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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
- indu
- с/2-1/670,
CONfl 651020-4


1985
NOV'S
II-I-1
ORNI -ALC - OFFICIAL
Ó.
isu -
A PULSE HEATING CAIORIMHIRIC TECHNIQUE FOR MEASURING
THE SPECIFIC HEAT OF ELECTRICAL CONDUCTORS AND ITS
APPLICATION TO PURE IRON FROM 100 TO 1400°C*
1. G. Kollie**
Oak Ridge National laboratory
Oak Ridge, Tennessee
RELEASED FOR ANNOUNCEMENT

IN NUCLEAR SCIENCE ABSTRACTS
ABSTRACT
.
WE
.
A pulse heating calorimetric technique for measuring the specific
heat of electrical conductors over a wide temperature range is described,
A direct current is used for Joule heating of an instrumented, rod-type
specimen suspended in- & constant temperature, blackbody vacuum chamber.
To determine the specific heat, the current flowing through the specimen
is pulseil and a digital voltmeter, capable of recording 300 readings per
second, measures the time dependence of the temperature change and the
power dissipation in a known length of the specimen during the pulse. Radi-
ation losses occurring during the nominally 4-sec pulse are accounted for
by using total hemispherical emittance values obtained with the specimen
at constant temperature. Errors in thermocouple measurements of surface
temperature of a self-heated rod suspended in a blackbody at room tempera-
ture were considered on the basis of resistance thermometry for pure iron.
MY:
An overall error analysis of the technique predicts an accuracy
in the specific heat results of $1.0% from 100 to 800°C. The accuracy
and reproducibility of the technique were demonstrated by measurements on
pure iron from 100 to 1400°C and by comparison with literature values.
Below 910°C the reproducibility was assessed as 10.5% and the agreement
with other investigators was 12.2%, except in the vicinity of the Curie
transformation. The specific heat values from 910 to 1400°C are within
f several literature sources.
At 772.8°C the specific heat of iron was found to change discon-
tinuously from a value of 0.3457 to 0.2672 cal/g °C. Consequently, the
Curie phenomenon was adjudged to be a second-order transformation caused
by a change in the rate of decoupling of aligned atoms at the ferromag-
netic to paramagnetic transition.
F
L
.
:itidisiu-Jit- INAO
*Research sponsored by the U. S. Atomic Energy Commission under
contract with the Union Carbide Corporation.
**Metallurgist in the Metals and Ceramics Division.
LEGAL NOTICE
This report mo prepared u an account of Government sponsored work. Neither the United
States, por the Commission, nor any person acting on behalf of the Commission:
A. Makot any warraty or representation, expressed or implied, with respect to the accu-
racy, completeness, or wefulness of the information contained in this report, or that the wo
of way information, apparatus, method, or process disclosed lo this report may not latringo
privately owned rights; or
B. Asmunes may liabilites with respect to the use of, or for damages resulung from the
use of any information, apparatus, method, or procou dleclosed in this report,
As used in the above, "porion acting on behalf of the Commission" includes any em-
ploys or contractor of the Commission, or employe of such contractor, to the oxtent that
quod employs or contractor of the Commission, or employee of such contractor prepares,
dienominatus, or provides accouto, my Information pursuant to his omployment or contract
with the Commission, or his employment with such contractor,
ORNI - AEC - OFFICIAL
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II-I-2
· ORNI - AEC - OFFICIAL
INTRODUCTION
been used to measure the
Numerous variations (1-15)* of pulse heating calorimetry have
been used to measure the specific heat of solids. The most commonly en-
countered techniques encploy self-heating of the specimen to produce_the_.
required temperature excursion. Although these techniques differ
radically in practice, they are alike in principle because they require
the measurement of the time dependence of the specimen temperature and
power dissipation during the pulse. A comparison of several of the
techniques which appear in the literature was facilitated by considering
the methods used to measure the quantities in the heat balance on the
specimen, which states that:
The rate of
the heat the net heat
energy applied absorption loss rate by
to the specimen = rate of the + convection 1
by an external specimen and conduc-
source
tion from the
specimen
the net heat
radiation rate
from the speci-
men
OLE
Q = .QA + Qc + QR
(2).
In the self-heating techniques which utilize a direct-current power source,
Q is given by
Q = I ,
=
where
E = the voltage drop across the test section of the specimen,
I = the current passing through the specimen.
If it is assumed that the temperature of the test section 18 uniform
throughout, Qis given by
QA = MC at ,
.
;;
A = MC dT"
where
t = the time,
I = the absoíute temperature of the test section at t,
M = the mass of the test section,
Co = the specific heat of the test section at T, .
one - the time rate of change of the temperature of the test
section at t..
ORNI - AEC - OFFICIAL
*References appear under the heading RHERENCES

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II-I-3
ORML- ALC - OFFICIAL
il
lib
In the methods reviewed, Quran was considerably reduced by making measure-
ments in a vacuum of at least 105 torr to eliminate essentially all :
gaseous convection and conduction from the sample. The net heat 1088
rate by radiation, Qo, cannot be expressed simply in general terms;
however, for methods in which the sample is suspended in a blackbody :
chamber, 2 is given by
23= A€0 (T4 -
TO4),
.
(5)
where
T = the absolute temperature of the test section,
A = the radiating area of test section at T,
€ = the total hemispherical emittance of the test section at T,
o = the Stefan-Boltzmann constant,
a = the total hemispherical absorptance of the test section at
To = the absolute temperature of the blackbody vacuum chamber.
Thus, for pulse heating techniques that utilize Joule heating by a direct. : .
current power source of a specimen suspended in a blackbody vacuum chamber, .......
Equation (1) becomes
EI = MC + Q + ACO (T4 - T04).
(6).
The fifteen techniques reviewed may be classified into two categories
which differ in the method used to maximize Q with respect to Qo. The
techniques of the first category. (148) utilized a furnace to minimize Q.
The second category (9–15) employed very large heating rates and the
specimen was allowed to radiate to the vacuum chamber wall. In both of
these categories, conduction heat losses from the specimen, Qime were
further diminished by using long specimens in which the temperature
gradient was negligible or by using a furnace with a long isothermal
zone. In other words, every effort was made by these investigators to
make an approximately equal to Q by minimizing Qc and Que
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--
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4
-
The method developed in the course of this study contains certain
aspects of the two categories, but in contrast to them, takes no elaborate
measures to maximize Qu. Instead, accurate measurements of total hemi-
spherical emittance are made to correct precisely for radiation losses.'
1: The details of this method are discussed below, and measurements of the
specific heat of pure iron are presented to demonstrate the accuracy and
reproducibility of the technique.
-
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...
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ORNL - AEC - OFFICIAL
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II-Ink
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DESCRIPTION OF THE TECHNIQUE
Method
The technique developed in the course of this work employed a i
direct current to self-heat a rod-type specimen suspended in a blackbody
vacuum chamber. A predetermined temperature was achieved by passing a
constant current through the rod, and the total hemispherical emittance ..
and electrical resistivity were determined by measuring the temperatura :::
and power dissipation in a known length of the specimen. The specific :
heat was determined by suddenly increasing the current and measuring the
temperature and power of the test section as a function of time using a :
high-speed digital voltmeter. By repeating this process at higher
temperatures, quasi-dynamic operation was accomplished. A schematic
· diagram of the circuitry of the technique is presented in Figure 1.
1:11:117
Energy Balance Equations
!!...!
At Steady ütate. Equation (6) represents the non-steady-state.
energy balance for the generalized pulse technique which employs joule
heating by a direct-current power source in a vacuum; however, at steady
state aT/at = 0, and Equation (6) becomes
EI1 = Aj€o (T24 -
To) + B,
.
(7)
where the subscripted one or superscripted prime refer to measurements at
a constant temperature.
For vacuums of less than 2005 torr, gaseous convection and conduca
tion effects are negligible; therefore, is composed of only two
components as follows:
.
(8)
:::::
where
Por = the power loss by conduction through the thermocouples
when the specimen is at T2,
Pa = the power lost by conduction through the specimen to the
electrodes when the specimen is at 12.
that
When Equation (8) 18 substituted into Equation (7), one can show
ELIZ – Pr - P's
€1=-
ORNI - AEC - OFFICIAL
Az o (Tz*
. 4) cyrus
(9)

IVIJ1310- 33V - IN
WIJISO - 33V - INTO
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LE SCHEMATIC DIAGRAM OF THE CIRCUTTRY USED IN THIS PULSE HEATING TECHNIQUE WITH THE POWER
AND STEADY-STATE AND NON-STEADY-STATE MEASUREMENT CIRCUITS SHOWN SEPARATELY FOR CLARITY.
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RESIUNT $
II
* RESISTORS
30.01 ohm
STANDARD
3 RESISTOR
CURRENT REVERSAL
MERCURY RELAYS
PAIRS I ANO 2
0.01 ohm 3
STANDARDS
RESISTOR Ş
SWITCH B
POSITION 8
K-3
SWITCH
9
SPECIMEN
POWER
RESISTORS
POWER
SUPPLY
SWITCH
CONSTANT
CURRENT .
CONTROL
RESISTOR
PigoRngo
SHUNT
SWITCH
Το
SPECIMEN
COLO
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SWITCH
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ALTERNATE
PULSE
SWITCH
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PULSEO
SWITCH
PULSE
SIZE
CONTROL
RESISTOR
Pigo Rho !
SWITCH
POWER CIRCUIT
STEADY-STATE MEASUREMENT CIRCUIT
SWITCH
STANDARD
RESISTOR
30.01 ohio
-
TO SWITCH 8
POSITION 11
AMPLIFIER
COMMUTATOR
BIAS
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COLD
JUNCTION
AMPLIFIED
ANALOG
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SHIELD
DIGITAL
CONVERTOR
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8
120 >
P-65'>>
AMPLIFIED
Figo
POSITION
PATCH
PANEL
TAPE
READING
CIRCUIT
TAPE
WRITING
CIRCUIT
SWITCH
SPECIMEN
ΔΕ
AMPLIFIED
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TELEPHONE
TRANSMISSION
LINES
IDENTIFIER
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CIRCUIT
POSITION
10
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FILTER
NETWORK
NONSTTADY-STATE MEASUREVENT CIRCUIT
RECOPO!:G DIGITIAL VOLTMETER
ORNL -AEC - OFFICIAL
. 7½
82%
ORNI - AEC - OFFICIAL


...
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II-I-6
· ORNL - AEC
Thus steady-state measurements of E1, 11, T2, To, Pne pas and the specimen
geometry and an estimate of the ratio avez allow a calculation of the
specimen's total hemispherical emittance. This was used to make an ac-
curate correction for heat lost from the specimen by radiation during a
specific heat determination.
At Non-Steady State. If the specimen is at a uniform and constant
temperature, a stepwise increase in the steady-state current will produce
an equivalent change in the voltage drop across the test section. This :
increase in power causes the temperature of the test section to increase
as a function of time. As the temperature of the rod rises, its resist-
ance changes proportionally; since the power supply was operated in the
constant current mode, the applied voltage across the test section changed
with time. Thus after a current pulse, Equation (6) may be rewritten as
Es + AE) (12 + AI) = A€O (T2 + AD)* -
To4] + MC, ale + Que
(10)
in
fi-
where
i'
.
AE = the change in voltage drop across the test section at
t o
from its steady-state value of Ev
AI = the change in current at t from its steady-state value Il,
AT = the temperature change at t from its steady-state value Tz.
If the first term on the right-hand side of Equation (10) 18 multi-
plied by ALEV AL€, and the value of Aq€ı obtained from Equation (9) is
substituted into the numerator, Equation (10) becomes
.. (E1 + AE) (IL + AT) =
B92 -2 -26. ACO [ 17 + 27% - 70'] + Mc F + p .
O(T24 - To“)
(11)
As in Equation (8), Qr can be expressed as a sum of its components,
Ps and Pop• Thus solving Equation (11).for Cojone obtains
(+ ) (12 + r) - B13 -
1972 + Apy* - 70*) - PA - PE
(T 4 - 1 To 4)
A1€7L.
M DE
(12)
In order to calculate the specific heat of the sample at any
temperature, T, all of the variables in Equation (12) must be measured. .
ORNE - AEC - OFFICIAL
i'. ! ; . Hill

OSNI - AEC - OFFICIAL
II-I-7
ORNL - AEC - OFFICIAL
A description of the components of the system will precede discussion
of the measuring methods. For discussion's sake, the components of this
technique are divided into six groups: the sample, the blackbody vacuum
chamber, the specimen power circuits, the temperature and voltage drop
circuits, the switching systems, the amplification circuits, and the
recording digital voltmeter circuit. Each of these is discussed below,
and further details are given elsewhere (16).
Sample
Preparation and Characterization. A piece uf the electron-beam
melted iron hillet which was used for thermal conductivity, Seebeck co-
efficient, and electrical resistivity measurements (17), was arc melted
to obtain a void free specimen. The resulting button-shaped sample was
arc drop cast into a mold 3/8 in. in diameter and then swaged and drawn
to a rod (62.0 $ 0.3) mils in diameter. The resulting rod was 6 ft long;
- and because great care was taken in the above forming operation, it was
believed to be of the same purity as the electron-beam melted material
(99.941%).
EFTA!.iii
Although the chance of voids being present in this rod was re-
mote due to the swaging and drawing operations, the sample density was
checked by two methods. The first method employed an immersion tech-
nique to determine the volume of the specimen. This method was non-
reproducible because of surface tension effects on the small diameter
specimen. In the other method, the volume of a 10-in.-long section of
the specimen was determined by length and diameter measurements. . This
yielded a density which was 0. y below the value quoted in the American
Society of Metals handbook (1 . Because this deviation was within the
experimental error of the technique, the specimen was assumed to be
100% dense.
Photomicrographs of the specimen were taken before and after
annealing and after testing. (16) In general, the microstructures were
typical of the physical state of the specimen. No second phases were
detected; however, two small, hairline cracks were evident in the before
and after annealing structures and probably originated from "overlapping"
divring swaging. These cracks were not observed in thèespecimen af
testing. It is felt that if the cracks were present during testing, a
negligible effect on the measured specific heat occurred.
OINT - AEC - OFFICIAL
To better characterize the specimen, the ratio of its resistivity
at room temperature to that at liquid helium temperature was determined.
In the cold-worked condition, this ratio was 7.0 and after annealing for
2 hr at 750°C was 22.2. After all the specific heat measurements were
performed, the ratio was found to be 20.8. This decrease from the an-
nealed value is indicative of some contamination occurring during +Ostirg.
ORNL - AEC - OFFICIAL
Finally, a section 25 in. long was cut from the middle of the
6-ft rod and was polished to a mirror finish to reduce its total
LAS
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Lin.... Miiul

- AEC - OFFICIAL
II-I-8
hemispherical emittance.
couples as follows.
The sample was then instrumented with thermo-

Thermocouple Attachment. A primary measurement invoived in
this technique was the specimen temperature, and for its determination
Sigmund Cohn PtgoRh1o/Pt thermocouples were chosen. Four annealed,
5-mil-diam thermocouples were attached to the specimen surface with a
tweezer welder, end the hot junction was made through the specimen by
separating the platinum and PtooRh 10 wires by about 1/32 in. Since the
thermocouples were also used as voltage taps, they were welded under a
stereomicroscope to ensure proper placement. To minimize the induced
voltage caused by the current passing through the specimen, called pickup,
the platinum and Ptgohnio wires were attached normal to the axis of the
specimen and exactly opposite each other,
Blackbody Vacuum Chamber
.
;
The blackbody vacuum chamber was a brass cylinder that was
29 in. tall and had an inside diameter of 14 in. The cylinder was sealed
by an O-ring to a stainless steel base plate 20 in. in diameter and
3/4 in. thick. Copper tubing was silver soldered to the outside of the
cylinder and bottom of the base plate to provide water cooling, which
maintained a chamber temperature of about 280°K. To ensure blackbody
conditions, all surfaces inside the chamber were spray-coated with a
pure colloidal synthetic graphite* dispersed in & volatile carrier.
This coating is assumed to have an emittance of approximately 1.0.
Gaseous convection and conduction heat 10sses from the specimen
were eliminated by evacuating the Chamber using an automatically filled
liquid nitrogen cold trap, a 4-in. oil diffusion pump, and a mechanical
pump connected in series. Chamber pressures, which ranged from 2 X 107
to 3 x 10-8 torr, were measured by a Bayard-Alpert ionization gage which
was mounted in the base plate.
The chamber temperature was monitored by four polyethylene-
sheathed thermocouples spot-welded to the external side of
one at the top, center, and bottom of the cylinder and one on the base
plate. No measurable temperature changes occurred during a run, and
variations of less than 0.5°C were observed between the top of the
chamber and the base plate,
and
:
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..
Specimen Power Circuit
..
..
Discussion of the specimen power circuit is divided into four
sections: the input electrodes, the current reversal switches, the
power supply, and the standard resistor.
ORNL - AEC - OFFICIAL
Miracle Power Products Corporation, brand name Dra.

II-I-9
OINL - AEC - OFFICIAL
717:.; it
is
Input Electrodes. The sample to be self-heated was suspended
in the chamber between copper input electrodes, which were sealed to the
chamber base plate by neoprene O-rings and electrically insulated from
it by spacers made of "Teflon"* TTE-fluorocarbon resins. To minimize
heat losses from the test section by conduction through the ends of the
specimen, the cross-sectional area of the electrcdes was reduced by using
short lengths of copper tubing for attachment to the specimen. Thermal
expansion and contraction of the specimen was allowed for by cutting the
bottom tube in two and rejoining it using a flexible copper cable.
Current Reversal Switches. Due to the pickup caused by the mis-
alignment of the thermocouples, it was necessary to take steady-state
data with the current flowing first in one direction through the speci-
· men and then in the other direction. This current reversal was accomp-
Lished using four single-pole, normally open, solenoid-controlled mercury
relayst which were wired in pairs and activated with a double-pole, double-
throw switch. To prevent a short circuit of the power supply through the
... relays, this switch required a pause between the activation of one pair
of relays and the deactivation of the other pair. This circuitry forced
the power supply to see" an open circuit during reversal, and since .
this was undesirable, a shunt was wired in parallel with the specimen.
A fifth, normally open relay was included in the shunting circuit and
was activated before and deactivated after the current direction was
reversed.
fit Ai Ci
-
1
Power Supely. i The specimen power source was a high-current,
voltage regulated supply# which employed silicon rectifiers to produce
a direct current. These rectifiers were regulated by power transistors
as series pass elements in a feedback-controlled, closed-loop regulation
system. The output of the supply ranged from 0 to 50 amp and 0 to 28 v
and was continuously adjustable in either voltage, or current.
The power supply was operated in the current control mode.
Current regulation was achieved by maintaining a null voltage across a
comparison bridge, one side of which consisted of the pulse switch and
the constant current and pulse size control resistors shown in Figure 1.
Any deviation from null balance was amplified, and the resulting error..
signal was used to drive the series pass transistor which alerted the
output of the power supply to reestablish the essential balance. Since
the pulse switch was closed during steady-state measurements, the
voltage drop across the pulse size control resistor was very small.
Therefore, the constant current control resistor was adjusted to main-
tas.. the current necessary to effect a desired steady-state specimen
DuPont registered trademark.
+Adams and Westlake Company, Catalogue No. 2101-06-115.
#Kepco Incorporated, Model Ks-18-50M.
ORNI - AEC - OFFICIAL
ORNI ~ AEC - OFFICIAL
7.
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iii, Firdi!!!
1
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Top
II-I-10
ORNI - AEC - 0
temperature. When the steady-state measurements were complete, the
pulse 'switch was opened, causing a large unbalance in the bridge. In
less than 50 usec, the null balance was reestablished, so that the
specimen experienced an almost instantaneous power increase.
Standard Resistor. Current measurements were accomplished by
determining the voltage drop across an 0.01-ohm standard resistor* in
series with the specimen. This resistor, calibrated by the Standards
Laboratory of the instrumentation and Controls Division of the Oak Ridge
National Laboratory, was certified to have a resistance of 0.009999+ ohm.
It was placed between the power supply and the reversal switches as shown
in Figure 1, so that the sign of the potential drop across the resistor
would always be the same. :-
Temperature and Voltage Drop Circuits
Precise measurement of the steady-state temperature and power
dissipation of the specimen was one of the more critical aspects of
this experiment. Thus, a description of the circuits involved is
essential (16).
The thermocouples (which also served as voltage taps) entered
the vacuum chamber through four drilled-out bolts in which the wires
were sealed in epoxy resin. These bolts were sealed to the base plate
by O-rings and grooves located underneath their heads. Inside the
chamber these leads, which wera of 10-mil-diam Sigmund Cohn wire, were
sheathed in aluminum oxide insulators. The platinum side of each
thermocouple was attached to one electrode and the PtgoRhzo to the
other. This provided support for them, as well as proper spacing,
which simplified. spot welding to the 5-mil-diam thermocoupl.es attached
to the specimen.
Outside of the chamber these thermocouples and those thermo-
couples welded to the chamber were insulated with polyethylene tubing
and extended to a Micartat tie-down block. At this block the wires
were mechanically connected to platinum and PtooRhio wires extending to :
the reference junction. To ensure that the thermocouple wire was not
in contact with any other metal, this mechanical connection was made by
pressing one wire on top of the other under nylon-coated steel screws,
The screws were placed in tapped holes in the tie-down block.
The reference junction was made by twisting the thermocouple
wires to 20-mil-diam, vinyl-insulated, copper wires. $ These junctions
were then insulated from each other by vinyl tubing and were placed
four each into the bottom of glass tubes partially filled with mineral
oil for thermal contact. To ensure that all the cold junctions were at
'ORNI - AEC - OFFICIAL
*Leeds and Northrup, Model 4361.
+Trade name, Micarta Division, Westinghouse' Electric and Man-
facturing Company.
#Western Electric Corporation telephone wire.
.


!_;;;. "!
ORNL - AEC - OFFICIAL
II-I-11
· ORNL - AEC - OFFICIAL
the same temperature, the bottom 3 in. of the glass tubes were fitted
in a drilled copper block which was immersed in an ice bath. The ice
bath was held in a cylindrical Dewar flask to minimize heat loss from
the bath.
The copper wires extended from the cold junction to the tie-down
block. For ease and flexibility, all the voltage drop and thermocouple
connections were made to these wires on the tie-down block with mechanical
connections of the type described above. These connections were made
using copper wires* from cables containing 25 pairs of color-coded wires.
The cables extended to two separate switching systems, one for steady-
state potentiometer measurements and the other for non-steady-state
digital voltmeter measurements.
Switching Systems
ves.
is
Each of the switching systems consisted of several thermal-free,
two-pole, twelve-position switchest held in vermiculite-filled boxes.
Connections of the cables to the switch lugs were accomplished using
thermal-free solder. Although only four specimen thermocouples were
used in this technique, the system was wired to accommodate as many as
eight. For the steady-state potentiometric measurements, four sw
were employed. Wired to two of these switches were the output of the
eight thermocouples, the associated seven voltage drops, the four chamber
thermocouples, the voltage probes from the 0.01-ohm standard resistor and
the output of the three bias voltages. The output of these switches ex- ,
tended to two additional switches, one of which fed à Leeds and Northrup
Type K-3 potentiometer used to make the steady-state measurements of
temperature, voltage, and current, as well as to calibrate the voltage :
and current amplifiers. The output of the other switch fed a Rubicon
six-dial potentiometer which was used to calibrate the temperature ampli-
fiers.
Three switches were incorporated in the non-steady-state switching
circuit - one for the thermocouple (emf), one for the voltage drops, and
one for the 0.01-ohm standard resistor. The output of these switches ex-
tended to a Micarta tie-down board where mechanical connections were made
to the amplification circuitry described below.
Ampl ification Circuitry
The measurement of the specific heat by pulse heating calorimetry
requires a measurement of the time dependence of the specimen temperature
*Western Electric Corporation telephone wire.
teeds and Northrup Model 31-30-2.
.
ORNL - AEC - OFFICIAL
ORNI - AEC - OFFICIAL
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Pinitou

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ORNI - AEC - OFFICIAL
II-I-12
11
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and power dissipation. These transient measurements were performed using
three amplification circuits coupled to a digital recording voltmeter.
The latter device is discussed in detail in the next section, and a de-
scription of the amplification circuitry is given below.
-

-.
.
.
Bias Voltage Source. As shown in Figure 1, the temperature,
voltage, and current signals were mated with their respective amplifica-
tion circuitry using the non-steady-state switching system described
above, A stable, direct-current voltage source was placed in series
opposition with each signal, and the resulting differential emf was
connected to the amplifiers. This allowed the input of the amplifiers
to be biased to any desired level. These voltage sources were built
at the Oak Ridge National Laboratory, * and to allow for greater flexi-
bility, their outputs were continuously variable within three ranges. t.
When incorporated in the measuring circuit, these units and the input
ibited an output impedance of less than 550 ohms, which
was acceptable for the amplifiers used.
AA!?
"
ir
Amplifiers. There were four operational criteria to be satis-
fied in the selection of the amplfiers:
1. Due to the high accuracy desired, it was important for each
amplifier to possess a low noise level.
2. The frequency response of the amplifiers had to be chosen :
to ensure that the output signal of the amplifier did not lag the input
signal in time or amplitude.
3. Since the magnitude of the input signals to the amplifiers
were variable whereas the input to the recording digital voltmeter was.
required to range from 0 to 10 v,, the gains of the amplifiers had to be
variable and of appropriate values.
4. It was not experimentally feasible to place the three signals
at the same ground potential; therefore, the amplifiers had to possess
high common-mode rejection capabilities.
As explained elsewhere (16), a number of amplifiers were tried before the
885 Astrodatat amplifiers were found acceptable for the current and
voltage circuits. For the temperature circuit, a series combination of
#Oak Ridge National Laboratory, Instrumentation and Controls
Division; Stable Millivolt Reference Supply, Model Q-2156-2.
The output ranges used were 0–50, 0-100, and 0-500 mv in the
temperature and voltage circuits, and 0-2.00, 0-500, and 0-1000 mv in the
current circuit.
#Astrodata, Incorporated, Model 885, Wideband differential direct-
current amplifier.
OINL AEC - OFFICIAL
.
.
1
THE Pyriniai
imili :
viloin
ORNL AEC - OFFICIAL
ORNL - AEC - OFFICIAL
II-I-13
TRIUK03 -
50 Centiis illis
a 120 Astrodata* amplifier followed by a "triple" P-65A Philbrickt
amplifier satisfied the above four criteria.
Recording Digital Voltmeter Circuit
The final link in the transient temperature and power measure-
ment circuits was an assembly of data processing equipment known collec-
tively as a "Millisadic." In most data processing systems, the speed
of data collection is limited by the output device. The Milli sadic, #
however, stores data on a digital magnetic tape at 300 readings per second
and recovers it from the tape on IBM cards at a slower rate of about
100 readings per minute. The logic of using a digital recorder instead
of an analog device was that data could be stored at one rate and recov-
ered at a slower rate without experiencing an increase in the signal-to-.
noise ratio. Thus, in essence, the Millisadic system may be viewed as a
rapid recording digital voltmeter.
LEFT 4A:ÜIN.
Beste
!!!!!!
!!
The Millisadic was located in a building 200 yd distant from the
equipment discussed above. Tie-in of the three amplification circuits *
to the Millisadic was accomplished by sending the signals through three
pairs of telephone lines which passed through the switchboard of the
ORNL telephone system. A schematic of the Millisadic is included in
Figure 1. This figure shows a fourth signal, which was also fed to the
Millisadic through a fourth telephone line. This was a run number
identifier signal from a variable output, battery powered, voltage
source and was used to distinguish between individual specific heat de-
terminations.
The Millisadic system consists of a filter'network, a patch
panel, a commutator, an amplifier, an analog-to-digital converter, a
magnetic tape writing circuit, a magnetic tape reading circuit, and an
IBM card punch unit. The signals from the three amplification circuits
and the identifier were first connected to the filter network of the
Milli sadic. This network consisted of a parallel-T rejection filter for
each signal, which was tuned to reject the 60-cps noise induced on the
telephone lines. The output of the filters extended to the patch panels
where the four signals were arranged so that they were read in a prede-
termined sequence by the commutator. Although the commutator was capable
of handling up to 100 individual channels, this experiment utilized only
twenty. The scanning sequence of the commutator was set to read the
identifier channel first, then the voltage, current and temperature.
channels six times in sequence, and lastly the calibration voltage
11
$:!!:11'..
:'
ORNI - AEC - OFFICIAL
*Astrodata, Incorporated, Model 120, Nanovolt amplifier.
+Philbrick Research, Incorporated, GAP/R Model P-65A, Solid State
Operational Amplifier. See Ref. 19 for circuitry of "triple" amplifier
design.
*Consolidated Engineering Corporation, Specification 984-018.
TO TYPU
ORNI - AEC - OFFICIAL
INT
.!!!:;ii, ri!!!!
:
II-I-14
ORNL - AEC - OFFICIA)

issimo
channel. Since it was an integral part of the Millisadic, any fluctua- ;
tion of the calibration voltage reading in the output of the M1211 sadic
was regarded as a malfunction of some component of the Millisadic system
and the data taken during that run were discarded. For this investiga-:
tion, the commutator was set to sample the signals at 300 readings per
second and its output fed a single-ended, wide band, inverting amplifier....
This amplifier had a gain of ten, and its output voltage activated the
converter which changed the analog signals into a digital form consisting
of three digits per signal. (For clarification, an analog signal of
0.31222 v from the output of the temperature amplifier was converted
into 031 in digital form.)
One of the outstanding features of this equipment was its
ability to identify the time at which each reading was taken. This was
accomplished by the writing circuit which recorded on magnetic tape the
digital data as well as the elapsed time between the readings of every
20 channels:
Usually 4 to 8 specific heat determinations were made before
the tape reading circuit was activated and the data on the tape were .
transferred to IBM cards. Each card was capable of handling 80 digits
of data. The first entry on the tape was the time signal and was placed in
columns 15 to 20 on the card. The first 3 digits of this signal were
the number of seconds of elapsed time and the next 3 were the number of
milliseconds. This time corresponded to the reading time of channel
Number O, the identifier channel which was listed in columns 21 to 23.
In the next 54 columns, the voltage, current, and temperature signals .
were recorded in this sequence ,by 6 repetitions of 3-digit wide fields.
Channel Number 19, the calibration voltage, was placed in columns 78 to
80. Columns 1 to 14 were reserved for comments, such as the date and
run number. These data were not on the tape but were manually set in
before each run was "played back" from the tape.
In summary, the transient measurements of the specimen tempera-
ture change and power dissipation were accomplished as follows:
1. The three signals were first biased to a desired level and .
the resulting differential signals were amplified from 0 to 10 v.
2. The amplified signals were extended to the Millisadic where
they were read in a prescribed sequence by the Millisadic commutator.
3. The commutated signals were amplified by a factor of 10 and
converted to a 3-digit signal.
R
1.
4. The digital signals along with the time, Milli sadic calibra-
tion voltage, and run identifier were stored on magnetic tape.
W.
.
ORNL - AEC - OFFICIAL
.
;
!
5. At the operatoris convenience, the data on the tape were
transcribed onto IBM cards.
.. -
-

DRNI-AEC
II-I-15
ORNL - AEC - OFFICIAL
lii): TODE
21?ST LINE: 77%
> 98 Coprinelli Pitit
6. Six voltage, temperature, and current measurements were placed
on each IBM card. Furthermore, each card also contained a time, calibra-
tion voltage and identifier reading. .'*
7. Three hundred data readings were taken for each second of a
The data of one second of a run required 15 IBM cards
run.
8. These stored data were processed to yield specific heat values
by means of a Fortran coded program on the Control Data Corporation 1604-A
digital computer. This operation is described below.
STEADY-STATE MEASUREMENTS AND CAICULATIONS
EFTE MARCIN
Although the pulse heating technique was a transient method, a
low member of aril omentam
la number of supplementary steady-state measurements were necessary. Most
of these measurements were required to calculate the heat losses Qm and
Qc during a specific heat determination. Also, the gains of the ampli-":
fiers used in the transient measurement circuitry were established by a
steady-state technique. These steady-state measurements are discussed
in detail in this section.
Specimen Physical Dimension Measurements
To establish the mass and radiating area of the specimen, the
length and diameter of the test section were measured. Since the PtgoRho
leads of the thermocouples served as the voltage taps, the separation of
two adjacent PtgRh10 wires determined the test section length. This
distance, which was approximately 1 in., was measured at room temperature
by passing a small direct current through the specimen and measuring the
voltage drops between the PtgoRhio leads as well as the voltage drop be-
tween two knife edges of known spacing placed on the rod perpendicular
to the current flow.
ORNL - AEC - OFFICIAL
The specimen diameter was a more. elusive measurement than the
length because of local variations in the surface of the specimen created
during drawing. In the initial experiments, several measurements were
made with a micrometer, and the resulting determinations were averaged
to correct for the surface fluctuations. It was found, however, that the
rod was not perfectly circular in cross section but had a small flat
which ran a long its length. Thus, an arithmetic average could be biased,
depending on the number of measurements made along this flat. Unfortunately,
this was discovered after the specific heat measurements had been made. To
determine the correct diameter to use in the specific heat calculations,
a 10-in. long section of the specimen stock was lapped to achieve diametric
uniformity. Measurements with a light-band micrometer established that its
diameter was (0.05992 $ 0.00003) in. In a technique similar to the method
for determining the test section length, a small direct current was passed
ORNI – AEC - OFFICIAL
!!! jo!!:,:''
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II-I-16
ORNL - AEC - Officia
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-
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M
through this rod and the voltage drop between the same set of knife edges :
was determined. The diameter of the specific heat specimen was calcu- .
lated by assuming that its resistivity was the same as that of the lapped
specimen, and the calculated specimen diameter and the average of the
micrometer readings agreed to within 0.1%.
Specimen Temperature Measurements
In the initial experiments, the specimen temperature was measured
by Pt. Rh10/Pt thermocouples spot welded to its surface. However, such
surface temperature measurements were of dubious value, because of the
temperature reduction in the vicinity of the thermocouple hot junction
caused by the heat transferred from the specimen via the thermocouples.
For this reason, a technique (17) accurate to +0.2% and precise to 10.1%
was used by Fulkerson (20) to measure the temperature dependence of the
electrical resistivity of the sample. This allowed the specimen to be
used as its own temperature transducer. To facilitate this procedure,
the resistivity data: (16) between 100 and 910°C were divided into five
intervals and fitted by the polynomials given in Table 1. These poly- det en "ia"!
nomials were obtained by a multiple-regression, least-square technique
and fitted the data to within 0.2°C. Unfortunately, the electrical re-
sistivity apparatus was limited to 1000ºC; therefore, Pallister's (8)
data on pure iron were used above this temperature. To do this, Pallistet!S
measurements were corrected for thermal expansion and were then altered
to agree with those of Fulkerson between 910 and 1000°C. These data*
were divided into the last two temperature intervals indicated in Table 1
to obtain the least-square fits, and the resulting temperature 'versus
resistivity relationships agreed with the data to at least 1.5°C.
ed
.
Using these resistance thermometry data', the temperature depres-
sion of the specimen in the vicinity of the thermocouple junction was .
determined by simultaneously measuring the sample resistivity and the
temperature indicated by the thermocouple. The first experiments were
conducted at 400°C and revealed a depression of about 8°, which was an
order of magnitude greater than anticipated. After an exhaustive but
fruitless search for possible errors in the resistivity measurements, it
was concluded that this anomaly could only be explained by an erroneous
thermocouple signal. An investigation of the 5-mil theimocouple stock
revealed that this wire had not been annealed after undergoing a 98% re-
duction in cross-sectional area* during forming. Since cold working ,
creates a heterogeneous structure, an erroneous thermal emf could be
generated by the thermocouple when placed in a temperature gradient.
Thus, an experiment (21) was conducted to determine the effect, if any,
of cold working on the emf of Pt9oRh10/Pt thermocouples. In this
experiment, the outputs of & calibrated 10-mil thermocouple, an unan-
nealed 5-mil thermocouple, and an annealed 5-mil thermocouple were
-
.
.
ORNI - AEC - OFFICIAL
he platinum
. wire.
**As determined by a Vickers hardness measures t on
AND TYPING
NO TYRIMO
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- INTO
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II-I-17
AEC - OFFICIAL
ORNI - All - ORBICI
- BOTTOM OM
01757 1.iN TAX;
SUNT CHAT!!! Tiri,
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TABLE 1. RESISTANCE THERMOMETRY EQUATIONS FOR PURE
IRON SPECIMEN
Temperature
Interval
(°C)
Equation
105-508
508–753
753–767
767–771
771-910
910–1050
R. 1050—1400
T = -299.011 + 1. 1151 (R) + 267.330(R2/3)
T = 340.324 + 8.41065 (R) - 0.000143413 (R3)
T = 1047.476 - 3.1375 (103.0 – R) - 0.09275(103.0 – R)2
T = 1048.060 - 3.88071(103.0 – R)2 + 1.024902(103.0 - R)3
T = 1051.938 - 7.1434 (103.0 – R) + 0.5977 (103.0 – R)2
T = 972.978 – 22.9105(103.0 – R) + 0.12742(103.0 – R)2
T = 975.745 – 18.9866(103.0 - R) + 0.39340(103.0 – R)2
PT MASIN
..
.
blue = temperature in degrees Kelvin; R = electrical resistivity
in microhm centimeters.
:
monitored as a function of temperature. The data obtained are plotted
in Figure 2 with the calibrated thermocouple as the bas
experiment demonstrated that errors of at least 8.5°C could be expected
with a highly cold-worked thermocouple. All thermocouple wire used in
the pulse heating calorimeter was annealed at 1200°C by self-heating in
air for about 2 min.
There were two other phenomena that contributed to the error in
the specimen temperature determined by the thermocouples welded to the
specimen's surface. The first of these was due to contamination of the
thermocouple by the specimen and was manifest above 500°C. The other
error-producing phenomenon was associated, with the internal temperature
gradient imposed on the rod by the heat generated within it. As shown
in Table 2, this increased with temperature and was calculated (16) to
be 0.12°C at 700°C.
Due to the above-mentioned errors, the electrical resistivity
of the specimen was used to determine the absolute temperature of the
specimen throughout this work.
Voltage and Current Measurements
ORNI - AEC - OFFICIAL
The steady-state voltage drop and current measurements were
essential to almost every calculation. They were accomplished using a
Ieeds and Northrup Type K-3 potentiometer which was coupled to the
signals by the steady-state switching circuitry previously described.
ORNI - AEC - OFFICIAL

VIDI
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· ORNL - AEC - Of
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..::::
line
FIGURE 2.
THE EFFECT OF COLD WORKING ON THE THERMAL ELECTROMOTIVE
FORCE OF A 5-MIL Pt9oRh10/Pt THERMOCOUPLE. THIS THERMO-
ELEMENT HAD UNDERGONE A 98% REDUCTION IN ITS CROSS-
SECTIONAL AREA. ANNEALING AT 1200°C FOR 2 MIN GREATLY
DIMINISHED THE EFFECT.
TABLE 2. THE MAXIMUM TEMPERATURE DIFFERENCE ACROSS
THE SPECIMEN AT STEADY STATE
Temperature
(°c)
...100)
*
**
100
300
500
1
S
3.32 x 10-4
4.85 X 10.63
2.89 x 10-2
1.21 x 10-1
2.27 x 10-2
*
.
.
700
.
*
.
900
.
ORNI - AEC - OFFICIAL
IVI)1310 - DJV=INIO
WIJ1310- 33V - İNIO
17-hr SOAK
'16-hr SOAK ON HEATING
..
-
CALIBRATED – 75- mit CC)
• ANNEALED 5-mil WIRE ON HEATING TO 250°
O UNANNEALED 5-mil: WIRE ON HEATING TO 250°
A ANNEALED 5-mil WIRE ON HEATING 250°-1000°
A UNANNEALED 5-mil WIRE ON HEATING 2500-1000
1 ANNEALED 5-mil WIRE ON COOLING :
O UNANNEALED 5-mil WIRE ON COOLING
· 74%
i Fia 7
17-hr SOAK
100
200
700
800
900
1000
+ 16-hr SOAK ON HEATING
300 400 500 600
.TCALIBRATED (°C)
6“ 74%
ORNI - AEC - OFFICIAL
ORNI - AC - OPSICIAL

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II-I-19
:- ORNL - AEC - OFFICIAL
The current was determined by measuring the voltage drop across an
0.01-om standard resistor placod in series with the specimen. TO
eliminate the Seebeck voltage of the specimen, the voltage drops were
measured with the current flowing in both directions through the spec-
erage of the two readings was taken as the true voltage.
Measurement and Calculation of the Amplification Factors
• Measurement. To make accurate measurements of the time dependence
of the temperature and power during a pulse, it was necessary to determine
the amplification factors of the amplifiers used in these measurements.
This was accomplished by feeding voltages of known value to the amplifiers
and reading the resulting amplified signals with the Millisadic system. .
The bias voltage sources were used to supply the above-mentioned voltages,
whose values were determined potentiometrically. In every calibration,
9 different voltage settings were supplied to each of the 3 amplifiers and
1* each signal was recorded for 3 sec on the Millisadic. In this time in- .
terval, the output of each amplifier was read 300 times. Thus, each set
of calibration data consisted of 8100 Millisadic readings and 27 potentio-
metric determinations,
;
...
;'.,
Calculation. Due to the large quantity of data, the calculation
of the amplification factors was Fortran coded for the Control Data
Corporation 1604-A computer. Since the Millisadic output was displayed
on IBM cards, only the potentiometric data had to be key punched for
inclusion in this program. Because it was possible for erroneous data
to be introduced by the Milli sadic system, it was necessary to check
each reading to ensure that it was not spurious. This was accomplished
by arithmetically averaging the 300 Milli sadic readings of each bias
voltage setting and checking every point to ensure that it was within
#100 counts of this average. Any point that did not fit within these
tolerance limits was discarded and another average was calculated. This
screening technique "as repeated with tolerances of $50, 125, 115, and
$5 counts, Normally, no more than 5 data points were eliminated by this
procedure. After the last tolerance check, the data were averaged again.
Since the output of each amplifier was a linear function of its input, a
least-square technique was used to obtain the relationships
P1 = b + a Mi,
(13)
where
i = 1, 2, or 3 for the voltage, current, and temperature
amplifiers, respectively,
= the potentiometer reading,
= the averaged Milli sadic reading,
the intercept determined by the fit,
a = the amplification factor or the slope of the fit.
1
T
.
ORNI - AEC - OFFICIAL
1
CI

1.1
Ort
inuli
II-I-20
OINLALC - OSSICIAL
0277.)'
!
After screening, all the average readings were within 0.2% of the de-
termined fits, and this emphasizes the excellent linearity of the
amplifiers.
The amplification factors, a.. are not the amplifier gains
referred to later; however, these quantities are related by the ex-
pression
20
(14)
where G, is the amplification gain. The factor 104 arises from the fact
that there were 100 Millisadic units (counts) for every volt output from
the amplifiers or, converting to microvolts, 10-4 counts/uv.
Steady-State Calculations
FT:niliilN.
Equation (9) is one form of the steady-state heat balance
equation, and measurements of the quantities E, I, A2,
pearing in this equation have been presented. The calculations which
were necessary to assess the remaining quantities
€1, and
€1, are discussed below.
-
-
-
-
Power Loss Through the Specimen Electrodes. To evaluate the
power loss, Por from the test section through each specimen electrode
required an ašsessment of the temperature gradient along the longitudinal
axis of the specimen. Due to the small temperature differences and the
inaccuracies of the surface temperature measurements, it was impossible
to measure the gradient accurately. This dilemma was realized when the
original concept of the technique was devised, so to circumvent this
problem, the specimen was designed to be 25 in. in length and 1/16 in.
in diameter. It was felt that this geometry (length-to-diameter ratio
of 400) would approach that of an infinitely long rod, and thus render
the test section isothermal and thereby eliminate the power loss down
the rod. However, assuming a parabolic temperature distribution and
using the measured temperature profile, the power loss Ps was estimated
(16) to be 6.9 X 10-3 w at 100°C and 1.3 X:10-4 w at 400°C. These losses
correspond to 47 and 0.06% of the total input power to the specimen at
these two temperatures. The large loss predicted at 100°C was important
in the steady-state calculation of the total hemispherical emittance;
however, it was not important in the transient measurements of the
specific heat as will be explained later.
Power Loss Through the Specimen Thermocouples. Fulkers
derived a mathematical model which related the power 1088 through the
specimen thermocouples, Pre to the surface temperature depression
created by this heat leakage. The basic &seumptions of his model were
the temperature depression was confined to a small region in the
vicinity of the thermocouple hot junction and that the temperature of
ORNI - AEC - OFFICIAL

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y

-
-
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C!.ASS15'101ION
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II-I-21
the center of the test section was unperturbed by the heat loss. As has
been shown (16) Por can be expressed as a function of the absolute tempera-
ture of the speciten by
PM = exp (–21.32 + 8.97 x 10-3 T) :
(15)
At 100°C the power loss calculated using Equation (15) amounted to 2.4%
of the total input power but decreased to 0.8% at 800°C. This relation-
ship was used to evaluate Pr in all calculations.
Total Hemispherical Emittance. Using the free electron theory.
of metals, Davisson and Weeks (22) derived an expression for the total:
hemi spherical emissivity, ex, in terms of the electrical resistivity, ,
and the absolute temperature, T. Abbott, Alvares, and Parker ( ex-:.
tended the same concept to the total hemispherical absorptivity, ay
These relationships are in the form of an infinite series in pr and
state that
Awit
E# = (0T2)1/2 + B4 (872) + C4 (02213/2 + ...
Alt = ag (PTO)2/2 + bs (To) + C5 (PTO)3/2 + ...
..
where
84, B4, C4, 85, B5, C5 constants,
T, = the absolute temperature of the specimen,
To = the absolute temperature of the blackbody radiating to
the specimen.
Although the absorptivity and emissivity are not necessarily equal to
the absorptance and emittance, respectively, Abbott et al. estimated
the ratio au/ez by proportioning Equations (16) and (175. To simplify
the resulting expression, they truncated the numerator and denominator
.. to their first terms and found that
.
(18)
All the quantities required for the calculation of the total
hemispherical emittance, 61, have been discussed. Due to the large un-
certainty in the determination of the power 1088 through the specimen
electrodes, Pn, it was not used in the emittance calculation. Conse-
quently, the emittance values are valid only above 400°C where Ps is of .
negligible size. The expression used to calculate the total hemispherical
emittance was obtained by substituting Equations (15) and (18) into
Equation (9) and obtaining
OZNI ONA-OSICIAL
4.1,
i
stilin
II-I-22
ORNL - AEC - OFFICIA
- E, I, - exp (-11.32 + 8.97 x 10-3 T2)
A Fortran code was written for the Control Data 1604-A digital computer
which utilized Equation (19) to calculate €2. The emittance values com-
puted with this code are plotted in Figure 3a versus the temperature and
in Figure 3b versus the pt as implied by Equation (16). If only the
first term of Equation (16) is of importance, a straight line of slope
a should fit all of the emittance data in Figure 3b. Although this WAS
not so, three straight lines were adequate to represent the data. One,
line extended from 400 to 550°C, another from 550 to 800°C, and the
last from 800 to 945°C.
Several interesting observations can be made from these data
and the three fits obtained above:
1. The total hemispherical emittance is a surface property and
not a fundamental property of a material as are the total hemispherical:
emissivity and the electrical resistivity. This is demonstrated in
Figures 38 and 3b.
: a.
The emittance data taken at about 400°C on cooling
(K Run) were about 6% lower than that taken on heating
(B, C, D, and H Runs) and,
b.
Inadvertently heating the specimen to about 1000°C
(between the K runs at 800°C) resulted in a 3% decrease
in emittance.
Both of these effects were ascribed to thermal polishing of the specimen
and demonstrated the importance of the surface.
2. The emittance values measured below 300°C were higher than
those predicted by the extrapolation of the emittance data from above
400°C. For example, the value calculated at 110°C was 39% higher than ·
that of the extrapolation. As discussed previously, this discrepancy
was caused by the omission of the conduction heat loss P from the
emittance calculations which was as much as.47% at 110°c.
3. The two abrupt changes in slope of the emittance versus
plot at 550 and 800°C may be physically significant. Similar effects
have been noted near these temperatures in measurements on other physical
properties of iron. For example, Moore, Fulkerson, McElroy, and Kollie
(17) found that the Seebeck coefficient of iron reaches a minimum at
about 500°C and the thermal conductivity has a minimum at 790°C.
OINI - ALÇ - OFFICIAL
ORNL - AEC - OFFICIAL
4. When least-square, straight-line fits were obtained for
the emittance as a function of temperature, the relationships found for
the temperature ranges 400 to 550°C and 550 to 800°C were essentially
10.1.1: ir AIT:)!

€ = 0.17965 + 5.2209X 10
ORNL - AEC - OFICIAL
1980
.
€ = 0.057150 + 2.129 X 10*x
militis
€, EMITTANCE
A B RUN
OC RUN
RUNS - NOT PLOTTED 7
FJ
H RUN
EI RUN
OJ RUN
BEFORE Q-Y
AFTER a-y
OL RUN ti
RUN
Tre = 0.055583 + 2.4386 X 104XT
.
THE TOTAL HEMISPHERICAL EMITTANCE, E, OF PURE IRON IS PLOITED
AS A FUNCTION OF THE CALCULATED TEMPERATURE, T., AND AŞ. A
FUNCTION OF THE PRODUCT OF THE ELECTRICAL RESISTIVITY, 8, AND
TEMPERATURE, T. (a) E VERSUS T. (b). € VERSUS STC. THIS :
EQUATION SHOWN IN THIS FIGURE WERE OBTAINED BY LEAST-SQUARIS
FITS. THE DATA ARE TABULATED IN REF. (16).
100
200
300
900
1000
400 500 600 700 800
T, CALCULATED TEMPERATURE (°C). .
ORNI FAEC - OFFICIAL
9216
12.
®
Problem
5%
80%

1310-23v-INYO
€ * 0.1485 + 2.1556 X10
ORNL-AEC - Oficial
€0.045620+ 5.6918 X10
POINT OF INTERSECTION
(pT612 = 243.0 :
€ = 0.1840
To ~ 595°C
.
.
-
-
€, EMITTANCE
-
-* 0.074154 to 4.5187 X 10
.
not
.
ir
,
..
A B RUN
O C RUN
D} RUNS - NOT PLOTTED
FJ
VH RUN
II RUN
• J RUN
KRUN BEFORE Q-yu
AFTER Q-Y
L RUN
-
ORNL - AEC-OFFICIAL
10.109
2.3
- AEC - OFFICIAL
110
150
190
230
270
340
350
390
430

.
.
RESISTIVITY X ABSOLUTE TEMPERATURE
5%
78%
.

LoLNO!!!;:;
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· II-I-24
ORNI - AEC - OFFICIA
Ari! 1S Liri
the same and are shown gure.3. The intercepts and slopes for these :
functions differed by 2.8 and 0.4%, respectively. This suggests that
the emittance of iron is a linear function of temperature from 400 to
800°C.'
Rel
nimi
Relatively accurate total hemispherical emittance data are
necessary to correct for the heat lost by radiation during a specific
heat determination. For this reason, none of the values obtained below
400°C were used in the specific heat calculation. Instead, the fit ob
tained from 400 to 550°C was extrapolated to determine the cmittance at
these lower temperatures. Also, due to the hysteresis noted in the i
emittance on cooling, the emittance-temperature functional relationship
for these runs was obtained by using the same slope as on heating but
correcting the intercept down 2.8%. The same type approximation was.
performed for measurements above 945°C, using the fit from 800 to 945 as
a comparison.
HARLIN
·
boom
Hectrical Resistivity. The electrical resistivity, p, of the
specimen was used to determine its temperature. The quantities requisite
to the calculation of the resistivity have already been presented and are
related by
1.
DE B mode,
(20)
· where
à = the diameter of the rod test section corrected for thermal
expansion,
b = the length of the rod test section corrected for thermal
expansion.
The steady-state measurements and calculations of this section were
necessary prerequisites to the transient measurements and calculations
presented below.
NON-STEADY-STATE MEASUREMENTS AND CALCULATIONS
The pulse heating calorimetric technique for measuring the
· specific heat requires the determination of the time dependence of the
specimen temperature and power dissipation during a power pulse. The'?
purpose of this section is to present the manner in which these transient
measurements were performed and the calculations necessary to determine
the specific heat.
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II-I-25
ORNL - AIC - OFFICIAL
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Procedure for the Non-Steady-State Measurements
.
After the steady-state temperature, voltage, and current measure-
ments had been performed, the current pulse size control resistor was ad-
justed to produce the power pulse that was desired. In addition, the .
gains of the amplifiers and outputs of the bias voltages of the tempera-
ture, voltage, and current circuits were selected to allow for a full-scale
deflection of the Millisadic during the specific heat determination. Since
these were differential measurements, the Milli sadic was started 4 sec
before the pulse switch was opened. The average pulse was of 4-sec dura-
tion, and a plot of the Millisadic output for a typical run is shown in
Figure 4. After the temperature signal had undergone a full-scale de-
flection, the pulse switch was closed and the specimen was allowed to
come to equilibrium. These transient measurements were repeated at least
three more times before the equilibrium temperature was changed and the
above procedure begun again.
SFT MARLIIN:
When 8 or 12 runs had been obtained, the data stored on the
digital tape were transcribed to IBM cards for use in the specific heat
calculations. These calculations were Fortran coded for the 1604-A com-
puter to utilize Equation (12). All the quantities of this expression
had been discussed previously except AI, AE, AT, and aT/at.
Measurement and Calculation of the Current Change, AI
The change in current, AI, at any time t after the pulse is given
.
AI = 22(MT - MI),
..
(21)
where
az = the amplification factor for the current amplifier,
M = the Millisadic reading of the current amplifier at t, ..
MI = the Millisadic reading of the current amplifier before the
O pulse.
Since
ere both constants, their values were assessed with the
the samě screening and averaging technique used to calculate the average
Millisadic reading in the determination of the amplification factors. TO
ensure that the transient data created by the finite frequency response
of the amplifier were not included in the averaging for Mt, only those
topoints which occurred 0.35 sec after the start of the pulse were used.
. Current amplifier gains of 60 or 200 were employed in all experiments,
and the appropriate value was dictated by the current pulse size used.
ORNL - AEC - OFFICIAL
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DIGITIZER
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FIGURE 4.
..
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momimumuman
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•
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· CURRENT,
VOLTAGE
-2
.
...
.
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TEMPERATUREmmanamunal
..
.. ..
..:
.
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..
.
...
....
.
.
..,
TIME (880)
ARE INDICATED...
THE MILLISADIC OUTPUT FOR A TYPICAL RUN.
RESPONDING TO THE TEMPERATURE, VOLTAGE, AND CURRENT SIGNALS
0 r to . :
THE CURVES
ech
0
3:
VOLTAGE
TEMPERATURE
CURRENT
i
..
.
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...
..
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..
32. .3
.......:
.....
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II-I-27
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---
Measurement and Calculation of the Voltage Change, AE
The change in voltage, AE, at any time after the pulse is given
by
AE = a(MT-MMM,
(22)
where
aq = the amplification factor for the voltage amplifier,
M = the Millisadic reading of the voltage amplifier at t,
M. = the Millisadic reading of the voltage amplifier before
the pulse.
"to
LEFT AAHO:n
Sinc
was a constant, its value was assessed with the same screening
: low ana averaging Technique
and averaging technique used to determine M
The value of M!
varied with time because the resistance of the rod 'increased with
temperature. To evaluate this quantity, a least-square fitting and
screening technique was employed. The fit used was a second degree
polynomial in time and was therefore of the form
M = x + byt + cyt?,
(23)
where a, by, and c, are constants determined by the least-square tech-
nique. Thiš fitting routine was employed to facilitate calculations on
the digital computer. To ensure that the transient was not included, the
n 0.35 sec after the start of the pulse and extended to the
end of the run. Each data point was then checked to ensure that it
differed by less than 1100 counts from the values calculated from
Equation (23). Any data point that did not fit within this tolerance
was replaced by the value from the fit. This fitting and screening
technique was repeated with tolerances of £10, 18, and +6. Normally, no
more than five data points were discarded by this technique. The values.
of a, b, and c. obtained after the last tolerance check were used in
all subsequent calculations. Voltage amplifier gains of 30, 100, or
300 were enployed in all experiments, and the appropriate value was dic-
tated by the current pulse size and the temperature coefficient of the
electrical resistivity of the sample at the temperature of operation.
Measurement and Calculation of the Temperature Change, AT
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As previously discussed, the electrical resistivity, p, was
used to determine the absolute temperature of the rod before and after
the current pulse. The resistivity before the pulse is given by
Equation (20) and after the pulse by
ORNI - AEC - OFFICIAL
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II-I-28
ORNL - AEC - OFFICIAL
now
h
-ti
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Es + a, (2, + byt +. c,t2 - M.
Il + a2 (MI - MI
---...
.....-
The thermometry equations were then used to determine the value of
Ti + AT.
Measurement and Calculation of the Rate of Temperature Change, dT/at
Since the output of the thermocouples was used to determine
the rate of change of the specimen temperature, it was necessary to
calculate the AT indicated by the thermocouples as a function of time
before dT/at could be evaluated. The measured output of the specimen
thermocouple consisted of its thermal emf plus the voltage induced on
to it due to the mi salignment of its elements. As shown elsewhere, (16),
the steady-state pickup, EMF, and the transient pickup, EMF, are given
: ****
by
(25)
EMF'= S
PMF, = E1 + a2 (a + byt + cut2 - M
. E
,
(26)
where ST is the difference in the thermocouple outputs when the current
is passed in both directions through the specimen. To find the cam-
ponent of the Millisadic readings associated with the thermal emf of the
thermocouple, one of the following two calculations was applied to each
Millisadic reading
(27)
.,
.
.
.
"
EMFE
18)
where
the component of the Milli sadic reading of the temperature
amplifier associated with the thermal electromotive force
of the thermocouple at t,
1 = the time before the pulse,
M = the component of the Millisadic reading of the temperature
amplifier associated with the thermal electromotive
force of the thermocouple at ^, .
My name = the Milli sadic reading of the temperature amplifier.
.
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II-I-29
ORHL-AIC - OFFICIAL
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The calculation of the temperature change, AT, required the
evaluation of the average of the MA readings. This was accomplished by
the same averaging and screening techniques used to determine Mand Mr
and the value of AT at any time after the pulse is given by
AT = 8: ago ( -
),
(29)
where
S = the sensitivity of the PtgoRh10/Pt thermocouple at T,
Mi a = the average of the Month readings.
1.
8T APLIN.
Since Ty was a constant and T2 + AT was equal to T, the rate of
change of the specimen temperature, dT/at, was equal to dAT/at. Thus,
to determine dT/at, the rate of change with time of at given by
5. Equation (29) was evaluated. To accomplish this the IT readings were
(a) checked for spurious points, (b) smoothed to render the function
continuous, (c) split into small overlapping time intervals, and (a)
fitted in each time interval to obtain
;
AT = By + bort + cinta ,
(30)
where Bype Bors and cm are constants. The resulting AT versus time functions
were differentiated' to yield
a = bez + 2Cipt,
(31)
and the values of AT/at obtained were averaged for use in calculating
the specific heat.
Spurious Data Removal. Spurious data points were eliminated
using the same fitting and screening technique employed in the evalua-
tion of M.
OKNI – AEC - OFFICIAL
Smoothing the AT Data. A moving-average technique was employed
to smooth the AT data. To utilize this technique required the selection
of (a) the function to be employed in smoothing, (b) the number of points
to be included in each smoothing interval, and (c) the number of times to
repeat the procedure. Although rigorous procedures existed for the se-
lection of these three smoothing parameters, trial and error methods were
used to establish them. Since the AT was approximately a linear function
of time over a small temperature interval, a second order polynomial in
time was employed. The number of points to be included in each smoothing
interval depended on the amplifier gain used. For a gain of 105, a .
45 point group was used, and for gains of less than 2 x 104 a 35 point
group was employed. Due to the time required by the computer to perform
this procedure, it was repeated only twice. .
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"
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II-I-30
· ORNL - AEC - OFFICIA
1
.
The moving-average technique, using the 45 point group as an example,
consisted of applying the smoothing function to data points number 1 to
45 and calculating the value from the fit for point 23, the center point :
of the smoothing interval. Since this calculation was being performed ..
on a computer, the original value of point 23 was replaced in the com'.
puter memory by the calculated value. Points 2 to 46 were then fitted
and a new value for point 24 was calculated. This procedure was con-
tinued in a similar manner until a new value had been obtained for
every point up to point number N-22, where N was the total number of
data points. New values for points 1 through 22 and N-22 through N were
calculated using the first and last fits, respectively. After this was
accomplished, the entire procedure was repeated again.
Time Intervals and Fitting Procedure. The length of the time
intervals into which the data were divided for fitting depended on the
amplifier gain. For a gain of 105, a 1.25-sec interval (125 points) was
used, and for gains of less than 2 x 204 a 0.65-sec interval (65 points)
trio was employed. Using the 65 point group as an example, interval 1 con-
sisted of points 1 to 65, interval 2 of points 2 to 66, interval 3 of
points 3 to 67, and so forth. The data of each time interval were
fitted by a multiple-regression technique to obtain Equation (30).
ALPIN
Calculation of aT/at. The equation for each time interval was
differentiated to obtain Equation (31) and aT/at was calculated for each
point in each interval. If a 65 point interval was being used, this i
resulted in 3 aT/at values for point 3, 5 at/at values for point.5, :
65 AT/at values for point 65, and 65 dT/at values for point 75. The
-values of AT/at were arithmetically averaged for each point, allowing a
calculation of the specific heat for each AT value.calculated by
Equation (29).
...
....
z
=
Calculation of the Specific Heat
Letting z be given by
€ (T2 + )4 - TO" AE.hen ()1/2 To*
Agen Touareg To Aci* 7+ - 0932/27*
Equation (12) can be rewritten as
EjIq (1 – 2) + E,41 + $E(I2 + 01) + Zipo – Pr + ZPS s
132)
c oss
Mehed
As discussed previously, only crude estimates of the value of Pa and Po..
.were possible. In fact, these estimates predicted that po decreased
with increasing temperature. Since Z was a positive quantity only
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slightly greater than one, the term ZP - Po was neglected in these
mea surements. What error was introduced by this approximation could
not be predicteț. Measurements of accurate values of Pa will be
investigated in the future development, of this techni
.
As described previously, the specific heat was evaluated at
every Milli sadic data point of the temperature amplifier using the
averaged values of aT/at and Equation (33). Thus, for a 4.35-sec run,
400 values of the specific heat were calculated. The temperature in-
terval covered by these data points depended on the amplifier gain and
the heating rate. The results of these calculations are presented
below.
RESULTS
LEFT. ARGIN: stom
In any absolute measurement the error and reproducibility of the
technique employed determines its value as a research tool. This con-
cept was realized at the inception of this work, and a preliminary .
analysis demonstrated that the assessment of the errors of the pulse
heating technique would be complex. For this reason, pure iron was
chosen to prove the reliability and reproducibility of the technique
since the specific heat of iron is well known between 100 and 1000°C
the temperature range of interest. Although many assumptions were
necessary, an error analysis of the technique was also performed
by assessing the accuracy of measurement of the quantities in Equation
This procedure demonstrated that the accuracy of the technique was 1.0%
from 100 to 800°C. Thus, two methods of assessing the accuracy of the *
technique were obtained and are compared during the discussion of
results.
Specific Heat Measurements of Pure Iron
The specific heat of pure iron was measured from 100 to 1400°C.
These data are considered tentative and the measurements will be re-
peated. From 100 to 600°C measurements were taken over 10° intervals
in steps of 100°C. At least 4 runs were made in each temperature in-
terval, and the specific heat was calculated at about every 0.1°.
Due to the Curie phenomenon at about 720ºC, the temperature..
range 720 to 890°C was investigated extensively. Sixty-seven runs were
! made, and each run covered about 30°. The majority of these data were
acquired within 120°C of the Curie point.
ORNI -AEC - OFFICIAL
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The measurements above the alpha to gamma transformation, 9.10
were of poor quality, but are included as a demonstration of the high-
; temperature potential of the technique. A number of runs were made
Lumut
09:15 ilin
iii.,1.1-leiril3:1
.
II-I-32
ORNL - AIC - OFFICI
between 910 and 940°C, but were for naught because of the large error
encountered in the radiation heat 1088 correction. One run encompassed
the temperature interval 980 to 1400°C.- Since a very large pulse size
was used, these data were the most meaningful of all taken above 910°C.
Interpretation of the Raw Specific Heat Measurements
To arrive at most probable values from the measured specific
heats, the data of all runs at the same temperature were averaged and
plotted versus temperature, A smooth curve was drawn through these
averages, and values were read off this curve at several temperatures.
To demonstrate this technique, a typical plot is shown in Figure 5.
The specific heat values obtained from these interpolations are listed
in Table 3 and plotted in Figure 6..
*. The Specific Heat Measurements of Iron from Other Investigations
The specific heat of pure iron from four other investigations
are compared with those of this work. Of these four sources, three are
direct measurements and one is a compilation of the work of several
authors. McElroy (24) utilized an adiabatic calorimeter from roam
temperature to 960°C to measure the specific heat of pure iron to
+0.5%. A pulse heating method, having an adiabatic shield to minimize
• radiation heat losses, was employed by Pallister (8) for measurements
to +2% from 0 to 1250°C. Wallace, Sidles, and Danielson (4) also used
a pulse heating technique and minimized radiation heat losses by sur-
rounding their specimen with a furnace. The stated accuracy of their
method was +2%. Even though the compilation of Hultgren, Orr, Anderson,
and Kelley 25) included the work of Pallister, it was used in this
comparison since the values presented were chosen to agree with other
thermodynamic measurements as well as the specific heat determinations
of several investigators. The data of these four sources are also
listed in Table 3 and are plotted in Figure 6. A better comparison of
these reported values can be obtained by plotting the percent difference
between them as a function of temperature, as shown in Figure 7. These
data comparisons are discussed in detail below. .
-
-
-
-
DISCUSSION OF RESULTS
The reproducibility. Sometimes called repeatability, of an
absolute measurement is equally important as the calculated accuracy;
therefore, a considerable percentage of the effort w
assessing the reproducibility of the pulse heating technique. As pre-
viously mentioned, at least four pulses were made at every temperature,
These measurements dumonstrated that the technique was reproducible to
+0.5% from 100 to 820°С. For example, the data of four typical runs
ORNI - AEC - OFFICIAL

TVIJIJ10 - )38 - INIO
: FIGURE 5.
NVIDI110-DIV-INIO
mon.
in
THE METHOD OF INTERPRETATION AND THE REPRODUCIBILITY OF THE RAW SPECIFIC HEAT DATA. DHE
RAW DATA OF RUNS 1-41 AS WELL AS THE AVERAGE VALUE OF THESE FOUR RUNS ARE PLOTTED VERSUS
TEMPERATURE. THE DATA OF MELROY FIT THE SAME CURVE AS THAT SMOOTHED THROUGH THE AVERAGE 3D
VALUES. THE DATA OF THREE OTHER INVESTIGATORS ARE ALSO SHOWN.
..
.-
-
,
...
0.1186
'
.
ii
.
.
.
.
... ... .-..........
'.
.
'
0.1482
-
• RUN 11
O RUN 21
KOLLIE <0 RUN 31
IRUN 41
A AVERAGE
----......
..0.1178
.
...........
5 0.1174
70
SPECIFIC HEAT (col/9°C)
1166
McELROY (5)
LII
.
WALLACE, SIDLES, AND
- DANIELSON (6)
.
HULTGREN, ORR,
| ANDERSON, AND KELLEY (32)
1158
..
..
..
.
.
.
. .
. .
.
1154
--PALLISTER (714
1150
145
119
123
121
TEMPERATURE (°C)
.. 125
.
RNL FAEC - OFFICIAL
7%
78%
.
· ORNL - AEC - OFFICIAL


II-I-34
ORNI - AEC -
TABLE 3.
THE SPECIFIC HEAT OF PURE IRON FROM FIVE
DIFFERENT INVESTIGATIONS
Specific Heat
cal/g-°C
Kollie
Most
Probable
(16)
Temperature
7°c)
Hultgren,
Orr,
Anderson,
and Kelley
(25)
McElroy
. (24)
Wallace,
Siales, and
Danielson
(4)
Pallister
(8)
IN
..
0.1172
0.1262
..0.1370
0.1475
0.1599.
.0.1820
0.1829
0.1840
0.2360
0.2406
0.2456
0.2509
0.2565
0.2610
0.2690
0.2800
0.2936
0.3015
0.1152
0.1242
0.1352
0.1464
0.1601
0.1841
0.1848
0.1857
0.2322
0.2372
0.2427
0.2486
0.2523
0.2617
: 0.2700
0.2823
0.3178
· 0.1165
0.1258
0.1364
0.1462
0.1572
0.1780
0.1787
0.1796
0.2286
0.2331
0.2380
0.2436
0.2487
0.2552
0.2650
0.2764
0.2910
0.3210
0.1152
0.1242
0.1352
0.1464
0.1601
0.1841
0.1848
0.1857
0.2370
0.2432
0.2498
...0.2569
0.2650
0.2766
0.2863
0.2990
: 0.3187
-
-
'*"
.
*
...
119,0
. 210.0
. 328.0
*416.0
· 502.0
615.0
618.0 :
621.0
720.0
725.0
730.0
735.0
740.0
. 745.0
750.0
755.0
760.0
765.0
766.0
767.0
768.0
769.0
770.0
771.0
772.0
772.8
772.8
774.0
775.0
776.0
777.0
778.0
779.0
780.0
785.0
790.0
795.0
800.0
805.0
0.1169
· 0.1263
0.1366
0.1477
0.1612
0.1860
0.1870
0.1881
0.2385
0.2428
0.2472
0.2518
0.2560
0.2639
0.2724
0.2816
0.2928
0.3084
0.3126
0.3170
0.3216
0.3264
0.3314
0.3364
0.3417
0.3457
0.2672
0.2597
0.2548
0.2508
0.2472
0.2441
0.2412
0.2387
0.2295
0.2238
0.2191
0.2152
0.2118
WOLA
iteen in die brands
0.2610
· 0.2287
0.2052
0.2690
i
L
r
0.2353
0.2275
0.2210
0.2162
0.2116
0.2083
2
0.2205
0.2143
0.2088
0.2042
0.2000
0.1962
0.2000
0.1960
0.1927
....0.1897.
0.1870
0.1851,..
0.2556
0.2428
0.2302
0.2183
0.207
0.1994
.. ';:::;:- S
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II-I-35
ORNL - AEC - OFFICIAL
70! 0 :
1926Of 71:7T
Frutta - TABLE 3 (continued)
Specific Heat
cal/s-°C
Kollie
Most
Probable
(16)
Wallace,
Sidles, and
Danielson
(4)
Hultgren,
Orr,
Anderson,
and Kelley
(25)
Temperature
7°c)
McElroy
(24)
Pallister
(8)
. 0.2059
10. 2027
0.2003
0.1930
0.1874
0.1827
0.1809
0.1497
810.0
815.0
820.0
840.0
860.0
880.0
890.0
950.0
1000.0
1050.0
1100.0
1150.0
1200.0
1250.0
1300.0
1330.0
AFGIN...
0.2087
0. 2059
0.2029
0.1952
0.1895
0.1854
0.1843
0.1582
0.1586
0.1589
0.1593
0.1596
0.1600
0.1605
0.1609
0.1612
0.1927
0.1905
0.1877
0.1778
0.1698
0.1630
0.1600
0.1320
0.1360
0.1400
0.1450
0.1490
0.1530
0.1560
0.1832
0.1815
0.1800
0.1748
0.1711
0.1685
0.1673
0.1454
0.1475
0.1500
0.1938
0.1907
0.1871
0.1775
0.1690
0.1643
0.1635
0.1465
0.1478
0.1493
0.1507
0.1521
0.1535
0.1547
0.1560
0.1573
.
.
.
-
-.
.ORNI - AEC - OFFICIAL
R
FIGURE 6.
O
:::.. ........ ......... .. . ........ ?VI1310 - )3
THE SPECIFIC HEAT OF PURE IRON FROM O TO 1400°C AS DETERMINED FROM THIS INVESTIGATION AND .. .
THOSE OF FOUR OTHER INVESTIGATORS.

:
0.39
:...
:
-
..
-
.
.
.
0.37
.'
.
SPECIFIC HEAT (calories/nºc).
• MCELROY (5) -
• WALLACE, SIDLES, AND DANELSON (6)
• PALLISTER (7)
• HULTGREN, ORR, ANDERSON, AND
KELLEY (32)
• KOLLIE, 1 st HEAT
• KOLLIE, 2nd HEAT :
HIIT
1:
.
0.17
...!"
.
.
0.13
* 100
200
300
400
500
600
700 - 800
TEMPERATURE (C)
900
1000
4100
1200
1300
...
.....
.
:
:
..
.
.
..
..
.
..
.
.' ORNI - AEC - OF
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Ī MARGIN -...
CHAPTER TITIE.
Į LINE OR TEXTI:
101 10:4 OF
-----..-
-
-
-
-
-
-
-
-
-
-
-
---
-
-
-
-
50"!.
0?
II-I-37
FIGURE 7.
DIFFERENCE PLOIS OF THE SPECIFIC HEAT VALUES OF THE FOUR LITERATURE SOURCES BASED ON THE
DATA OBTAINED BY THIS TECHNIQUE. (a) THE PLOT FROM 100 TO 800°C. (b) THE PLOT FROM
DUETO 1350°C. .
ORNI - AEC - OFFICIAL
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.
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.
.
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:...
JVIJ1310- 33V - INIO
VI3510
....
..
.
1.
.
'. PERCENT DIFFERENCE IN SPECIFIC HEAT
KOLLIE-
• McELROY (5)
O WALLACE, SIDLES, AND DANIELSON (6)
A PALLISTER (7)
HULTGREN, ORR, ANDERSON, AND
KELLEY (32)
**
-6.0

100
200
300
400
500
600 700" 720
TEMPERATURE (°C)
740
760
780
800
820.



.
...
..
.:
:
:. :--
:
...
.
.
.. ..
.
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?...
.
.
1.750
800
{..
.
850
900
960 :
KOLLIE
36" 84%
1000
TEMPERATURE (°C)
1050 1100
.
1150
.
1200
A PALLISTER (7)
• MCELROY (5)
KELLEY (32)
O HULTGREN, ORR, ANDERSON, AND
A WALLACE, SIDLES, AND DANIELSON (6)
1250
1300
1350 ..
.
..
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*
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II-I-38
:ORNL - AEC - OFFICIAL

-*--*
are plotted in Figure 5, and are within 10 • their average value.
These data show a sinusoidal temperature dependence of the specific heat,
Such a functional relationship is, of cour:se, false and was generated
by the smoothing and averaging techniques used to calculate at/at.
This oscillation was more apparent in runs in which a high gain was .
used on the temperature amplifier. However, a smooth curve through the
averages of these runs predicts the correct temperature dependence of
the specific heat.
*---***
Regarding the accuracy of the technique, two variables were
important and are the pulse size used and the temperature interval
over which the signal was followed. The latter variable was dependent
on the gain of the amplifier, which had 12 fixed-step values from 200 to
10°. Since the pulse size depended on the setting of a variable resistor,
its value was continuously adjustable from 0 to about 20 amp. Thus, a
wide latitude was possible in the choice of these variables. How the
choice of the pulse size and temperature interval affected the accuracy
.of the specific heat results is discussed below. For convenience this
discussion is divided into the temperature ranges: 100 to 450°C, 450 to
720°C, 720 to 910°C, and 910 to 1400°C.
lit
The Temperature Range 100 to 450°C
All of the initial measurements were made between 100 and 450°C
and served as a proving ground, so to speak, for the }
tests which followed. During these measurements, various equipment
changes were made, and the operation and calculation methods were de-
vised. With each major equipment or operational change, the letter of
the run number designation was changed. The date of the A to G sets are
not reported. These orie hundred-or-80 runs, along with the majority of
the H runs, were discarded due to instrumentation difficulties in the
non steady-state measurement circuitry. In this temperature interval,
the measurements were performed with a temperature amplifier gain of
1 x 105, and AI/I, ratios which ranged from 0.67 to 3.34. However, in
runs 31–34K at 436°C, a gain of 2 x 104 was used.
:
Runs 27-34K were accomplished after the specimen had been at
temperatures between 700 and 850°C for many days. Since the thermo-
couples were contaminated and the total hemispherical emittance changed
by this high-temperature soak, the specific heat determined by these
eight runs was about 1% higher than that predicted by interpolating
between the data taken on heating. These results were thereby deemed
invalid and are not entered in Table 3.
With a temperature amplifier gain of 105, a 10° temperature
change of a PtgoRh10/Pt thermocouple produced a full-scale deflection
on the Millisadic. Consequently, the specific heat measurements between
100 and 450°C were taken over a 10° interval with ä wide latitude of
AI/Ių ratios. As shown in Figure 7, the specific heat values were within.
£0.3% of McEnroy, were between 0.2 and 1.0% higher than Wallace et al.,
ORNI - AEC - OFFICIAL

QANL AEC
ORNL - AEC - OFFICIAL
II-I-39
- OFFICIAL
7770)81 VI
Sili!! (iii!"
> CHAPTER Firii do
and were within 2.0% of Pallister and Hultgren et al. Two conclusions
can be drawn from these results. The first is that measurements of the
specific heat of pure iron agrees to within $1.0% in this temperature
range and the second is that the AI/I, ratios had no measurable effect
on the accuracy of the pulse heating technique. Due to the latter con-
clusion, a AI/I, ratio of about 1 was used in all experiments at higher
temperature, rendering the heat absorbed by the specimen three times that
lost by radiation.
-
-
-
-
-
In the detailed error analysis, the errors of runs at 116°C
(AI/I1 = 3.34) and 1 to 4H at 412°C (11/I2 = 0.67) were estimated to:
be less than 11.0%. The experimental results verified these estimates.
Thus, the accuracy of the pulse heating technique is better than $1.0%
between 100 and 450°C.
The Temperature Range 450 to 720°C
F7 MARGIN : 1
.
Only nine runs were made in the temperature range 450 to 720°C.
Four of these were at 494°C (Runs 13-161) and five were at 612°C (Runs 17-21
Of the latter set of runs, only Run 17 and 21 are reported since the others
were discarded due to a malfunction of the Millisadic caused by its over..
heating. Because of the larger pickup on the specimen thermocouple created
by the misalignment of the thermoelements, a temperature amplifier gain of:
4 X 104 was used in these runs.
The specific heat calculated from these two sets of runs indicated...
the following:
1. These measurements were 1.0% higher but possessed the same
temperature dependence as those of Pallister and Hultgren et al.
....
2. The data of Runs 13–161 were 1.0% higher than those of
McElroy and 2.5% higher than those of Wallace et al.
....
....
3. For Runs 17 and 211, the data of McElroy was 2.3% lower and
those of Wallace et al. were 4.3% lower.
..
4. In this temperature region, the measurements of Wallace et al.
. and McElroy have the same temperature dependence.
....
...
.
5. The values of the other four investigators disagree by as
much as 3.5% in this temperature range; and at 600°C, none are
than 1.0%. Thus, including the results of the seven I runs, the specific
heat of iron is known to $2.2% between 450 and 720°C.
:
.
.
OINI - AEC - OFFICIAL
Although an error analysis was not performed on either of these
: sets of runs, the accuracy of runs possessing the same choice of variables
: was checked for temperatures above and below the temperatures studied.
Thus by interpolation, the error analysis predicts an accuracy of 21.0%, ·
ORNI - AEC - OFFICIAL

IVI:
161;;';.17 )N
II-I-40
.ORNI - AEC -
but the compared measurements are no better in accuracy than £2.2%.
one disregards the data of Wallace et al. the agreement is 11.5%.
If
od
The Temperature Range 720 to 910°C
.
. .
.
.
.
.
As shown in Figure 6, the specific heat of iron rises to a , .
distinct maximum at about 770°C, the Curie temperature. Consequently
the measurement of the specific heat of iron between 720 and 910°C is
quite difficult. For this reason, measurements were not made in this
region until the proper values of the pulse size and temperature ampli-
fier gain had been established. Previous measurements at the lower
temperatures suggested a gain of 2 x 104 and a AI/I, ratio of 1. These
settings were used in all runs in this temperature region.
-....
--
.
.
.
.
- .
-
Referring to figures 6 and 7, it is found that the relatively
good agreement that had been observed between the other four investiga-
som tions below 720°C is no longer present in the Curie region. In fact,
at 775°C, which is at least 6° above the Curie temperature reported by
these sources, a disagreement of at least 22% exists in the reported .;
specific heat data. Also, at 890°C, these measurements disagree by as
much as 13%. Obviously little can be learned about the accuracy of the
technique by measurements near the Curie point; however, data were taken
to demonstrate that meaningful measurements could be made in this ex-
tremely difficult temperature region.
;'
.::;:
-
.
As discussed previously, 67 runs were made between 720 and 910°C
and the data from these runs are plotted in Figure 6. Since an amplifi-
cation gain of 2 X 104 was employed, each pulse extended over 30°; and
therefore, a run which began 30 or less degrees below the Curie point .
passed through this transformation. The Milli sadic output for run 9J,
which was a typical run, is shown in Figure 8. If the slope of the
temperature-time relationship is discontinuous at the Curie temperature,
the specific heat is discontinuous; and likewise, if the slope of the
temperature curve is continuous the specific heat is continuous. These
two cases are illustrated in Figure 8. By plotting the Millisarlic output
on an expanded scale, the specific heat of iron was interpreted as being
discontinuous at the Curie temperature, undergoing a change from 0.3457
to 0.2672 cal/g °C. Such a change is designated a "second order" trans-
formation in thermodynamics. This terminology arises from the fact that
a discontinuous specific heat implies that the second derivative of the
Gibbs free energy with respect to temperature (at constant pressure) is
discontinuous.

Regarding the physical meaning of this discontinuous change,
the following is offered. Ferromagnetism is usually attributed to the
coupled spin of atoms of a material to produce a net alignment of these
spins. Therefore, the increase in the specific heat above that pre- ..
dicted by theory is attributed to the energy necessary to break this
coupling as the material approaches the paramagnetic state. Suppose
: that as the temperature is increased below the Curie point, the rate
ORNI - AEC - OFFICIAL
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II-I-41
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LEFT MARGIN.
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FIGURE 8. THE MILLISADIC OUTPUT FOR A RUN THROUGH THE CURIE POINT." CASE I
INDICATES THE SHAPE OF THE TEMPERATURE-TIME RELATIONSHIP AT THE
CURIE TEMPERATURE IF THE SPECIFIC HEAT IS DISCONTINUOUS, UNDER-
GOING A SECOND ORDER PHASE TRANSFORMATION. CASE II INDICATES
THE TEMPERATURE-TIME RELATIONSHIP FOR A HIGHER ORDER CONTINUOUS
CHANGE IN THE SPECIFIC HEAT.
of decoupling is increased due to the increase in thermal energy available
to break the bonds and maintain their misalignment. Now suppose that at
the Curie temperature, the rate of decoupling changes in a discontinuous
manner. The amount of energy necessary to heat the material to higher
temperatures should sharply decrease. That the specific heat does not
fall to that of the theoretical limit at the Curie temperature and in
fact continues to decrease at higher temperatures, may be attributed to
further decoupling, which is occurring at an ever diminishing rate due
to depletion of the number of aligned atoms.
ORNL - AEC - OFFICIAL
It is thought that the sharp break in the specific heat at the
Curie temperature is not due to a first order transformation, which would
involve a heat absorption at constant temperature because a thermal arrest
was not detected. The limits of detection of this transformation corre-
spond to an enthalpy change of about 6 cal/mole.
ORNI - AEC - OFFICIAL

1000
CURRENT
-
....
-
.
-.-
-
' : 700
1
..
CASE I
.
VOO
VOLTAGE
.
.
L
DIGITIZER
CASE II
TEMPERATURE
.
.
.
CURRENT
VOLTAGE
'.
--
TEMPERATURE
mammamumununmin mammaman
I
.::.-3..
-2..
:
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TIME (sec).
teret
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767..
ORNI - AIC - OFFICIAL
II-I-442
Regarding the temperature of the Curie phenomenon, Pallister and
Hultgren et al. reported 760°C, McElroy listed 768°C, and Wallace et al.
measured 769°C. The temperature found in this work is (772.8 $ 0.5)°C.
These differences are undoubtedly due to temperature measurement errors,
and consequently, the specific heat values reported by the various in-
vestigators near this transition are in wide disagreement.
From 780 to 820°C, the measurements of McElroy are less than
1.5% lower than those measured by the pulse heating technique (Runs 13J
to 16K) and possess the same temperature dependence. From 820 to 890°C
(Runs 19K and above), the measurements were found to be 2.29% above those
of the previous measurements (Runs 13J to 16K). This was caused by inad-
vertently heating the specimen to about 1000ºC during Run 17K and thereby
reducing the emittance. This introduced an uncertainty into the radiation
correction, and the one employe.. was too small, resulting in a higher
measured specific heat. The data of all runs taken after Run 17K were ..
corrected down 2.29% to agree with the earlier runs. After this correc-
tion, the data above 820°C were within 2.0% of McElroy and had the same
temperature dependence. Due to the close agreement of these two sets of
measurements, the data of the other three investigators were ignored.
Therefore, these comparisons indicated that the pulse heating
technique is accurate to +1.5% from 780 to 820°C. If the correct
emittance-temperature relationship above 820°C had been obtained, the
measurements would have agreed with McElroy to within 12.0% to 890°C.
The error analysis indicates an accuracy of £1.0% at these temperatures.
Comparison of the measurements between 720 and 780°C were not meaningful
due to the presence of the Curie phenomenon.
The Temperature Range 910 to 1400°C
The specific heat measurements above 910°C were of poor quality
and are considered accurate to no better than $5.0%. Due to the few
emittance measurements made, the temperature dependence of the specific
heat above 910°C is probably incorrect due to erroneous radiation cor-
rections. From a positive viewpoint, these measurements demonstrate
the high temperature capabilities of the technique and laid the ground-
work for future experiments at elevated temperatures. In fact, the
specimen was actually heated into the delta region (body-centered cubic
se The temperature of this transformation predicted
by the measured electrical resistivity was 1393°C, which is within 7°C
of the commonly accepted transformation temperature of 1400°C.
CONCLUSIONS
ORNI - AEC - OFFICIAL
The equipment, measurements, and calculations requisite to a
pulse heating calorimetric technique for measuring the specific heat of

· II-I-43
· ORNL - AEC - OFFICIAL
nemend
electrical conductors over a wide temperature range were presented. A
detailed error analysis of the technique predicted an accuracy of 1.0%
from 100 to 800°C. The accuracy and reproducibility of the technique
were demonstrated by measurements from 100 to 1400°C on pure iron and
by subsequent comparisons with other literature values. These measure-
'ments and comparisons indicate the following:
.
1.
to 820°C.
The reproducibility of the technique was £0.5% from 100..
".
.
..
pulse did not affect the accuracy of the technique.
3. From 100 to 450°C, the specific heat values of this work
and those of McElroy, Wallace et al., Pallister, and Hultgren et al. are
all within 21.0%.
4. From 450 to 720°C, these data and those of the other four.
investigators agree to within +2.8 2%. In this temperature range, the i
temperature dependence of the specific heat determined is the same as torf.
that of Pallister and Hultgren et al. but is different from that of
McElroy who agrees with Wallace et al.
..in.:.?!
uri .
!'.
5. Due to the wide spread in the data of the other authors
between 720 and 910°C, little was learned about the accuracy of the
technique between these temperatures. However, the data of McElroy is
within $2.0% of these measurements above 780°C.
6. Above 920°C, the specific heat values are accurate to no
better than 45.0%. Due to the few emittance measurements made, the
temperature dependence of the specific heat is probably incorrect in
this temperature range.
7. Run 24L demonstrated the high temperature capability of
the technique by showing the temperature 'arrest at the gamma to delta
transformation (1400°C).
---....- .
...
..
During the course of this study, the following phenomena were
observed:
-
-
..
---...
.
-.-
1. The Curie transition of pure iron occurs at (772.8 $ 0.59°C.
At this temperature, the specific heat is discontinuous,
a value of 0.3457 to 0.2672 cal/g-°C, and therefore, the Curie tran-
sition is second order,
2. The gamma to delta transformation in pure iron was found to
occur at 1393°C.
ORNL - AEC - OFFICIAL
.
. -
3. The total hemispherical emittance of a material is a sur-
face property, and its value can be altered by any treatment which
affects the surface character of the specimen, even though the bulk of
the specimen is unchanged.
rii
.
4
II-I-44
ORNI - ACC - OFFICIAL
Cinsipinilit'
pe
4. Two abrupt changes at 550 and 800°C were noted in the slope
of the emittance versus PT plot and may be physically significant.
Similar effects have been noted near these temperatures on other physical
properties of iron.
5. The total hemispherical emittance of iron is a linear function
of temperature between 400 and 800°C.
6. Measurements of the ratio of the electrical resistivity at :
room temperature to that at liquid helium temperatures indicate (a) the
specimen was slightly contaminated during the specific heat measure-
ments, and (b) the electrical resistivity at liquid helium temperatures
is drastically increased by cold working.
7. Highly cold working a PtgoRhıd/Pt thermocouple creates a
temperature measurement error which may be as large as 8.5°C between
200 and 1000°C.
IT MATliini
humo
::
:CIN |
This work demonstrated the need for several improvements in the
· experimental technique. Included in these are: (a) improved methods of ?
calculating the power loss down the electrodes and thermocouples, (b) a
more accurate method of determining dT/at, and (c) the need for more
precise thermometry. These constitute the basis of future work.
ACKNOWLEDGEMENTS
The author gratefully acknowledges the assistance of R. R. Gaddis,
R. K. Adams and the late Ei G. Davisson in providing, maintaining, and
operating the Millisadic system. To D. L. McElroy, whose leadership the
author has been privileged to follow for the past six years, is extended
the author's humble thanks. W. Fulkerson is thanked for his electrical
resistivity measurements, power loss model and helpful discussions.
C. R. Brooks and E. E. Stansbury of the University of Tennessee, are
acknowledged for their acceptance of this work in partial fulfillment
for the degree of Master of Science. To W. A. · Iang, Jr., and W. P. Murray,
cooperative students from the University of Cincinnati, the author is in-
debted for their help in the compilation of the Fortran program and the
final tabulation of the data. Also, thanks are extended to all the other
persons who contributed to this work, especially the members of the
author's group,
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II-I-45
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REFERENCIES
.
Lapp, E., "Study of the True Specific Heat of Nickel," Annales de
Physique Series 10, 12(1929), pp. 442-521.
.
ལ
Grew, K. E., "The Specific Heat of Nickel and of Some Nickel-
Copper Alloys," Proceedings of the Royal Society (London) Series A,
145(1934), pp. 509-522.
：
Krauss, F., "The Measurement of the Specific Heat of Metals at High
Temperatures," Zeitschrift für Metallkunde, 49(July 1958), pp. 386m;
392.
Wallace, D. C., P. H. Sidles, and G. C. Danielson, "Specific Heat
of High Purity Iron by a Pulse Heating Method," Journal of Applied
Physics, 31 (1960), pp. 168–176.
.
Strittmaker, R: C., G. J. Pearson, and G. C. Danielson, "Measure-
ments of Specific Heat by a Pulse Method," Proceedings of the
Iowa Academy of Science, 64 (1957), pp. 466-470.
☺
.
Kunrelmeyer, B., W. H. Mais, and E. H. Green, "Heat Capacity of
Fine Wires," Review of Scientific Instruments, 14 (1943), pp. 349–
355.
Pochupsksy, T. E., "Determination of the Heat Capacity by Pulse
Heating," Review of Scientific Instruments, 25(1954)
Pallister, P. R., "The Specific Heat and Resistivity of High-
Purity Iron up to 1250°C," Journal of the Iron and Steel Institute,
161 (1949), pp. 87-90.. .
Taylor, R. E. and R. A. Finch, "The Specific Heat and Resistivities
of Molybdenum, Tantalum, and Rhenium," Journal of the Less-Common
Metals, 6(1964), pp. 283–294.
Rasor, N. S., and J. D. McClelland, "Thermal Properties of Materials,"
WADC-TR-56-400, Part 1, (1957).
Baxter, H. W., "Determination of Specific Heat of Metals," Nature,
153(1944), p. 316.
Nathan, A. M., "A Dynamic Method for Measuring the Specific Heat of
Metals," Journal of Applied Physics, 22(1951), pp. 234-235.
Avramescu, A., "Temperature Dependency of the True Specific Heat of
tic Copper and Pure Aluminum up to Their Melting Points,"
Zeitschrift für Technische Physik, 20(1939), pp. 213-217.
ORNL - AEC - OFFICIAL
na web stranitikan nilai ir kitiems spreading the fourteen
m o wake
mido
-
t
CRNI - IEC
II-I-46
si Chait1
TITI..1:
Khotovich, V. I., and N. N. Bagrov, "Impulse Method of Determining
Specific Heat," Doklady Akademii Nauk SSSR, 81 (1951), pp. 1055-
1057.
(15)
Cezairliyain, A., "A High-Speed (Milliseconds) Method for the
Simultaneous Measurement of Enthalpy Specific Heat, and Resistivity
of Electrical Conductors at High Temperatures, " Proceedings of the
Third Symposium on Thermophysical Properties, The Americal Society
of Mechanical Engineers, New York, (1965), pp. 253-263.
Kollies T. G., "The Development of a Pulse Heating Calorimetrici
Technique for Measuring the Specific Heat of Electrical Conductors
and its Application to Pure Iron from 100 to 1400°C," ORNL-TM-2187
(1965).
.
.
.-
.
(17)
Moore, J. P., W. Fulkerson, D. L. McElroy, and T. G. Kollie, "Com-
parison of the Thermal Conductivity, Electrical Resistivity, and
Seebeck Coefficient of a High-Purity Iron and Armco Iroil to 1000°C
paper read at the United States Radiological Defense Laboratory,
San Francisco, California, October 13, 1964.
FT ARGIN- . per
(1.8)
Lyman, Taylor (ed.), Metals Handbook, The American Society for
Metals, Novelty, Ohio, (1961), Vol. 1, 8th ed., p. 1206.
(19)
GAP/R Application Brief, George A. Philbrick, Incorporated, Boston,
(1963), D9, pp. 1-2.
Personal correspondence received by T. G. Kollie, Oak Ridge National
Laboratory, from W. Fulkerson, Oak Ridge National Laboratory,
December 1, 1964.
(21)
"High Temperature Thermometry Work at the Oak Ridge National
Laboratory," ed. by N. H. Briggs and D. L. McElroy, pp. 13,1-13.2.
This paper was presented at the United States Atomic Energy Committee
High-Temperature Thermometry Meeting, Washington, D.C., February 24,
1965.
Davisson, .C. and J. R. Weeks, "The Relation Between the Total Ther-
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::(23)
Abbott, G. L., N. J. Alvares, and W. J. Parker, "Total Normal and
Total Hemispherical Emittance of Polished Metals," WADD-TR-61-94
(1961).
ز :
in!!!!!11.!!!
Oi iring
McElroy, D. L., "Calorimetry of High Purity Iron and Steels," un-
published Ph.D. Thesis, the University of Tennessee, 1957.
: .. : رز - ن .
Hultgren, R., R. L. Orr, P. D. Anderson, and K. K. Kelley, Selected
Values of Thermodynamic Properties of Metals and Alloys, John Wiley
& Sons, Inc., New York, (1963).
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:
END
DATE FILMED
11/26 /65