Keithley 7057A User manual

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Model 7057A
Thermocouple Scanner Card
Instruction Manual
Contains Operating and Servicing Information
Publication Date: January 1992
Document Number: 7057A-901-01 Rev. D

WARRANTY
LIMITATION OF WARRANTY

SafetyPrecautions
The following safety precautioos should be obsewed before using this product and any asno-
ciated instrumcntatioo. Although some inrtromeots and accessories woold nonnally bo used
with nowhazardous voltages, there arc situations wberc hazardous conditions may be present.
This product is intended for use by qualified personnel who rccogoiu: shock hazards and are
familiar with tbc safety pnxaotions rcqoircd to avoid possible injuly. Read lbe operating it]-
formation carefully before using the product.
‘The types of product users arc:
Kesponsiblc body is tbe iodividunl or group responsible for the USCsod owinleoaoce of
equipment, for ensuring tlnt the equipment ia operated within its spccilications and operat-
ing limits, and for ensuring that operators are adequately trained.
Operators use the product for its intended function. Tbey most be trained in electrical safety
procedures and proper use of the iostrument. ‘lhey most be protected from electric shock and
~onmt with hazardous live circuits.
Maintenance personnel perform mutioe procedures oo the product to keep it operadog, for
example, setting the hoc voltage or replacing consumable materials. Maintenance proccdurcs
am dcacribed in the manual. The procedures explicitly state if the operator ~nay perform them.
Othcrwisc, they should be performed only by senice pcnonoel.
Service personnel are trained to work on live circuits, sod perfoonn safe installations sod re-
pairs of products. Ooly properly trained setvice personocl may perform installation and scr-
vice procedures.
Exercise extreme caution whco a shock hazard is present. Lethal voltage may be present on
cable coonector jacks or test fixtures. 111~American National Standards lostitute (ANSI)
stam that a shock hazard exists wheo voltage levels greater than 30V RMS, 42.4V peak, or
60VDC are present. A good safety practice is to expect that hazardous voltage is present
in any unknown circuit before measuring.
Users of this product must be protected fmm electric shock at all timer. The responsible body
must eosum thtatwets aw pwented a.cce~saod/orinsulatcd from every connection point. lo some
cases, conoectiuns most be exposed to potential buman cootact. Product usa io these circuo-
stances must be trained to protect themselves from the risk of electric shock. If the circuit is ca-
pable of operating at or abovc 1wO volts, no conductive part of the circuit may be exposed.
AY described in the Ioteroational Electratechnical Commission (IEC) Standard IEC 664, dig-
ital multimcter measuring circuits (e.g., Keifhley Models 175A, 199, 2OOQ,2COl, 2002, and
2010) are Installation Category II. All other instruments signal tennioals are Installation Cat-
egory I and must oat be conoected to mains.
Do not conoect switching cards directly to unlimited power circuits. They are inlendcd to bc
used with impedance limited sources. NEVER connect switching cards directly to AC mains.
Wheo conoccting sources to switching cards. iostall protective devices to limit fault current
sod voltage to tbc card.
Before operating ao instrument, make sure the line cord is connected to a properly grounded
power receptacle. Inspect the connecting cables, test leads, and jumpers for possible wear,
cracks, or breaks bcforc each oso.
For maximum safety, do not touch the product, test cables, or any other instrumcots while pow-
er is applied to the circuit under test. ALWAYS remove power from the entire test system sod
dischuge soy capxitors before: coooccting or disconnecting cables or jumpers, installing 01

removing switching cards. or making iotemtil chaogcs, socb as installing or nzmoviog jumpers.
Vu not touch soy object that could provide a con-cot path to tbc common side of the circuit
under test or power line (eatth) ground. Always make measurements witb dry hands while
standing oo a dly, insulated surface capable of withstanding tbc voltage bciog measured.
The instrument and accessories most be used in accordance with its specifications and op-
eratiog iostructioos or tbe safety of the equipment may be impaired.
Do not exceed the maximum signal levels of the instruments and accessories. as defined in
tbe speciticationr sod operatiog information, and es show on the instrument or test fixture
panels, or switcbiog cant.
When fores are used in a product, replace with same type sod rntiog forcootioued pmtectioo
against fire hazard.
Cbassir connections must only be used as shield coooectioos for me~suriog circoits, NOT as
safety eaflh ground connections.
If you are using II test fixture, keep the lid closed while power is applied to the device under
test. Safe operation requires tbe we of a lid interlock.
1ra@ screw is present, connect it to safety earth ground uaiog the wire recommended in
the user documentation.
The ! symbol on an iostroment indicates that the user should refer to the operating ill-
n
stmctions located io tbc manual.
The h symbol on al iostmment shows that it CNI source or IIICRIIUII: loo0 volts or more, ill-
eluding the combined etTect of normal ad common mode voltages. Use stiuldarrl safety precau-
lions to avoid pcrsooal cootect with these voltages.
TIE WARNING beading in Amanual enplaios dangers that might result in personal injury or
death. Always read the associated information wy carefully hcfore ptxformiog the indicated
pC"CCdU~C.
The CAUTION beading in a manual explains hazards that could damage the instrument.
Such damage may invalidate the warrmty.
lostrumcntatioo and accessories shall not be connected to humans.
Before performing any maintenance, disconnect the line cord and all test cables.
To maintain pmtcctioo from electric shock and ftre, replacement components in mains cir-
coils, including the power transfouner, test leads, and ioput jacks, must he purchased from
Keithley Instruments. Standard fuses, with applicable national safety appmvals, may be used
if the ratiog sod type are the same. Other components that are not safety r&ted may hc por-
chased from other suppliers as long as they are equivalent to tbe original component. (Note
that selected parts should be purchased only through Keithley Iostmmcnts to maiotain acco-
racy sod fonctiooality of the product.) If you we unsure about the applicability of a replacc-
ment component, call a Keithlcy Instruments office for information.
To clean an instrument. use a damp cloth or mild, water based cleaner. Clean the exterior
of the instrument only. Do not apply cleaner directly tb the instrument or allow liquids to
enter or spill on the instrument. Products that consist of a circuit hoard with no case or cbas-
sis (e.g., data acquisition board for installation into a computer) should neverrequire clean-
ing if handled according to instructiuns. If the board becomes contaminated sod operation
is affected. the hoard should he returned to the factory for proper cleaninglserviciog.
tie”. 2rB

SPECIFICATIONS
CHANNELS PER CARD: 9 plus temperature reference.
CONTACT CONFIGURATION: 2 Pole Form A with common guard.
CONNECTOR TYPE: Screw terminals in isothermal block, No. 18 AWG wire
maximum.
RELAY DRIVE CURRENT: 12mA lper relay).
TEMPERATURE OFFSET: i0.05°C maximum from HI to LO of any input or be-
tween any two adjacent channels in one column on the isothermal block. * O.lOC
maximum between an two ferminals on the isothermal block. Maximum addi-
tional dynamic offset Jue fo 10°C step chsngo in environment: *O.l°C after one
hour settling.
TEMPERATURE REFERENCE: Thermistor in a linearized bridge.
REFERENCE OUTPUT: - ,m”,°C, ,Om” at +3O”CI.
REFERENCE ACCURACY: f0.2S°C ,,O’=C to 35OC,, +0.5OC
,O”C to 10% and 35°C to 60°Cl.
WARM UP TIME: 1 Hour to rated accuracy.
CONTACT OFFSET VOLTAGE: I,,“.
ACTUATION TIME: < 5ms, exclusive of mainframe.
CONTACT LIFE: > lo* cbs”res.
CONTACT RESISTANCE: < 2n (<O.,O inidall.
C”ANNEL ISOLATION: ‘109O. 1OpF.
INPUT ISOLATION: a 10’R. 15OpF.
COMMON MODE VOLTAGE: 200” peak.
ENVIRONMENT, SPECIFIED: ,O’=Cto 35°C. up to 70% R.H.
ENWRONMENTAL, OPERATING: O°C to 50°C, up to 35OC at 70% R.H.
ENVIRONMENTAL. STORAGE: -25OC to +55”C.
DIMENSIONS, WEIGHT: 32mm high x 114mm wide x 272mm long I1 %*’ x
4%“~ 10%“) net weight 0.54kg Illb. 5,502.).
Signaf Level: 42”. 1DDmA. 2VA maximum Inon-inductive load only).

1.1
1.2
1.3
1.4
2.3
2.4
2.5
2.6
2.7
3.1
3.2
3.3
3.4
3.5
4.1
4.2
4.3
4.4
4.5
:
3
4
ii
;
9
10
:
3
4
5
TABLE OF CONTENTS
SECTION l-GENERAL INFORMATION
Introduction .............................................
Warranty Information .....................................
ManualAddenda .........................................
Safety Symbols and Terms ................................
SECTION Z-OPERATION
Introduction ............................................
Wiring ...................................................
Operating Considerations,, ................................
Operating Hints ..........................................
Thermocouple Measurement Considerations, .................
Measurement Procedure ..................................
SwitchTerminology.. .....................................
SECTION 3-SERVICING INFORMATION
CalibrationProcedure., ...................................
CalibrationProcedures ....................................
Test of Calibration........................................
Channel Isolation,, .......................................
Input Isolation, Common Mode .............................
SECTION 4-REPLACEABLE PARTS
introduction, ............................................
ReplaceableParts ........................................
OrderingInformation .....................................
FactoryService ..........................................
Component Layoutand Schematic Diagram ..................
LIST OF FIGURES
TypicalThermocouple Connections .........................
Plug-In Board Assembly. ..................................
Using GUARD Connection.................................
Typical Multiple ChannelAnalog Connections. ...............
TypicalThermocouple Measurements ......................
Switch Terminology .....................................
Chsnnel~lsolationTest Setup ..............................
Common Mode IsolationTest Setup .......................
Model 7057A. Component Location Drawing ................
Model 7057A. Schematic Diagram .........................
LIST OF TABLES
Summary of Temperature Measurement Procedure ...........
NBS Quwtic Coefficientsfor Types S, R, B, E,J, K and T ......
Recommended Test Equipment. ...........................
Model 7057A Rep!aceab!eparts .: .... : .. : .,: ................
7
2:
23
Model 7057A Replaceable Parts,Mec”a”~ca,, 24
21
;1
21
22
23
ii
23
23
3
4
5
5
6
7
22
22
26
27

SECTION 1
GENERAL INFORMATION
1.1 INTRODUCTION
The Model 7057A isa thermocouplescannercardwhich isfield-installablein an
appropriatescanner mainframe (e.g. Model 7051. Since it combines the func-
tions of a thermocouple scanner and uniform temperature reference, it is
especiallyusefulfor scanningthermocouples.The inputterminalsaie HI0 alloy-
copper set in an isothermalblock to minimizetemperature differences. A ther-
mistorsensorwithin the isothermalblock is usedwith a bridge network located
on the Model 7057A to givean indicationof the temperature referenceor cold
junction. The temperature of the heat sink is used to calculate the corrected
thermocoupleoutput. The output voltagesof each thermocouple must be con-
verted to temperature PC or OF) using appropriate thermocouple tables or
polynomialequations. In addition any channel may be usedfor monitoringlow-
level signals. The Model 7057A uses Z-poleform A contacts for witching of
signalsup to 35V peak or IOOmApeak. Input and output connections818made
through the rearpanelof the scannermainframeusing#4screw terminalsonthe
Model 7057A.
1.2 WARRANTY INFORMATION
Warranty informationisstated onthe insidefront coverof the manual. If there is
a needfor service,contactthe Keithleyrepresentativeorauthorizedrepairfacility
in your area. Check the back cover of this manual for addresses.The service
form supplied at the end of this manual should be used to providethe repair
facilitywith adequate information concerningany difficulty.
1.3 MANUAL ADDENDA
Any improvementsor changesto this manualwill be explainedon an addendum
includedwith this manual.
1.4 SAFETY SYMBOLS AND TERMS
The symbol A denotes that the user should refer to the operating instruc-
i;;i;TbolN denotes that a high voltage may be present on the ter-
The WARNING used in this manual explains dangers that could result in
personal injury or death.
The CAUTION used in this manual explains hazardsthat could damage the
instrument.
1

SECTION 2
OPERATION
2.1 INTRODUCTION
This section provides information needed to use the Model 7057A with an
*ppropriate scanner mainframe.
2.2 WIRING AND INSTALLATION
1. Wiring Configuration-The Model 7057A has a Z-pole switching configura-
tion. It may be used to connect one of nine signalsto the output. The tenth
scannerposition(Channel 1) isused to monitorthe temperature of the input
terminals with a thermistor bridge. Bridge power is derived from a non-
isolatedinternalsupplywith jumper provisionsfor an externalisolatedsupply.
A. lnwt and output connectionsare made to the screw terminalsshown in
Fi& 1.
8. Signal path resistance,includingboth polesof a channelrelay, istypically
lessthan 1.4?, lessthan 2Q et end of life.
C. A guard surrounds 811signal paths and is connected to the heat sink
surroundingthe input terminals. Connection to the guard is made at the
isothermalblock.
2. Installation-Refer to the scannermainframe instructionmanual for scanner
instructions.
I
I-==
Figure 1. Typical Thermocouple Connections.
3

2.3 OPERATING CONSIDERATIONS
1. Signal Level-IOV peak, 1OmA peak with a resistiveload for expected life.
Maximum peak instantaneousrating is 35V.
2. Contact Potential (Laboratory Environment)-Less than I$/ from input to
output when copper wires are used.
3. Isolation-Guarded interchannel resitanceis nominally@!?. Guarded cap*-
citance is lessthan 1OOpFbetween any two channels.
4. Maximum Levels-A 2OOV peak between channels or from channel to
guard or mainframe (digital) common.
5. Operating Environment-OQC-50°C, up to 35°C at 70% relative humidity.
2.4 OPERATING HINTS
1. The clamp-type screw terminals will accept #I8 to #36 AWG (0.044 to
0.005 inch) wire. Figure 2 shows the mechanical features of the Model
7057A which prevent lead movement after the board is wired.
Figure 2. Plug-h Board Assembly
2. Thermal offset on any given channel is typically repeatable to within a few
hundred nanovolts each time the channel is selected. That is, every time a
channel isselected and allowed to stabilizefor a periodof time, the channel
will exhibit the same thermal offset to within a few hundred nanovolts. This
offset may be accounted for in the measurement and subtracted from each
reading, to obtain a more precise measurement.
3. To effectively eliminate error voltages produced by leakage current, the
GUARD terminal should be connected to the reference connection on the
channel which is most sensitive to error (that is, the one which has the
lowest source voltage versus the highest resistance). For instance. two
sources are connected to the Model 7057A; one having an equivalent
sourcevoltage of IV with a seriesresistanceof IOOkR and the other having
a source voltage of .lV with a lkn series resistance. The lOOka source
resistance will develop 100 times the error voltage as the lkn Knwze
resistance. Its source voltage however, is only 10 times as great. which
means that the percentage error is 10times as largeon the lV/lOOkn chan-
4

nel. The GUARD would therefore be connected to the reference point of
this channel. ISee Figure3).
Figure 3. Using GUARD Connection
4. The relayswitching time includesa 9&s time interval between releasesend
operate conditions. The actuation time is lessthan 5msec.
5. Reactances in the system cause transients during switching.
6. Forscannersystemsusing two or more plug-in boardsoutput HI and LO on
all Model 7057A plug-in boards should be made using continuous copper
wires. This ensures that the number of copper-to-copper junctions is at a
minimum and therefore unnecessarythermal effects are avoided. Figure 4
shows the method of continuous board-to-board connections.
Figure 4. Typical Multiple-Channel Analog Connections
2.5 THERMOCOUPLE MEASUREMENT CONSIDERATIONS
A thermocouple is B junction formed between two dissimilar metals. If the
junction temperature isT, a voltage E, will be developed between leads A and
B. When connected to Bvoltmeter two more junctions are formed with meter
terminals, which are usuallycopper as shown in Figure 5.

Figure 5. Typical Thermocouple Measurement
The voltage measured by the voltmeter is proponional to the difference be-
tween temperature T, and T2. To determine T,, T2the thermoelectric proper-
ties of the thermocouple are needed. Data isavailableto determine the voltage
versustemperature relationshipbased on a reference temperature IT*) of 0°C.
Thus, if the thermocouple-to-copper junctions were maintained at O°C it
would be possible to determine T, directly by referring to thermocouple
reference tables*, which give temperature as a function of the meter reading
V,. If these junctions are different from 0°C a voltage E2will be introduced,
where V, = E,-E,.
2.6 MEASUREMENT PROCEDURE
In the Model 7057A the reference temperatwre T is measured by a dual ther-
mistor in a bridge circuit. The temperature of a thermocouple connected to
Channels2 through 10 is determined by the following procedure:
1. Measure the voltage for the reference junction V and calculate Tz. T2 =
30-w, x 1031.
2. Determine the reference junction voltage, E2, either from thermocouple
reference tables’ or by the calculation**:
5 = a0+ A, T + a,p + aaT + a,,+ where T = T2 as determined in step 1
above. Q is expressed in microvolts. The constant a0 through a4 are a
function of the thermocouple type connected to the channel. The coeff-
CiWntS,aO,a,, a?, a3 and a4 are dependent on the thermocouple type and
temperature range under consideration.
3. Measure the thermocouple voltage V, at the channel output. Convert to
microvolts.
4. Add b to V, to determine E,. E,=V, +E, (where V, is expressed in
microvoltsl.
5. Determine the thermocouple temperature, T,, either from thermocouple
referencetables* or by calculation**:
TI = a, + %EI. + %E12r+ e,E? + %EI+ (where E, is expressedin microvoltsl.
6. For example, consider a type J iron-constantan thermocouple at 300°C
(T,I. The reference junction temperature will be 6 to 10°C above ambient,
say36% IT2).
A. The bridgeoutput ichannel II will be -.006V. Since the bridge output is
zero when T, = 30°C this indicatesT2 = 36OC.
B. Using NBS Monograph 125 to determine the referencevoltagefor a type
J thermocouple gives b 4 1649,[e-mail] the most accurate quark
approximation formula (Table 21for this range gives lB49.085@,
C. The voltage at Channel 1, which isV,, will be 14476,OpV. IV, = E,-b).
D. Add 6 to V, and get E, = 16325.0@,
6

E. Using Table A6.2.1 to find the thermocouple temperature gives
300.00°C. Using the formula (Table 2) gives299.995°C.
* Thermocouple Reference Tables, Based on the IPTS-66 National Bureau
Standards Monograph 125. (SD Catalog No. C13.44~1251
** See also Table 2 which summarizesthe quartic coefficients.
Table 1. Summary of Temperature Measurement Procedure
channel output V,.
Determine equivalent
Measured desired
Calculatecorrection
Quantity
V2
bLSl
F
VI
(volts)
Tz = 30-I!!, x 103)
lCalcuiat~~olt.age E,. ) -- 1 E, = E2 + V,.x-lO-” 1 mic~v,lts 1
Calculateequivalent T, = a, + a,E, + a,P, + T, IW
temperature TV. *Pl + Wl
2.7 SWITCH TERMINOLOGY
Throughout this manual the terminology Form A is used. The term Form A is
used in switch terminology and is described as follows:
1. Form A is simply a single pole normally open ISPNOI switch (refer to
Figure6). A Z-pole switch normally open is classifiedas 2 Form A.
2. Form B is similar to Form A except that its contacts are normally closed
(refer to Figure61. A Z-pole switch normallyclosed is classifiedas a 2 Form
B.
3. Form C is shown in Figure6 as a single pole double throw switch. It could
also be a multipole switch such as a Z-polewhich would be classifiedas a 2
Figure 6. Switch Terminology
7

1
16% to 176%
Reference Junction
Correction
” tn m
Table 2. NBS Quartic Coefficients for Types S. R. B. E. J. K. and T.
a0 =I =2 a3
Argument hp. Argument EXP. Arg”me”t Exp. Arg”ment EXP.
5.5439639
5.9791m
6.2516%!3
6.5554!232
Ma34421
8.7228147
9.5827994
9.4531354
2.9873073
3.4129348
6.4091373
3.9952876
*.co4320*
1.3532278
5.3994446 +o 1 I.2467754 -2
a4
Argument Exp.
Error
Range ILNV)
Exact-Approx.

c
I
4.1137317 +1
4.4507790 +1
4.1670535 + 1
-3.0938374 +1
z!2zm7 +7
1.3866867 +2
1.3923740 +2
4.6133695 +3
2.3131446 +4
-2.0241757 -5-2.0241757 -5
-m349c6, -5-m349c6, -5
-9.cl763455 -6-9.cl763455 -6
-7.0073775 -6-7.0073775 -6
-6.319500, -6-6.319500, -6
-1.8612979 -6-1.8612979 -6
-,.33496,, -6-,.33496,, -6
- I .6,62,80- I .6,62,80 - 6- 6
-4.9,94442 -6-4.9,94442 -6
-3.2873314 -6-3.2873314 -6
4.659nc8 -84.659nc8 -8
7.7266682 -87.7266682 -8
1.032002 -41.032002 -4
4.934,196 -44.934,196 -4

80
4rgumem Exp.
-4.0674108 +*
-5.mm84 +*
-5.4505828 +*
1.6618169 +3
1.5132838 +3
2.4m3703 +3
1.5787334 +3
-7.1904948 +4
8.8532076 14
a1
Zrgumenf Ex*.
5.4295008 +o
5.7622558 +o
6.1429772 +!I
6.4615269 +o
6.596212u+o
8.7490234+o
9.673111, +o
9.5942872 +o
2.3048626 +O
*.795%247 +o
4.1604579 -1
*.6321,44 +o
1.94423a3 +*
- ,.5014129 +*
1.1446885 -2
9.2715271 -3
7.1515857 -3
5.7010917 -3
5.1559203 -3
1.7115155 -3
-2.6994046 -4
-1.2813352 -4
8.7635426 -3
8.1571403 -3
1.0549178 -2
8.31co314 -3
- 1.7913090 - 1
9.5376167 -2
-1.1295306 -5
-7.1346883 -6
-3.7639447 -6
-1.8683292 -6
-1.2385309 -6
7.5039035 -7
2.5536988 -6
2.4468512 -6
-2.3016?318 -6
-1.9701159 -6
-3.0383621 -6
-2.0332036 -6
7.9264764 -6
-1.6644901 -5
-0.01 to +o.o,
5.w2w96 -9
2.5877454 -9
9.6963832 -10
2.3636365 -10
1.m3.27643 -111.m3.27643 -11
-3.oo96280 -10-3.oo96280 -10
-8.9155191
-8.915549, - 10 - 10
-8.6286758 -10
7.4284923 -11
6.5568964 -12
1.8540516 -10
1.6260416 -11
- 1.3167245 -8
-8.3062870 - 10-8.3062870 - 10
-7 to 16
7
- 16 to 12
-35to25
-551036
-661036
- .4 to .5
-1~7 to 1.6
-2.1 to 1.8
- .05 to .05
- .05 to .05
- 45 to .05
- .05 to .05
-1.0 to 1.3
.05 to .05

=0
,rg"ment Exp.
4.5509556 +1
4.9160016 +1
4.8343651 +1
-4.1134469 10
3.7487318 +1
8.0559850 +1
1.4180146 +3
3.176!3333 +3
1.2683437 +4
1.6251434 -1
1.5239494 -1
1.4441607 -1
1.3344190 -1
1.3752efj? -1
1.12ed875 -1
1.1054689 -1
1.1098270 -1
1.2738464 -1
1.1515zc4 -1
1.0442877 -1
9.0181346 -2
-5.m2431 -1
- 2.6747958 + 0
a2
Argument Exp.
-2.0454379 -5
-1.3755675 -5
-9.5014952 -6
-7.4485484 -6
-6.7661171 -6
-2.86ces78 -6
-2.3559046 -6
-2.4353s9o -6
-4.3132296 -6
-2.9827002 -6
-1.9Enm -6
-7.4069329 -7
5.6190639 -5
2.2334214 -4
2.5404935 -9
1.2610922 -9
6.2073358 -10
3.8266182 -10
3.M2c473 -10
8.6173702 - 11
3.9276246 -11
84
Argument Exp.
-1.1767904 -13
-4.4281251 - 14
-1.9622497 -14
-7.4617277 -15
-5.4254672 -15
-1.1440038 -15
3.33-4 -16
1.8172612 -16
-1Ea3798 -15
-3.78Gss57 -16
2.4513433 -16
9.4290495 -16
3.0369250 -14
1.0882779 -13
-13to3
-4to7
-6 to 10
-7to13
-7 to 14
-.0tto.o4
-.08tom
-.lOfO .12
- .m* to .x3*
-.Oll to ,011
-.x05 to .wo5
.wo5 to .ooo5
-.ll to .I8
.ccm to .a307

a0
4rg”ment EXP.
1.3740347 +1
-2.5321108 +1
-1.1708354 +*
-9.8446269 +2
1.3702395 + 3
~4.76445Sl +*
- 6.4mas29 + 2
‘Quadratic. cubic. and quark approximations f
E=ag+alT+a*T*+a3T3+aqT4where E is in
=I =*
PIrgument EXp. Argument Exp.
- I.3749133 - 1 6.3446673 -3
-3.2914888 -1 5.9766638 -3
-9.9736579 -2 5.4976533 -3
3.smx94 -1 4.5539656 -3
3.367OEsS +o 8.2282215 -4
~f!Eiy~~
7e dafa as a function Of temperat”le ,Y
:rwolfs and T is in degrees Celsius.
a3
Argument Exp.
-5.6339756 -7 -1.1808558 -10 -22f0.14
-5.9983692 -7 -9.7c41131 -11 -.,*to.*o
- 5.7165679 7 -1.0818193 -10 -.,m,.o
~3.3057S24 -7 -2.w18428 10 -4to5
-9.1094186 -8 -2.8098361 -10 -*to9
-8.0141311 -7 - 2.7203972 - 1, - .05 fO .05
-3.6623964 -7 -3.6S6Slcc -10 -2.0 fo 1.8
3.6623964 -7 -3.69691cc -10 -2.010 1.8
*.‘lm1224 -6 -7.7901142 -10 .05 ro .05
3.W5686 -6 -9.4548852 -10 .05 fO .05
2.2417410 -6 ~7.6471224 10 - $5 fO .05
2.4305578 -6 -8.1518033 -10 - .05 to .05
-1.2267180 -6 0.01 fO +o.o,
1selecied temperat”re ranges. me expansion is 0‘ the form

80
,rgument Ex
1.8946288 4
2.0949015 4
2.2394664 i
3.2188156 4
3.44,5x4 t
7.2874oE6 -1
5.7822214 -1
4.SS2Slrn -1
4.6255054 -1
3.ux.6136 -1
2.7222162 -1
2.4988761 -1
1.8282378 -1
1.7031473 - 1
1.5828913 -1
1.4979551 - 1
-5.7447033 -4
-3.177193, -4
-1.6039309 -4
-1.0349686 -4
-8.2176262 -5
-6.81oo680 -5
~3.6330332 -5
-2.71@33,2 -5
-1.1561743 -5
-8.9696912 -6
-7.0050689 -6
~6.n762S3 -6
E,,W
Range
WV1
EX*Ct-App,OX.
-301075
-35row
-45 to 110
-5otom
1
-50 TO130
-.09fO,.O
-3to3
-5to5
-.cmro.o03
-.0*5 to .o*o
- .W, 10 .w,
- ,031 to .Wl
n is Of the form

‘Cluadr*tic, cubic. and qu‘Cluadr*tic, cubic. and qu
E=ar,+a,T+a*T2+,3T:E=ar,+a,T+a*T2+,3T:
*0
Argwnent Exp.
-8.5384268 +2
-1.383%33 +3
-5.1503130 +4
5.9287179 +15.9287179 +1 7.0983783 -2
5.6754764 +15.6754764 +1 5.7443085 -2
5.8943714 +15.8943714 +1 5.611850, -5
5.8318736 +15.8318736 +1 5.4292960 -2
5.m7691 +15.m7691 +1 5.3761106 -2
5.8734537 +15.8734537 +1 5.0763!?31 -2
6.5022W +16.5022W +1 3.4354900 -2
6.7*111*6 fl6.7*111*6 fl 3.1669230 -2
-1.6691278 +2-1.6691278 +2 4.1877018 -1
5.8637565 +1 p4.67*w25 -2
*3*3
\rgument hp.\rgument hp.
5.*421&u -55.*421&u -5
-5.GmmTn2 -5-5.GmmTn2 -5
-5.9506584 -5-5.9506584 -5
-5.6286941 -5-5.6286941 -5
-5.2870696 -5-5.2870696 -5
-4.7621793 -5-4.7621793 -5
-2.9763494 -5-2.9763494 -5
-2.9237913 -5-2.9237913 -5
-3.1228607 -4-3.1228607 -4
-1.443202 -6
aq
*rgument Exp.
3.8137875 -7
1.3960921 -7
2.2327737 -8
2.0825828 -8
1.5352840 -8
1.465!3118 -8
7.w39401 -9
8.1514671 -9
8.5283044 -8
-5to5
- .5 to .4
-6oto3n
-8704
-3ro4
-,8tol7
-2 to 2.5
- .03 to .03
-.06to.oE
- .12 70 + .24