.486 37.8 0.525 39.7 0.565 41.1 0.607 42.2 0.649 43.0

0.693 43.6 0.736 44.0

0.781 44.3 0.825 44.6

0.870 44.7 0.914 44.9 0.959 45.0

1.004 45.1 1.050 45.3

1.095 45.5

1.141 45.7

1.187 46.0

1.233 46.4

1.279 46.8

1.326 47.3 1.374 47.8

1.422 48.3

1.471 49.0

1.520 49.6

1.570 50.3

1.621 51.1 1.672 51.9 1.724 52.7

1.778 53.5

1.831 54.4 1.886 55.2

1.942 56.1 1.999 57.0 2.056 57.9 2.114 58.8 2.173 59.6 2.234 60.5 2.294 61.3 2.356 62.1 2.419 62.9

2.482 63.7

2.546 64.5 2.611 65.2 2.677 65.9 2.743 66.6 2.810 67.2 2.877 67.8 2.945 68.4 3.014 69.0

T E K F

M

60 82.49

61 85.53

62 88.65

63 91.84

64 95.10

65 98.43

66 101.83

67 105.30

68 108.85

69 112.46

70 116.15

71 119.92

72 123.75

73 127.66

74 131.65

75 135.71

76 139.84

77 144.05

78 148.33

79 152.68

80 157.12

81 161.62

82 166.21

83 170.87

84 175.60

85 180.41

86 185.30

87 190.26

88 195.30

89 200.42

90 205.62

91 210.89

92 216.24

93 221.66

94 227.17

95 232 • 75 96 238.41

97 244. 14 98 249.96

99 255.85

100 261 .83

101 267.88

102 274.01

103 280.22

104 286.51

105 292.87

106 299.32

107 305.85

108 312.45

109 319.14

110 325.90

111 332.75

112 339.67

113 346.68

114 353.77

115 360.93

116 368.18

117 375.50

118 382.91

119 390.39

120 397.96

s ds/dT

pV/K nV/K2

3.014 69.0 3.083 69.5 3.153 70.0 3.223 70.5 3.294 70.9

3.365 71.3 3.437 71.7

3.509 72.1 3.581 72.5 3.653 72.8 3.726 73.1 3.800 73.4 3.873 73.7 3.947 73.9 4.021 74.2 4.095 74.4 4.170 74.6 4.245 74.8 4.319 75.0 4.395 75.2 4.470 75.4 4.545 75.6 4.621 75.8 4.697 76.0 4.773 76.1 4.849 76.3 4.926 76.5 5.002 76.6 5.079 76.8 5.156 77.0 5.233 77.1 5.310 77.3 5.387 77.5 5.465 77.6 5.543 77.8 5.620 77.9 5.698 78.1 5.777 78.2 5.855 78.4 5.933 78.5 6.012 78.7 6.091 78.8 6.170 79.0 6.249 79.1 6.328 79.2 6.407 79.4 6.487 79.5 6.566 79.6 6.646 79.7 6.726 79.8 6.805 79.9 6.885 79.9 6.965 80.0 7.045 80.0 7.125 80.1 7.205 80.1 7.285 80.1 7.366 80.1 7.446 80.1 7.526 80.1 7.606 80.0

TK

EMv

120

121

122

123 124

397.96

405.60 413.33 421.14

429.02

125 126

127

128 129

436.99

445.03 453.16 461.36

469.64

130

131

132 133 134

478.01 486.45 494.97

503.57

512.25

135

136 137

138 139

521.00

529.83 538.75

547.74

556.80

140

141 142 143 144

565.95

575.17

584.46

593.84 603.29

145

146 147

148 149

612.81

622.42 632.09

641.85 651.67

150

151 152 153 154

661.58

671.55 681.60

691.73

701.93

155

156 157

158 159

712.20

722.54 732.96

743.45

754.02

160

161 162

163 164

764.65

775.36 786.14

797.00

807.92

165

166

167

168 169

818.92 829.98

841.12 852.33

863.61

170

171 172

173

174

874.95

886.37

897.86

909.42

921.05

175

176

177

178 179

932.75

944.51

956.35

968.25 980.23

180 992.27

s ds/dT

/aV/k nv/K 2

7.606 80.0 7.686 80.0 7.766 79.9

7.846 79.9

7.926 79.8 8.005 79.7

8.085 79.6 8.164 79.4 8.244 79.3 8.323 79.2

8.402 79.0 8.481 78.8 8.560 78.6 8.638 78.5 8.717 78.3 8.795 78.1 8.873 77.8 8.950 77.6 9.028 77.4

9.105 77.2 9.182 76.9 9.259 76.7 9.336 76.5 9.412 76.2 9.488 76.0 9.564 75.7 9.640 75.5 9.715 75.2 9.790 75.0 9.865 74.7 9.939 74.5 10.014 74.2 10.088 74.0 10.162 73.8

10.235 73.5 10.309 73.3

10.382 73.1 10.455 72.8 10.528 72.6

10.600 72.4

10.673 72.2 10.745 72.0

10.816 71.8 10.888 71.5

10.960 71.3 11.031 71.1 11.102 70.9

11.173 70.7

11.243 70.5 11.314 70.3 11.384 70.1 11.454 69.9

11.524 69.7

11.594 69.5 11.663 69.3

11.732 69.1 11.801 68.9

11.870 68.7

11.938 68.4

12.007 68.2

12.075 67.9

44
Table 27. Type Ag-28 at% Au versus KN—thermoelectric voltage, E(T) , Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) —Continued

T E S ds/dT

K fj.V/K nv/K 2

180 992.27 12.075 67.9

181 1004.38 12.143 67.7

182 1016.55 12.210 67.4

183 1028.80 12.277 67.1

184 1041.11 12.344 66.8

T E 5 ds/dT

K /AV /iV/K n V/K 2

240 1825.04 15.443 46.5

241 1840.51 15.490 46.2

242 1856.02 15.536 46.0

243 1871.58 15.582 45.7

244 1887.19 15.627 45.4

T E S dS/dT

K fJ-V /J.V/K nV/K 2

185 1053.48

186 1065.93

187 1078.44

188 1091.02

189 1103.66

190 1116.37

191 1129.14

192 1141.97

193 1154.87

194 1167.84

195 1180.87

196 1193.96

197 1207.11

198 1220.32

199 1233.60

200 1246.94

201 1260.33

202 1273.79

203 1287.31

204 1300.89

205 1314.52

206 1328.21

207 1341.96

208 1355.77

209 1369.63

210 1383.55

211 1397.53

212 1411.55

213 1425.64

214 1439.78

12.411 66.5

12.477 66.2 12.544 65.9

12.609 65.6

12.675 65.2 12.740 64.8 12.804 64.5 12.869 64.1 12.932 63.7

12.996 63.2 13.059 62.8

13.122 62.4 13.184 61.9

13.245 61.5

13.307 61.0

13.367 60.5 13.428 60.0

13.487 59.5 13.547 59.0 13.605 58.5 13.664 58.0

13.721 57.4

13.778 56.9 13.835 56.4

13.891 55.9 13.947 55.4

14.002 54.9 14.057 54.4

14.111 53.9 14.164 53.4

245 1902.84

246 1918.53

247 1934.27

248 1950.05

249 1965.88

250 1981.75

251 1997.66

252 2013.62

253 2029.61

254 2045.64

255 2061.71

256 2077.82

257 2093.97

258 2110.15

259 2126.37

260 2142.62

261 2158.90

262 2175.21

263 2191.55

264 2207.92

265 2224.32

266 2240.74

267 2257.19

268 2273.66

269 2290.16

270 2306.69

271 2323.24

272 2339.82

273 2356.43

274 2373.08

15.672 45.0 15.717 44.5

15.761 44.1 15.805 43.5

15.848 42.9

15.891 42.2

15.933 41.4

15.974 40.6 16.014 39.7

16.053 38.7

16.091 37.7

16.128 36.6 16.164 35.4 16.199 34.2 16.233 33.0

16.265 31.8 16.296 30.6 16.326 29.4 16.355 28.3 16.383 27.3 16.410 26.4 16.436 25.8 16.462 25.4

16.487 25.4

16.512 25.8 16.539 26.7

16.566 28.2 16.595 30.4 16.627 33.5 16.663 37.5 215 1453.97

216 1468.21

217 1482.51

218 1496.86

219 1511.26

14.218 52.9 14.270 52.5 14.323 52.1 14.374 51.6 14.426 51.2275 2389.76

276 2406.48

277 2423.26

278 2440.09

279 2456.99

16.703 42.7

16.748 49.2

16.801 57.2 16.863 66.9

16.936 78.6

220 1525.71

221 1540.21

222 1554.76

223 1569.37

224 1584.02

225 1598.72

226 1613.47

227 1628.27

228 1643.12

229 1658.02

14.477 50.8 280 2473.97 17.021 92.4

14.528 50.5 14.578 50.1 14.628 49.8 14.678 49.5 14.727 49.2

14.776 49.0

14.825 48.7

14.873 48.5

14.922 48.3

230 1672.97

231 1687.96

232 1703.00

233 1718.09

234 1733.23

235 1748.41

236 1763.65

237 1778.93

238 1794.25

239 1809.63

24Q 1825.04

14.970 48.1

15.018 47.9

15.066 47.8

15.114 47.6

15.161 47.5

15.209 47.3

15.256 47.2 15.303 47.0

15.350 46.9

15.397 46.7

15.443 46.5

45
Table 28. Type TP versus Ag-28 at% Au

thermoelectric voltage, E(T) , Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T)

T E K

0 -1 39

1 -1

19

2 -1. 03

3 -0. 91 4 -0< 82

5 -0< 76

6 -0. 71

7 -0. 68

8 -0. 65

9 -0< 63

10 -0. 59

11 -o« 55

12 -0. 48

13 -o. 39

14 -0 < 2

15 -0< 1

16 Oi 07

17 0. 31

18 0. 59

19 0< 93

20 1

31 21 1 75 22 2. 25 23 2, 81 24 3. 43

25 4 10 26 4i 84 27 5. 64 28 6< 51 29 7< 43

30 8, 42

31 9, 46

32 10, 56 33 11, 72 34 12 94

35 14, 20 36 15, 52 37 16. 89 38 18, 31 39 1 9 < 77

40 2 1

28 41 22, 8 3 42 24, 42 43 26, 04 44 27, 70

45 29 39 46 31 1 1 47 32 86 48 34 ,64 49 36 44

50 38 26

51 40 10 52 41 95 53 43 82 54 45 71

55 47 .61 56 49 52 57 51 .44 58 53 37 59 55 .30

60 57.24

S <JS/dT

/J.V/K nV/K2

0.222 -46.0

0.178 -41.9

0.138 -36.9

0.104 -31.4

0.076 -25.4

0.054 -19.1 0.038 -12.6

0.028 -6.1 0.026 0.4 0.029 6.8 0.039 12.9 0.055 18.8 0.077 24.4 0.104 29.7 0.136 34.6 0.173 39.1 0.214 43.2 0.259 46.8 0.307 50.1 0.359 52.9 0.413 55.3 0.469 57.3 0.528 58.9 0.587 60.1 0.648 61.0 0.709 61.5 0.771 61.7

0.832 61.5 0.894 61.1 0.954 60.4

1.014 59.5

1.073 58.3

1.131 57.0 1.187 55.4

1.242 53.7

1.294 51.9 1.345 49.9

1.394 47.9

1.441 45.8

1.486 43.6

1.528 41.4

1.568 39.1 1.606 36.8

1.642 34.5 1.675 32.3 1.707 30.0 1.736 27.8

1.762 25.7

1.787 23.6

1.809 21.5 1.830 19.5 1.848 17.6 1.865 15.8 1.880 14.0 1.893 12.3 1.905 10.7 1.915 9.2

1.923 7.8

1.930 6.5 1.936 5.3

1.941 4.2

T E K

60 57.24

61 59.18

62 61.13

63 63.08

64 65.03

65 66.97

66 68.92

67 70.87

68 72.82

69 74.77

70 76.71

71 78.65

72 80.59

73 82.52

74 84.45

75 86.38

76 88.30

77 90.22

78 92.13

79 94.04

80 95.95

81 97.86

82 99.76

83 101.65

84 103.55

85 105.44

86 107.32

87 109.21

88 111.09

89 112.96

90 114.84

91 116.71

92 118.59

93 120.46

94 122.32

95 124.19

96 126.05

97 127.92

98 129.78

99 131.64

100 133.50

101 135.36

102 137.22

103 139.08

104 140.94

105 142.80

106 144.66

107 146.52

108 148.38

109 150.24

110 152.10

111 153.96

112 155.82

113 157.68

114 159.55

115 161.41

116 163.27

117 165.14

118 167.00

119 168.87

120 170.74

S ds/dT

^.v/tc nv/K2

1.941 4.2 1.945 3.1 1.947 2.1 1.949 1.3 1.950 0.5 1.950 -0.3

1.949 -0.9

1.948 -1.5

1.946 -2.0

1.944 -2.4

1.942 -2.8

1.939 -3.1

1.935 -3.3

1.932 -3.5

1.928 -3.7

1.925 -3.8

1.921 -3.8

1.917 -3.9

1.913 -3.9

1.909 -3.8

1.906 -3.8

1.902 -3.7

1.898 -3.6

1.895 -3.4

1.891 -3.3

1.888 -3.1

1.885 -3.0

1.882 -2.8

1.880 -2.6 1.877 -2.4

1.875 -2.3

1.872 -2.1

1.870 -1..9 1.869 -1.7

1.867 -1.5

1.866 -1.4

1.864 -1.2

1.863 -1.0

1.862 -0.9

1.861 -0.7

1.861 -0.6

1.860 -0.5

1.860 -0.3

1.859 -0.2

1.859 -0.1

1.859 -0.0

1.859 0.1 1.859 0.2 1.860 0.3 1.860 0.4 1.860 0.5

1.861 0.5 1.861 0.6

1.862 0.7

1.863 0.8 1.864 0.8 1.864 0.9 1.865 1.0 1.866 1.1 1.867 1.1

1.869 1.2

TKEMv

120

121

122 123 124

170.74

172.61 174.48

176.35

178.22

125

126

127

128 129

180.10

181.98

183.85

185.73

187.62

130

131

132

133 134

189.50

191.39

193.28 195.17

197.06

135

136 137

138 139

198.96 200.86

202.76 204.67

206.57

140

141 142

143 144

208.49

210,40

212.32

214.25 216.17

145

146 147

148 149

218.11 220.04

221.98

223.93 225.88

150

151 152

153 154

227.83

229.79

231.76

233.73

235.71

155

156

157

158 159

237.69

239.68 241.67 243.67

245.67

160 161

162 163 164

247.69

249.70

251.73

253.76 255.79

165 166 167

168 169

257.84

259.89

261.94

264.00

266.07

170

171

172 173 174

268.15 270.23

272.32

274.41

276.52

175 176 177

178

179

278.62 230.74

282.86

'284.99 287.12

180 289.26

S dS/dT

/tiV/K nv/K2 1.869 1.2 1.870 1.3 1.871 1.4 1.873 1.5 1.874 1.6 1.876 1.7 1.878 1.8 1.879 1.9 1.881 2.0 1.883 2.1 1.885 2.2 1.886 2.3 1.890 2.5 1.893 2.6 1.895 2,7

1.898 2.9 1.901 3.0 1.904 3.1 1.907 3.3 1.911 3.4 1.914 3.6 1.918 3.7 1.922 3.9 1.926 4.1 1.930 4.2 1.934 4.4

1.938 4.5

1.943 4.7

1.948 4.8

1.953 4.9 1.958 5.1 1.963 5.2 1.968 5.4 1.974 5,5 1.979 5.6 1.985 5.7 1.990 5.8 1.996 5.9 2.002 6.0 2.008 6.1 2.014 6.2 2.021 6.2 2.027 6.3 2.033 6.4

2.040 6.4

2.046 6.5 2.053 6.5 2.059 6.5 2.066 6.5 2.072 6.6 2.079 6.6 2.085 6.6 2.092 6.6 2.098 6.6 2.105 6.6 2.112 6.5 2.118 6.5 2.125 6.5 2.131 6.5 2.138 6.5 2.144 6.5

16
Table 28. Type TP versus Ag-28 al% Au

thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T) —Continued

T1 dS/dT T e

K fJiV/K nv/K2 K fI.V /i.V/K

160 289.26 2 • 144 6.5 240 431.13 2 .608

1 o i 1 O 1 291.41 2*151 6.5 241 433 . 74 2.615

182 293 . 56 2 • 1 57 6.4 242 436 .36 2.621

1 83 295.72 2 . 163 6.4 243 436.98 2 .628

184 297.89 2.170 6.4 244 441.61 2.634

18 5 300 06 2 • 1 76 6.4 245 444 .25 2 . 640

1 86 302 • 24 2.183 6.4 246 446 .89 2 .647

187 304.43 2 o 189 6.4 247 449 .54 2 .653

188 306.62 2 .196 6.4 248 452.20 2.659

189 308.82 2.202 6.5 249 454.86 2.665

190 311.03 2.209 6.5 250 457.53 2.672

191 313.24 2.215 6.5 251 460 .21 2 .678

192 315.46 2.222 6.6 252 462. 89 2.685

193 317.68 2 .228 6.6 253 465 . 58 2 . 692

194 319.91 2.235 6.7 254 468.27 2.700

195 322. 15 2 • 24

6.7 255 470 .98 2 .708

1 Of. 1 TO 324. 39 2 • 248 6.8 256 473 . 69 2 .716

1 0"7 17 f 326.65 2 .255 6.9 257 476 .41 2 . 725

198 328.90 2 .262 7.0 258 479. 14 2 . 734

199 331.17 2.269 7.0 259 481.88 2.744

200 333. 44 2 . 276 7.1 260 484 « 63 2.755

201 3 35. 72 2.283 7.2 261 487 * 39 2 . 766

202 338.01 2.291 7.4 262 490 . 16 2 .777

203 340. 30 2.298 7.5 263 492 .94 2 . 790 204 342.61 2.306 7.6 264 495.74 2.802

205 344. 91 2.313 7.7 265 498. 55 2.815

206 347.23 2.321 7. 8 266 501 .37 2 • 829

207 349. 56 2.329 8.0 267 504.20 2 . 842

208 351. 89 2 .337 8.1 268 507 .05 2.855

209 354.23 2.345 8.2 269 509.91 2.868

210 356. 58 2 .353 8.3 270 512.79 2 . 879

211 358.94 2. 362 8.4 271 515.67 2 . 890

2 12 361. 30 2 .370 8.6 272 5 18.57 2 . 899 213 363.68 2.379 8.7 273 521 .47 2. 905 214 366.06 2.387 8.8 274 524.37 2.908

215 368.45 2.396 8.9 275 527.28 2 .908 216 370. 85 2.405 8.9 276 530. 19 2.902

217 373.26 2.414 9.0 277 533.08 2. 890 218 375.68 2.423 9.1 278 535.97 2.871

219 378.11 2.432 9.1 279 538.82 2.843

£ £ U 380.55 2 .44

9.1 280 541 .65 2 . 804

221 382 • 99 2 .451 9.2

222 385.45 2 .460 9.2

223 387.91 2 .469 9.1 224 390.39 2.478 9.1 225 3 92 . 87 2 .487 9.1 226 395 . 36 2 .496 9.0

227 397 . 86 2.505 8.9 228 400 .37 2 .514 8.8 229 402.89 2.523 8.7 405.42 2.531 8.6

231 407.95 2 • 540 8.4

232 410.50 2.548 8.2

233 413.05 2 .556 8.1 234 415.61 2.564 7.9 235 418.18 2.572 7.7

236 420.75 2.580 7.5 237 423.34 2.587 7.3 238 425.93 2.594 7.1 239 428.52 2.601 6.9

240 431.13 2.608 6.8

dS/dT T E S ds/dT nv/«2 k fj.v fiV/K nv/K2

6.8 6.6

6.5

6.3

6.3

6.2

6.2 6.2

6.2 6*4

6.5 6.7

7.0 7.3

7.7

8.1 8.6

9.1 9.7

10.2

10.8 11.4 11.9

12.4 12.9

13.2

13.3

13.3 12.9

12.3

11.2 9.7

7.7 4.9

1.4 -3.1

-8.6 -15.3 -23.4

-33.1 -44.6

47
Table 29. Type Pt versus Ag-28 at% Au

thermoelectric voltage, E(T), Seebeck coefficient, S(T), and derivative of the Seebeck coefficient, dS(T)

1 K

n 0.00

1 -1.11

2 -1 .99

3 -2.63

-3.07

5 -3.31

6 -3.36

7 -3.23

8 -2.92

9 -2.45

10 -1.81

11 -1.01

12 -0.04

13 1.08

14 2.37

15 3.82

16 5.43

17 7.20

18 9.13

19 11.23

2n 13.48

21 15.90

22 18.48

23 21.22

24 24.13

25 27.19

26 30.41

27 33.79

28 37.33

29 41.02

30 44.86

31 48.85

32 52.99

33 57.27

34 61.69

35 66.24

36 70.93

37 75 • 74

38 80.68

39 85.73

40 90.90

41 96. 18 42 101.56

43 107.04

44 112.62

45 118.29

46 124.04

47 129.87

48 135.77

49 141.75

50 147.79

51 153.88

52 160.03

53 166.23

54 172.48

55 178.76

56 185.08

57 191.43

58 197.80

59 204.20

60 210.61

S ds/dT

-1.242 264.1 -0.989 242.6 -0.756 224.6 -0.539 209.7 -0.336 197.6 -0.143 187.8 0.041 180.0 0.217 174.0 0.389 169.4 0.557 166.1 0.721 163.7 0.884 162.2

1.046 161.3 1.207 160.9

1.368 160.8 1.529 161.0

1.690 161.3

1.851 161.6

2.013 161.9 2.175 162.2 2.337 162.2 2.500 162.1 2.662 161.8 2.823 161.2 2.984 160.3 3.144 159.1 3.302 157.7 3.459 155.9 3.614 153.9 3.767 151.5 3.917 148.8 4.064 145.9 4.208 142.7 4.349 139.2 4.487 135.6 4.620 131.6 4.750 127.5 4.875 123.2 4.996 118.7

5.113 114.1 5.225 109.4

5.332 104.5 5.434 99.6

5.531 94.6

5.623 89.5 5.710 84.4 5.792 79.3 5.868 74.2 5.940 69.1 6.007 64.0 6.068 59.0 6.125 54.0 6.176 49.1 6.223 44.3

6.265 39.5 6.302 34.9 6.334 30.3 6.363 25.9 6.386 21.5 6.406 17.3 6.421 13.2

TK

60 210.61

61 217.04

62 223 .48 63 229.92

64 236.36

65 242.80

66 249.24

67 255.67

68 262.06

69 268.49

70 274.87

71 281 .24

72 287.58

73 293.89

74 300.18

75 306 .44 76 312.67

77 318.86

78 325.02

79 331.13

80 337.21

81 343 . 25 82 349.25

83 355 .20 84 361.11

85 366 . 97

86 372.79

87 378.55

88 384.27

89 389.93

90 395 . 55 91 401 • 1

Q9 406.62

94 417.48

95 422 .82 96 428 .12 97 433.35

98 438.53

99 443.66

100 448 • 72 101 453.73

102 458.68

103 463.58

104 468.41

105 473.19

106 477.91

107 482.57

108 487.17

109 491.71

110 496. 19

111 ill con - ft

112 504.97

113 509.27

114 513.51

115 517.69

116 521.82

117 525.88

118 529.88

119 533.82

120 537.70

S ds/dT

/iV/K nV/K2 6.421 13.2 6.432 9.3 6.440 5.5 6.443 1.8 6.443 -1.8

6.440 -5.2

6.433 -8.5

6.423 -11.6

6.410 -14.6

6.394 -17.5

6.375 -20.2 6.353 -22.8 6.329 -25.3

6.303 -27.7

6.274 -29.9

6,243 -32.0

6.210 -34.0

6.175 -35.9

6.138 -37.7

6.100 -39.3

6.060 -40.9

6.018 -42.4

5.975 -43.8

5.930 -45.1

5.885 -46.3

5.838 -47.4

5.790 -48.5

5.741 -49.5

5.691 -50.4

5.640 -51.2

5.588 -52.0

5.536 -52.8

5.483 -53.5

5.429 -54.1

5.375 -54.7

5.320 -55.2

5.264 -55.7

5.208 -56.2

5.152 -56.6

5.095 -57.0

5.038 -57.4

4.980 -57.7

4.923 -58.0

4.864 -58.3

4.806 -58.6 4.747 -58.8

4.688 -59.0 4.629 -59.2

4.570 -59.4

4.511 -59.5

4.451 -59.7

4.391 -59.8

4.331 -59.9

4.272 -60.0

4.211 -60.1

4.151 -60.1

4.091 -60.2

4.031 -60.2

3.971 -60.2

3.911 -60.3

3.850 -60.3

TK

E

/iV

120

121 122

123 124

537.70

541.52 545.28

548.98

552.62

125

126

127

128 129

556.20

559.72

563.18 566.58

569.92

130

131 132

133 134

573.20

576.42 579.58

582.68

585.72

135 136

137

138 139

588.71 591.63 594.50

597.30 600.05

140

141 142

143 144

602.75

605.38

607.96 610.47

612.94

145 146

147

148

149

615.34

617.69

619.98

622.22 624.40

150

151 152

153 154

626.52

628.59

630.61 632.57

634.47

155

156 157

158 159

636.32

638.12 639.86

641.56

643.19

160

161 162

163 164

644.78

646.31 647.79

649.22 650.60

165

166 167

168 169

651.92

653.20

654.42 655.59

656.72

170

171

172 173

174

657.79

658.81 659.78

660.71 661.58

1 75 176 177

178 179

66 2.41 663.18

663.91

• 664.59

665.22

180 665.81

s ds/dT

/J.V/K nv/K2

3.850 -60.3

3.790 -60.2

3.730 -60.2

3.670 -60.2

3.609 -60.1 3.549 -60.1 3.489 -60.0

3.429 -59.9

3.370 -59.8

3.310 -59.7

3.250 -59.6

3.191 -59.4

3.131 -59.3

3.072 -59.1 3.013 -59.0

2.954 -58.8

2.895 -58.6

2.837 -58.4

2.779 -58.2

2.721 -58.0

2.663 -57.8

2.605 -57.6

2.548 -57.3

2.490 -57.1

2.433 -56.8

2.377 -56.6

2.320 -56.3

2.264 -56.1

2.208 -55.8

2.152 -55.5

2.097 -55.2

2.042 -55.0

1.987 -54.7

1.933 -54.4

1.878 -54.1

1.824 -53.8

1.771 -53.5

1.717 -53.3

1.664 -53.0

1.611 -52.7

1.559 -52.4

1.506 -52.2

1.454 -51.9

1.403 -51.6

1.351 -51.4

1.300 -51.1

1.249 -50.8

1.198 -50.6

1.148 -50.3

1.098 -50.1

1.048 -49.9

0.998 -49.6

0.948 -49.4

0.899 -49.2

0.850 -49.0

0.801 -48.7

0.752 -48.5

0.704 -48.3

0.656 -48.1

0.608 -47.9

0.560 -47.7

48
Table 29. Type Pt versus Ag-28 at% Au

thermoelectric voltage, E(T) , Seebeck coefficient, S(T) , anrf derivative of the Seebeck coefficient, dS(T) —Continued

J s ds/dT x s ds/dT

K /xV {J.V/K nv/K2 K Mv fj.V/K nV/K2

18q 665.81 0.560 -47.7 240 621.33 -1.915 -36.2

181 666 . 34 0.512 -47.5 241 619.39 -1.951 -36.1

182 666. 33 0.465 -47.3 242 617.43 -1 .987 -36.1

183 667.27 0.418 -47.1 243 615.42 -2.023 -36.0

184 667.67 0.371 -46.9 244 613.38 -2.059 -35.9

185 668.02 0.324 -46 • 7 245 611.30 -2.095 — 35.6

186 668. 32 0.277 -46. 5 246 609. 19 -2.131 -35.7

187 668.57 0,231 -46 . 3 247 607.04 — 2 . 166 -35.5

1 68 668 • 78 0.185 -46 .

248 604.86 — 2 . 202 —35 .4 189 668.94 0.139 -45.9 249 602.64 -2.237 -35.2

190 669.06 0.093 -45.7 250 600 .38 -2 . 272 -35.0

191 669. 13 0.047 -45. 5 251 598.09 -2.307 -34.7

192 669. 15 0.002 -45.3 252 595 . 77 -2 . 342 -34.5

193 669. 13 -0.043 -45. 1 253 593.41 -2.376 -34.2

194 669.07 -0.088 -44.9 254 591.02 -2.410 -33.8

195 668.95 -0. 133 -44. 7 255 588.59 -2 .444 -33.4

196 668.80 -0. 178 -44.4 256 586.13 -2.477 -33.0

197 668 . 60 -0.222 -44.2 257 583.64 -2.510 -32.6

198 668.36 -0.266 -44,0 258 581.11 -2.542 -32.2

199 668.07 -0.310 -43.8 259 578.55 -2.574 -31.7

200 667.74 -0.354 -43.5 260 575.96 -2.605 -31*1

201 667.36 -0.397 -43.3 261 573.34 -2.636 -30.7

202 666.94 -0.440 -43.0 262 570.69 -2.667 -30.2

203 666.48 -0.483 -42.8 263 568.01 -2.697 -29.8 204 665.98 -0.526 -42.6 264 565.30 -2.726 -29.4

205 665.43 -0.568 -42.3 265 562.55 -2.756 -29.0

206 664.84 -0.610 -42.0 266 559.78 -2.784 -28.8

207 664.21 -0.652 -41.8 267 556.99 -2.813 -28.6

208 663.54 -0.694 -41.5 268 554.16 -2.842 -28.6

209 662.82 -0.735 -41.3 269 551.30 -2.871 -28.9

210 662.07 -0.776 -41.0 270 548.42 -2.900 -29.3

211 661.27 -0.817 -40.7 271 545.50 -2.929 -30.1

212 660.43 -0.858 -40.5 272 542.56 -2.960 -31.2

213 659.55 -0.898 -40.2 273 539.58 -2.992 -32.7

214 658.63 -0.938 -40.0 274 536.57 -3.025 -34.7

215 657.68 -0.978 -39.7 275 533.53 -3.061 -37.3

216 656.68 -1.018 -39. 5 276 530 .45 -3. 100 -40.6

217 655.64 -1 .057 -39.2 277 527.33 -3. 143 -44.7

218 654.56 -1.096 -39.0 278 524. 16 -3, 190 -49.6

219 653.45 -1.135 -38.8 279 520.95 -3,242 -55.7

220 652.29 -1.174 -38.5 280 517.68 -3.302 -62.9

221 651.10 -1.212 -38.3

222 649.87 -1.251 -38.1

223 646.60 -1.289 -37.9

224 647.29 -1.326 -37.8

225 645.95 -1 .364 -37.6

226 644. 56 -1 .402 -37.4

227 643.14 -1 .439 -37.3

228 641.69 -1 .476 -37. i 229 640. 19 -1.513 -37.0

230 638.66 -1.550 -36.9

231 637.09 -1.587 -36.8

232 635.49 -1.624 -36.7

233 633.84 -1.660 -36.6

234 632.16 -1.697 -36.5

E s ds/dT

(1V/K2

235 630.45

236 628.70

237 626.91

238 625.09

239 623.22

240 621.33

-1.733 -36.5 -1.770 -36.4

-1.806 -36.3 -1.843 -36.3 -1.879 -36.2 -1.915 -36.2

49
50
Table 30. Orthonormal polynomials, F n (T)

F( 1) = 2. 62695799729*10"3 T

F( 2) = [ 3. 21 644559388*10" 5 T - 1. 1 1 69231 3742*1 0"2

] T

F( 3) = [( 3. 58994672085*1 0~7 T - 1 . 55668898366* 10

4

) T

+ 1 . 81 141779139*10" 2

] T

F( 4) = [( [5. 34771916750* 10

9 T - 3 . 0500 1 96765 3*1

O"6

] T

+ 5. 54667177985*10" 4

) T - 3. 34658422520*10" 2

] T

F( 5) = [ ( [ ( 6. 07172355876*10"n T - 4. 2 7432 761 2 50*1 0

8

) T

+ 1. 07134115475*10" 5

] T - 1. 13778202262*10" 3

) T +4. 64639951890*10" 2

F( 6) = [ ( [ ( [8. 82401710220*10"13 T - 7. 282 1 55 345 31 *1 0" 10

] T

+ 2. 24773793974*10" 7

) T - 3. 18955000427*10" 5

] T + 2 . 05440454443*1 0

" 3

- 5. 17932580803*10" 2

] T

F( 7) = [([([ (1 . 33824606626*10"14 T - 1 . 32028601 056*1 0" 11

) T

+ 5. 1325930551 1*10" 9

] T - 9. 9331 1925650*10" 7

) T + 9 . 9 1 984763 1 83*1 0

" 5

- 4. 75 613476303*10" 3

) T +8. 88013836676*10" 2

] T

F( 8) = [([([ ( [1 . 911 32074699 *10"16 T - 2. 1 6764477633*1 O"13

] T

+ 1. 003431 83849*1 O"10

) T - 2 . 43 62 753 6044*1 0" 8

] T + 3. 31 5 1 1 839 3 1 0*1 0" 6

- 2. 49812576663*10" 4

] T + 9 . 57751 308277*1 0" 3

) T - 1 . 5063295481 3*1 0" 1

F( 9) = [([([([ (2. 92699640234*10"18 T - 3. 70260683908*1 0"15

) T

+ 1. 95 728888009 *10-12

] T - 5. 6062 6859 32 6*1 0" 10

) T + 9. 43455906591*10" 8

- 9. 46059087662*10" 6

) T + 5 . 47509430874*1 0" 4

] T - 1 . 67843839799*10" 2 + 2. 24865631061*10" 1

] T

F(10) = [([([([( [3. 95878009884*10"20 T - 5. 60672761438*10"17

] T

+ 3. 38846529678*1

-14

) T - 1 . 140 1 7603261 *1 0"11

] T + 2. 33739535638*10" 9

- 3. 00235955099*10" 7

] T + 2. 39472835021*10" 5

) T - 1 . 1 3608914666*1 0" 3 + 2. 93503055072*10" 2

) T - 3. 465 77248522*1 0" 1

] T

F(ll) = [([([([( [(5. 38594950415*10"32 T - 8. 3244925 1443*1 O"19

) T

+ 5. 56752245363*10-16

] T - 2. 1 1 081 095546*1 O"13

) T + 4. 99305085248*1 O"11

- 7. 6453395 363 6*10" 9

) T + 7. 61 38831531 6*10" 7

] T - 4. 832 35 619795*10" 5 + 1. 86364817796*10" 3

] T - 4. 00502423767*10" 2

) T + 4. 09600033130*10" 1

F(12) = [([([([([( [8. 2625801 653 7*1 0"24 T - 1. 39945594083*1 O"20

] T

+ 1 . 03888019552*10"17

) T - 4. 441 03690669*1 0" 15

] T + 1.207998733131

- 2. 18091879863*10-10

] T + 2. 64614938335*10" 8

) T - 2. 13892665858

+ 1. 11908345512*10" 4

) T - 3. 59445386267*10" 3

] T +6.49375809159*

- 5. 70520840814*10" 1

] T

F(13) = [([([([([([ (1 . 25468717991*10"25 T - 2. 30116953479*10"22

) T

no

= 10'

^io-

-12

: 10"17

) T + 2. 72633781444*10"14 -lO"10

] t - 8. 14236157658*10" 8

: 10" 4 )T + 6. 83930829183*10" 3 ao- 1

] T

F(14) = [([([([([([( [1. 85361805469---10"27 T - 3. 661 1 8430728*1 0"24

] T

+ 3. 2351 121 9579*1 0"21

) T - 1 . 687749 68707*1 0" 18] T + 5. 77794561 728*10 -1S

:<10" 13

1 T + 2. 27608365626*1 O" 11) T - 2. 6981 7191 322*1 0" 9

+ 1. 87050454270*10"19

] T - 8.87619885518=:

- 5. 67992988009*10"12

) T + 8. 1 78858799751

+ 5. 51694463147*10" 6

] T - 2 . 461 3750201 7

=

- 1.08276043179*10" 1

) T + 8.45979503380*

- 1. 364681196971

+ 2. 258218783271

- 1. 241748548931

; 10" 7

) T - 1 . 30846653820*10" 5

] T + 5.06904044529*10"

10" 2

] T + 1. 76141425155*10" 1

) T - 1 . 25 341 332 333 ] T

51
Table 31. Orthonormal polynomial coefficients for thermocouple types T, E, K, Pt versus TP,

KP (or EP) versus Pt, and Pt versus KN; E = f(T)

Orthogonal

polynomial

coefficients

A,._.

A(l).

A (2). A (3). A (4). A(5).

A (6). A(7). A (8). A (9). A (10) A(ll)

A(12)

A(13)

A(14)

Thermocouple Type

T E K Pt versus TP KP versus Pt Pt versus KN

0 0 0.0 0 0 1.39 0 79 -0 22 10,673 449 16,803.073 11,244 719 -442.405 6572 181 4672 551 1,947 339 2,969.618 2,174 984 -695.540 1717 903 457 074 -158 363 -404.812 —297 765 -123.572 — 122 875 -174 884 44 549 65.116 5 348 107.723 -87 182 92 560 -34 604 -22.801 -4 536 -45.512 57 285 -61 819

11 028 3.257 -0 486 3.506 -11 373 10 886 -0 281 1.746 2 117 5.395 -3 425 5 557 -2 977 -1.931 -1 922 -4.032 5 110 -7 052

2 087 0.340 0 780 0.601 -2 236 3 026 -1 098 .107 -0 288 1.034 0 262 -0 555 -0 055 - .720 -1.055 445 587 558 .581 0.635 609 822

641

.430 -.348

Table 32. Orthonormal polynomial coefficients for thermocouple types Pt versus TN (or EN), KP (or EP) versus Ag-28 at% Au, Ag-28 at% Au versus KN, TP versus Ag-28 at% Au, Ag-28 at% Au versus TN (or EN), and

PT versus Ag-28 at% Au; E = f(T)

Orthogonal

polynomial

coefficients

Thermocouple Type

Pt versus TN KP versus Ag-28 AuAg-28 Au

versus KN

TP versus Ag-28 AuAg-28 Au

versus TN

PtAgversus

-28 Au

Ac 0.0 0 79 -0.22 -1 39 0.0 0.0

A(l) 10,230.996 6,956 840 4,287.892 827 064 9,846.336 384.659

A (2) 1,251.750 1,107 199 1,067.778 84 835 1,862.454 -610.705 A (3) -281.919 -246 253 -51.506 0 194 -158.541 123.378

A (4) 152.320 47 181 -41.803 26 640 17.957 134.363 A (5) -80.096 -12 833 8.299 -24 606 -9.978 -70.118

A (6) 14.588 -0 096 -0.391 7 771 3.310 11.277 A (7) 5.157 2 649 -.517 0 679 -0.917 6.074 A (8) -7.032 —2 283 .342 -3 361 .361 -7.393

A (9) 2.637 1 069 -.279 2 704 - .668 3.305

A(10) -0.111 -0 365 .072 -1 661 .516 -0.627

A(ll) -1.147 216 .074 0 394 - .486 -.661

A(12) 1.178 111 .102 085 .458 .720 A(13) -0.681 511 .511 511 -.170 - .511 A(14)

52
Table 33. Standard deviations (nV) of reduced order fits for thermocouple types T, E, K,

Pt versus TP, KP (or EP) versus Pt, and Pt versus KN; E = f(T)

Number

of

coefficients

Approximate Standard Deviation

T E K Pt versus TP KP versus Pt Pt versus KN

4 5 3 1 6

'8 9

5 - 1.6 0.6 0.5 1.1 1.7 2 6 0.7 .5 .4 1.0 0.9 1.2

7 ___________ .6 .4 .3 0.6 .8 1.0 8_ .4 .2 .13 .3 .4 0.4

9 .3 .19 .09 .2 .16 .18 1U __ _ .2 .18 .08 .19 .15 .17 11 .15 .15 .13 .13 .15 12 .13 .13 .10 .11 .10 13 .09 .12 14 .07

Table 34. Standard deviations (fiV) of reduced order fits for thermocouple types Pt versus TN (or EN), KP (or EP)

versus Ag-28 at% Au, Ag-28 at% Au versus KN, TP versus Ag-28 at% Au, Ag-28 at% Au versus TN (or EN),

and PtVersus Ag-28 at% Au; E = f(T)

Number

of

coefficients

Approximate Standard Deviation

Pt versus TN KP versus Ag-28 AuAg-28 Au

versus KN

TP versus Ag-28 AuAg-28 Au

versus TN

Pt versus Ag-28 Au

4 11 13 14 12 15 10

5 3 3 3 3 4 2

6 1.3 1.7 1.9 1.8 2 1.4

7 1.1 1.4 1.5 1.3 1.6 1.1 8 0.6 0.7 0.7 0.6 0.8 0.5

9 0.5 0.4 0.5 0.4 0.6 0.18

10 0.4 0.3 0.4 0.3 0.5 0.16

11 0.3 0.2 0.3 0.2 0.4 0.14

12 0.15 0.15 0.14 0.14 0.18 0.09

13 0.12 0.08 0.08 0.08 0.15 0.08

14 0.07 0.07 0.07 0.07 0.07

15 0.06 0.06 0.06 0.06 0.06

16 0.05 0.05 0.05 0.05 0.05

Table 35. Number of digits necessary in computations to reduce round-off errors below certain

limits for thermocouple types E, K, and T

Error criteria (microvolts)

Number of digits necessary for thermocouple

Type E Type K Type T

0.01

0.1

1 50

binary 3329

24

decimal 10

9

8

binary 2624

24

decimal 8

8

8

binary 38

3532

24

decimal 12

11108

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54
9. References

[1] MacDonald, D. K. C, Thermoelectricity: An Introduction

to the Principles, pp. 103-116 (John Wiley and Sons,

Inc., New York, London, 1962).

[2] Shenker, H., Lauritzen, J. I., Jr., Corruccini, R. J., and

Lonberger, S. T., Reference tables for thermocouples,

Nat. Bur. Stand. (U.S.), Circ. 561, 84 pages (1955).

[3] Brombacher, W. G., Johnson, D. P., Cross, J. L., Mercury

Barometers and Manometers, Nat. Bur. Stand. (U.S.), Monogr. 8, 59 pages (May 1960).

[4] Brickwedde, F. G., van Dijk, H., Durieux, M., Clement,

J. R., Logan, J. K., The 1958 He4 Scale of Temperatures,

Nat. Bur. Stand. (U.S.), Monogr. 10, 17 pages (June

1960).

[5] Sparks, L. L., and Powell, R. L., Calibration of Capsule Platinum Resistance Thermometers at the Triple Point

of Water, Fifth Symposium on Temperature, Washington, D.C., June 21-24, 1971. To be published in Temferature—Its Measurement and Control in Science and

ndustry 4, Ed. H. H. Plumb, (Instrument Society of America, Pittsburgh, Pennsylvania, 1972).

[6] Stimson, H. F., Precision Resistance Thermometry and

Fixed Points, Third Symposium on Temperature, Washington, D.C., October 28-30, 1954, Temperature—Its Measurement and Control in Science and Industry 2, Ed. H. C. Wolfe, (Reinhold Publishing Corp., New

York, 1955).

[7] Berry, R. J., The Temperature Time Dependence of the

Triple Point of Water, Can. J. Phys. 37, 1230-1248

(1959).

[8] Riddle, J. L., Notes to Supplement Resistance Ther- mometer Reports, Precision Measurement and Calibration. Selected NBS Papers on Temperature, Ed. J. F. Swindells, Nat. Bur. Stand. (U.S.), Spec. Publ. 300, Vol. 2, 150-1

(Aug. 1968).

[9] Hust, J. G;, Thermal Anchoring of Wires in Cryogenic

Apparatus, Rev. Sci. Instr. 41, 622-624 (1970).

[10] Brooks, P. P. B., Calibration of Mueller Thermometer

Bridge, Nat. Bur. Stand. (U.S.), Internal Report, 29

pages (1965).

[11] Tuttle, W. F., Connectivity in Graphs, (University of Toronto Press 1966).

[12] Youden, W. J., Measurement Agreement Comparisons,

Paper 5.1, Nat. Bur. Stand. (U.S.), Misc. Publ. 248, 254

pages (1963).

[13] Essam, J. W., and Fisher, M. E., Some Basic Definitions

in Graph Theory, Rev. Mod. Phys. 42, No. 2, 271-288

(April 1970).

[14] Hust, J. G., A compilation and Historical Review of Temperature Scale Differences, Cryogenics 9, No. 6, 443-455 (December 1969).

[15]

[16]

Bjorck, A., Solving Linear Least Squares Problems b Gram-Schmidt Orthogonalization, Bit, Nordi

for Informationsbehandling 7, 1-21 (1967).

sms by

idsprift

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

Powell, R. L., Hall, W. J., and Hust, J. G., The Fitting of Resistance Thermometer Data by Orthogonal Functions,

Fifth Symposium on Temperature, Washington, D.C., June 21-24, 1971. To be published in Temperature—Its Measurement and Control in Science and Industry 4, Ed. H. H. Plumb, (Instrument Society of America,

Pittsburgh, Pennsylvania, 1972). Finch, D. I., General Principles of Thermoelectric Ther- mometry, Fourth Symposium on Temperature, Columbus,

Ohio, March 27-31, 1961, Temperature—Its Measure- ment and Control in Science and Industry 3, Ed. A. I. Dahl, (Reinhold Publishing Corp., New York, 1962. Wilson, E. B., An Introduction to Scientific Research, 272-274 (McGraw-Hill Book Company, Inc., New York,

1952). Ku, H. H., Notes on the Use of Propagation of Error Formulas, J. Res. Nat. Bur. Stand. (U.S.), 70C (Eng. and

Instr.), No. 4, 263-273 (Oct.-Dec. 1966). Reference Base of the Volt to be Changed, Nat. Bur.

Stand. (U.S.), Tech. News Bull. 52, 204-206 (Sept. 1968).

International Practical Temperature Scale of 1968, Adopted by the Comite International des Poids et Messures, Metrologia 6, No. 2, 35-44 (April 1969). Bedford, R. E., Durieuz, M., Muijlwijk, R., and Barber,

C. R., Relationships Between the International Practical Temperature Scale of 1968 and the NBS-55, NPL-61,

PRMI-54, and PSU-54 Temperature Scales in the Range

from 13.81 to 90.188 K, Metrologia 5, No. 2, 47-49

(April 1969). Bedford, R. E., and Kirby, C. G. M., Notes on the Application of the International Practical Temperature Scale

of 1968, Metrologia 5, No. 3, 83-87 (July 1969). Rogers, J. S., Tainish, R. J., Anderson, M. S., and Swenson, C. A., Comparison Between Gas Thermometer,

Acoustic, and Platinum Resistance Temperature Scales Between 2 and 20 K, Metrologia 4, No. 2, 47-58 (April 1969). Plumb, H. H., and Cataland, G., Acoustical Thermometer

and the National Bureau of Standards Provisional Temperature Scale 2-20 (1965), Metrologia 2, No. 4, 127-139

(1966). NBS (U.S.), Internal Reports (1968-1969).

Manual on the Use of Thermocouples in Temperature

Measurement, Ed. R. P. Benedict, ASTM Special Technical Publication 470 (1970).

Appendix A. Standard des

ANSI, ASTM, and ISA (American National Standards Institute, American Society for Testing and

Materials, and Instrument Society of America, re- spectively) have adopted the following letter designations for thermocouples described in this monograph:

THERMOCOUPLE COMBINATIONS:

The positive thermoelectric material is conventionally written first.

Type E Nickel-chromium alloy versus coppernickel alloy.

nations for thermocouples

Type K Nickel-chromium alloy versus nickel- aluminum alloy.

Type T Copper versus copper-nickel alloy.

SINGLE-LEG WIRES:

N The negative wire in a combination.

P The positive wire in a combination.

EN or TN A copper-nickel alloy, often referred to

as Adams' constantan; Advance 1

, Cup- ron4

, nominally 55 wt% Cu, 45% Ni.
A nickel-chromium alloy, often referred

to as Chromel2

; T— 1\ ThermoKanthal

KP\ Tophel4

; nominally 90% Ni, 10%

Cr. A nickel-aluminum alloy, often referred

to as Alumel2

; T— 2

1

, ThermoKanthal

KN\ Nial4

; nominally 95% Ni, 2% Al,

2% Mn, 1% Si.

Copper, usually Electrolytic Tough

Pitch.

Registered Trademarks:

1 Trademark—Driver-Harris Co.

2 Trademark—Hoskins Manufacturing Co.

3 Trademark—Kanthal Corp.

4 Trademark—Wilbur B. Driver Co.

The use of trade names does not constitute an endorsement of any manufacturer's products. All materials

manufactured in compliance with the established

thermoelectric voltage standards are equally acceptable.

56

it U.S. GOVERNMENT PRINTING OFFICE: 1972 O—453-146
form NBS-114A (i-7i> U.S. DEPT. OF comm. 1 . PU B LIC AT ION OR R E PORT NO. 2. Gov't Accession BIBLIOGRAPHIC DATA NBSMN-124 N°'

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Reference Tables for Low- Temperature Thermocouples

5. Publication Date June 1972

6. Performing Organization Code

7. AUTHOR(S)

Larry L. Sparks, Robert L. Powell, and William J. Hall

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS , Boulder Labs

DEPARTMENT OF COMMERCE

Boulder, Colorado 80302

10. Project/Task/Work Unit No.

11. Contract/Grant No. R-45

12. Sponsoring Organization Name and AHdress Space Nuclear Propulsion Office, Cleveland Extension

NASA Lewis Research Center

21000 Brook Park Road

Cleveland, Ohio 44135

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) The experimental program to establish low-temperature reference tables for

the commonly used thermocouples has been completed. Details of the experimental

system, instrumentation, data analysis, error analysis, and materials tested are

given in order to allow the user to better evaluate and apply the results. The results

presented here include:

(1) Reference tables for thermocouple types E, K, and T, both as E = /(T) and

T = /(E). The shorter /(E) tables have a 0°C (273. 15 K) reference temperature while all other tables have a 0 K reference temperature.

(2) Reference tables for Pt and Ag - 28 at % Au vs the materials used in thermocouple types E, K, and T. These data are presented as E = /(T) only.

(3) Orthogonal polynomials and the associated coefficients necessary to generate the data with reduced order approximations.

(4) Power series coefficients for full precision reproduction of the reference

data.

The data presented in the E = /(T) tables cover the temperature range from 0 to 280 K

The T = /(E) tables cover the temperature ranges from 273. 15 K down to the lowest

temperatures allowed by table resolution.

17. KEY WORDS (Alphabetical order, separated by semicolons) „ . , ., , , -, • • j Cryogenics; homogeneity tests; liquid

helium; liquid hydrogen; liquid nitrogen; thermocouples.

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