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SPECIFIC HEAT AND HEAT OF FUSION OF ICE
By H. C. Dickinson and N. S. Osborne
CONTENTS
Page
Introduction (^49)
PRE\aOUS WORE 50
Description of calorimetric method (^52) Material, and preparation of (^) samples (^53) Experimental procedure (^55) Specific heat (^) of ice (^63) Experimental (^) results , (^63) Relation (^) between apparent specific heat of ice and dissolved impurities ... (^69)
Discussion of results 73
Conclusion (^76)
Heat of fusion of ice 77
Summary 78
Table of total heat of ice and water (^79)
INTRODUCTION
The present investigation is one of a series undertaken, (^) at the
request of the refrigeration industries, for the determination of
constants which are of fundamental importance in the design and
operation of refrigeration machinery.
A determination made at the Bureau ^^ of the heat of fusion of
ice was pubHshed in 191 3. In this pubHcation is given a review
of previous work on this subject. As stated there the results
presented are subject to a slight imcertainty on accoimt of the
lack of adequate knowledge of the specific heat of ice near the
melting point. For this reason and also on accoimt of the direct
technical significance of the specific heat of ice, it has been made
the subject of the work here presented.
1 Dickinson, Harper, and Osborne, this Bulletin, 10, p. 235, 1913, Scientific Paper No. 209.
50 Bulletin^ of the^ Bureau^ of Standards
PREVIOUS WORK
[Vol, la
A review of previous determinations of (^) the heat of fusion (^) of ice
is given^ in^ the^ pubHcation^ cited^ above.
The results of previous experimental (^) determinations of the spe-
cific heat of ice are summarized in (^) Table i.
TABLE 1
Specific Heat of (^) Ice—Results (^) of Previous Observers
Date Observer Temperature range^ Mean perature^ tem-
Heat
capacity cal/gram
degree
1910 Nemst*. -^ 7.
- (^15)
- (^) 29.
- (^) 48.
- (^39)
- 48
- -•. (^) Koref 3 - 2.9 to- 76.
- (^) 15.3 to- 75. - (^) 81. 7 to -189.
1904 Bogojawlenski *
1849 to -^78
to -
- (^18) to - (^78)
- (^78) to -
-188 to -252.
1907 Nordmeyer and Bernoulli f^ ..
Dewar s
Gad^in i"
« Nemst, K. Ak. d. Wiss. Sitzb.. 1910, p. 262.
' Koref, K. Ak. d. Wiss. Sitzb., 1910, p. 253.
* Bogojawlenski. Schr. der Dorpater Naturf. Ges.. 13, p. i.
6 Regnault, Ann, d. Chim. (3), 26, p. 261, 1849-
« (^) Value given by Nemst (loc. cit.), recalculated from original on basis of specific heat of lead.
^ Nordmeyer and Bernoulli, Verb. d. Deutch. Phys. Ges.. 9, p. 175; 1907.
8 Dewar, Proc. Roy. Soc. Lond., 76, p. 330; 1905.
' Person, Ann. Chim. et Phys. (3), 21, p. 29s; 1847.
" (^) Review by Angstrom, Ann. d. Phys., 90, p. 509; 1853- Original, Nov. Act. Reg. Soc. Upsala, 5.
Nemst and^ his^ associates^ have^ deduced^ an^ empirical^ equation expressing their^ results^ on^ the^ specific^ heat^ of^ ice^ relative^ to^ its temperature. The^ graphical^ representation^ of^ this^ equation,
together with^ the^ observed^ results^ of^ different^ experimenters,^ is
shown in Fig. i. The^ mean^ temperatures^ of^ the^ determinations
52 Bulletin^ of the^ Bureau^ of Standards^ [Voi.^12
are all below —7°^ C. From the trend of these results in (^) the
upper part of the range a very significant increase in the specific
heat on^ approaching^ the^ melting^ point^ is^ suggested.^ This^ might
not appear remarkable^ except^ for^ the^ fact^ that^ A. W. Smith^ '^^ has
obser^ed that while^ with^ impure^ ice^ an^ apparent increase^ in specific
heat is obtained on approaching^ the melting point, ice of a high
degree of purity shows no such abnormal change in specific heat
up to a temperature very close to zero. The presence of certain dissolved impurities lowers the freezing point of water. At any given temperatiure not too far below
zero a certain proportion of an ice sample containing impurity is
imfrozen, due to this lowering. A portion of the heat of fusion is thus made to appear as sensible heat, and the observed appar-
ent heat^ capacity^ of^ such^ ice,^ especially^ near^ zero,^ is^ larger^ than
for ice containing^ no^ such^ impurity.^ Smith's conclusion^ that the
specific heat of^ pure^ ice^ does^ not change^ appreciably^ on^ approach-
ing zero is therefore plausible, notwithstanding the fact that it
appears to be in^ contradiction^ to the results^ of^ others.
DESCRIPTION OF CALORIMETRIC METHOD
The experiments here described were planned with the object of attaining a high precision in the thermal measurements upon ice of a high degree of purity, and especially of extending the
experiments to temperatures near zero, where the specific heat is
more important technically and is most in doubt.
For making^ the^ measurements^ a^ calorimeter^ was^ adopted which is described in detail elsewhere. ^^^ An important feattu-e of (^) this
calorimeter is the employment^ of^ a^ shell^ of^ copper^ inclosing the
specimen under investigation,^ the^ copper^ acting^ as the calori-
metric medium^ for^ the^ transmission^ and^ distribution^ of heat
developed in an^ electric^ heating^ coil^ which^ is^ built into the shell.
Temperature changes in calorimeter and contents are (^) measured
by means of an^ electric^ resistance^ thermometer^ likewise built into
the shell.^ The^ calorimeter^ is^ suspended^ in^ an air space within
an inclosing metal jacket. Multiple thermocouples distributed
about the surfaces of the calorimeter and the jacket serve to indi-
" Smith, Physical Review, 17, p. 193; 1903. " Dickinson and Osborne, this Bulletin, 12, p. 23, 191s.
DickinatnX
Osborne J Specific^ Heat^ and^ Heat^ of^ Fusion^ of^ Ice^53
cate at any instant the^ difference^ between^ the^ average^ tempera-
tures of the surfaces. This^ enables^ the^ corrections^ for^ thermal
leakage between calorimeter^ and
its surroundings to^ be^ controlled
and measured. The jacket containing the calo-
rimeter is immersed in^ a^ stirred
liquid bath which, by means^ of
a refrigerating coil using liquid
carbon dioxide, an^ electric^ heat-
ing coil, and a thermoregulator,
is maintained at any tempera-
ttu-e between —55°^ C and^ -^40° C to within a few thousandths
of a degree. Using current fur-
nished by a storage battery, the
heat supplied to the calorimeter
and the contained specimen is
developed at a nearly constant
rate, which (^) is determined by po-
tentiometer measurements of cur-
rent and of potential drop.
By this method (^) the heat in-
volved in the temperature changes
of the material is measured di-
rectly in terms of electrical units,
from which it may (^) be reduced (^) to
customary heat units (^) by using the
proper constants.
The ice specimens were con-
tained in a metal cell which
fits inside the calorimeter shell.
To promote the rapid equaliza-
tion of temperature, the cell is
provided with radial copper vanes attached to the interior
surface. The details (^) of construction of the container are shown
in Fig. 2.
7ZZZZZZZZZ2.
SECTION A-B
Fig. 2. Specimen container
oifJme'^] Specific^ Heat^ and^ Heat^ of^ Fusion^ of^ Ice^55
Sample No. 4 was distilled^ directly^ into^ the^ container,^ the^ con-
densed water touching no^ surface^ which^ was^ not^ tinned.^ In
doing this the container was^ first^ inverted^ so^ that^ the^ condensed
water would drain^ out,^ thus^ washing^ the^ entire^ interior^ surface
with steam and hot^ distilled^ water.^ After^ about^800 cc^ had^ been
thus passed through,^ the^ container^ was^ placed^ erect^ and^ sur-
rounded with ice.^ Water^ was^ condensed^ until^ the^ container^ was
nearly full, leaving about 700 cc in the distilling flask. Thus,
only the middle fraction was retained for the sample. The water
used in the distilling flask was specially prepared double distilled
water. Before sealing the sample in the container, the contained
water was boiled to expel any air which might have been absorbed
after condensation.
Measurements of the electrical conductivity of the samples,
made after the various determinations were completed, failed to
show any considerable difference in the observed conductivities
of the different samples.^ These^ were^ all^ of^ the^ order^ of 3 X io"°
ohm~^ cm~^
While the specimens were being frozen the (^) calorimeter was
cooled to a^ temperature^ slightly^ below^ zero.^ The^ object of this
was to avoid^ melting^ any^ considerable^ portion^ of^ the^ ice^ when^ the
container was introduced into the calorimeter. The operation (^) of
inserting the^ specimen^ into^ the^ calorimeter^ at^ a^ temperature of
zero was accompanied by the unavoidable condensation of moisture
on the calorimeter, as the work was done when the dew point (^) was
above zero. To absorb this moisture and to maintain the (^) dryness
of the air within, a small dish of calcium chloride was placed at (^) the
bottom of the jacket.
EXPERIMENTAL PROCEDURE
A detailed description of the various operations involved in
determination of heat capacity is given in the previous paper
referred to above. Briefly stated, the sequence as to manipula-
tions and observations is as follows:
The calorimeter containing the (^) specimen is cooled to the initial temperature of the experiment. The jacket is brought under
control of the thermoregulator at the temperature of the calo-
rimeter. The resistance of the built-in platinum thermometer is
56 Bulletin^ of the^ Bureau^ of Standards^ [Voi.^12
observed to determine the initial temperature ^^^ of the calorimeter.
Electric current^ is^ passed^ through^ the^ heating^ coil^ of^ the^ calo-
rimeter for a measured interval of time. During this time alter-
nate readings^ of^ current^ ^^^ and^ potential^ drop^ are^ made^ at^ equal
intervals of time to determine the rate of energy supply to the
calorimeter. Meanwhile^ by hand control of the jacket heating
current the temperature of the jacket is kept as nearly as practi-
cable equal to the rising temperature of the calorimeter. The
readings of the thermocouples, which are recorded at intervals of
30 seconds throughout^ the entire experiment, indicate^ the tem-
perature difference between the calorimeter and jacket, and serve
the double purpose of guiding the jacket control and giving the
data for determining the thermal leakage. After the interruption
of the calorimeter heating current, the jacket is again brought
under control of the thermoregulator, and when the calorimeter
attains thermal equilibrium the thermometer resistance is again
observed to determine the final temperature.
The rate of thermal leakage is determined by a separate experi-
ment, in which, with the calorimeter and jacket at different tem-
peratures, alternate readings are made^ of^ the^ resistance^ ther-
mometer and of the thermocouple between calorimeter and jacket.
An approximate value of the heat capacity of the calorimeter at
the time of this supplementary experiment is adequate to enable
the computation of the rate to be made.
The mass of the sample is determined from weighings^ in air
against brass weights of the empty container, and of the container
with specimen included. The difference between these weigh-
ings corrected for air buoyancy gives the mass of the specimen.
An example of the record of a single experiment in determining
the specific heat of an ice specimen is given in Fig. 3.
1' (^) The temperatures d employed in this paper are expressed in degrees of the centigrade scale determined by a resistance thermometer of the Heraeus purest platinum according to the equations
\ioo / 100 Kioo—Ko
The value of d here taken, viz, 1.48. was obtained by a direct comparison of platintun resistance ther-
mometers of Heraeus purest platinum, in the interval o" to 100° with verre dur thermometers stand-
ardized at the Bureau International des Poids et Mesures, and thus serves to reproduce the hydrogen
scale of that bureau. The difference between the scale above defined and the thermodynamic scale as reproduced in the inter.
vaJ —50°^ to -f 500°^ by means^ of the platinimi resistance^ thermometer standardized at the temperatures
of melting ice, steam, and sulphur vapor, consists in the use of 5= 1.48 instead of (^) 1.49+, which would be the value for platinvun^ of the purity here employed when the sulphur boiling point is taken as 44496. At
-f so" the^ difference^ between^ the^ two scales is less than^ 9oo3, which is within the limits of accuracy of
reproduction of the hydrogen scale.
** All electrical quantities are expressed in terms of the units adopted by the Bureau of Standards, as
given in Bureau Circular No. 29, ist ed.
58 Bulletin^ of the^ Bureau^ of Standards^ [Voi.^ iz
The initial and final readings of thermometer resistance cor- rected for bridge errors give the initial and final thermometer resistances R^ and R^. The difference between the initial and final resistances, JR, multiplied by the difference factor, K^,
gives the change in temperature of the calorimeter, JO. In
obtaining K,n from the chart Fig. 4 the mean resistance R^ (^) is used.
The average^ thermocouple^ deflection^ multiplied^ by the rate and by the^ time^ between^ initial^ and^ final^ thermometer^ readings
gives the correction^ for^ thermal^ leakage.
The mean potentiometer readings for potential drop and for current, corrected for instrumental errors, and multiplied by the proper reduction factors, give the potential drop, E, and cinrent /.
The product of the ciurent and potential drop is the power, and
this multiplied by the time is the total energy electrically supplied
to the calorimeter. This total energy corrected for thermal leak-
age gives the corrected energy, i. e., the amount of energy received
by the^ calorimeter^ and^ contents^ during^ the^ experiment.
The corrected energy^ divided^ by the^ change^ in^ temperature, JQ, (^) gives the heat capacity of calorimeter and specimen in (^) joules
per degree.
The heat capacity of the calorimeter^ is obtained from the
curve, Fig. (^) 5, at a point corresponding to the mean temperature,
^(^1 +^ ^2). 2 Deducting from the total mean heat capacity the heat (^) capacity
of the calorimeter, the mean^ heat^ capacity^ of^ the^ specimen is
obtained over the temperature interval of the experiment.
The mean heat capacity of the specimen divided by the mass and by the number of joules ^^^ in one 20°^ calorie," gives the mean specific heat of the ice specimen in 20°^ calories per gram per degree.
^* (^) The relation between the 20° calorie and the joule (international watt second) is taken as represented
by the^ equation
I calorie2o=4.i83 joules 1' (^) The 20° calorie used in this paper is taken as the quantity of heat per gram (mass) per degree centigrade
required to raise the temperature of water at 20° C.
Dickinsonl
Osborne J Specific^ Heat^ and^ Heat^ Fusion^ of^ Ice.^59
40 -30 -20 -10 (^10 20 )
Fig. 4. Calibration of resistance thermometer in calorimeter
DEGREES & CENTIGRADE
oifome^] Specific^ Hcat^ and^ Heat^ of^ Fusion^ of^ Ice^ 6i
where
5 =^ mean specific^ heat^ of^ specimen^ in^ 20°^ calories^ per gram per degree over the interval of temperature
employed.
C =^ mean heat^ capacity^ of^ calorimeter^ in^ joules^ per^ degree. / =^ cirrrent in^ amperes^ (mean^ value) E =^ potential^ drop^ in^ volts^ (mean^ value) T =^ dtiration^ of^ energy^ supply^ to^ calorimeter^ in^ seconds. d =^ average thermocouple^ deflection^ in^ millimeters^ during experiment.
/ =^ time in^ minutes^ between^ initial^ and^ final readings of
calorimeter resistance thermometer.
B=rate of^ thermal^ leakage^ to^ calorimeter^ from^ surround-
ings in joules per minute per millimeter thermo-
couple deflection.
i^i =^ initial^ resistance^ of^ thermometer^ in^ ohms. i?2 =^ final^ resistance^ of^ thermometer^ in^ ohms. ^i? =^ difference^ between^ initial^ and^ final^ resistance^ of^ the
thermometer in ohms.
Km =^ the^ difference^ factor^ for^ the^ resistance^ thermometer,
i. e., -—=^ in degrees per ohm.
M =mass of specimen in^ grams. The current and potential drop^ were always so nearly constant
that the approximation in taking the product of their mean values
multiplied by the time as the total energy^ is well^ within the limit
of allowable error.
A complete description of the method and^ results of the cali-
bration of^ the^ calorimeter^ resistance thermometer and of the
determinations of the heat capacity of the calorimeter are given
in a preceding paper.*^
The values of the difference factor K as there determined are
given graphically in Fig. (^) 4. This chart was used in making
calculations of specific heat determinations, the difference factor
for any observed interval being taken from the curve at the point corresponding to the mean between the initial and final ther- mometer resistances. Since the performance of the thermometer
" Dickinson and Osborne, this Bulletin, 12, p. 23, 1915, Scientific Paper No. 247.
6844°— 15 5
62 Bulletin (^) of the Bureau (^) of Standards [Voi. 12
was found to depend upon the previous thermal treatment, in
the use of the chart the appropriate calibration line was chosen to
correspond with the initial temperature of the experiments on the
particular day.
The values of the heat capacity of the calorimeter are given
graphically in Fig. (^) 5. The two curves there shown represent (^) the
values obtained with the two arrangements of the thermocouples
which were used in the determinations. When the earlier arrange-
ment was used, consisting^ of^ a^ single^ set of thermocouples, the
junctions of which^ were so placed^ as to indicate the difference in
temperature between the surface of the calorimeter and a point
in the liquid near the jacket, the upper ciu*ve was obtained. The
lower curve was obtained with the later arrangement, making (^) use
of an additional^ set of^ couples^ the^ junctions^ of which^ were so
placed that when joined in series the two sets of couples indicated
the difference in temperature between the calorimeter and the
jacket surfaces.
These later results showed that in the original arrangement the
true temperature^ difference^ between^ calorimeter^ and^ jacket^ had
not been indicated^ owing^ to^ the^ effect^ of^ lag^ in^ liquid^ and^ jacket.
The significance^ of^ this^ fault^ in^ the^ apparatus^ did^ not^ appear^ until
after the experimental^ work^ on^ samples^ 1,2, and^3 had^ been com- pleted, but errors from this cause in^ the^ final^ results for these samples could be avoided in the manner explained below. The value of the observed total heat capacity of the empty calorimeter and of the calorimeter containing a specimen would be affected to the same extent by the improper placing of the ther- mocouple, provided that in the two experiments the manipulation of (^) the jacket was similar. If, therefore, in computing (^) the result
of a specific heat determination a value of heat capacity of the
calorimeter be used, determined under experimental conditions
similar to those in the specific heat determination, no error is
introduced into the resulting value of specific heat. It was necessary therefore (^) to employ the false values of heat capacity shown by the upper ctirve in Fig. 5 in computing the earlier results. It was ascertained that the variations in manipulation which did occur, such as the use of different amounts of refrigeration and compensating heating, etc., were not sufficient to cause any large systematic error.
64 Bulletin^ of the^ Bureau^ of Standards
TABLE 3
Specific Heat of Ice
Sample No. 1, Reduction of Results
IVoLzs
Initial
tem-
pera- ture ^
Final
tempera-
ture ^IdA-G 2 d-d'^ Aid-d")
Mean specific heat
6,10 6^=
Specific heat corrected
^obs
\alc.
^^obs-
^^calc
degC degC degC degC degC
caho O'deg
41.853 31.648 36. 395 36. 750 .355 .0007 .4382 .4389 .4380 (^) +.
- 559 21.553 26. 080 26. 556 .476 .0009 .4555 .4564 .4572.
- 648 21. 729 26. 224 26. 688 .464 .0009 .4563 .4572 .4569 (^) +.
- 548 11. 799 15.945 16. 674 .729 .0014 .4744 .4758 .4764 -.
- 726 12.016 16. 157 16.871 .714 .0013 .4743 (^) .4756 .4760 - (^). 11.799 7.014 9.097 9.406 .309 .0006 .4899 (^) .4905 .4900 +. 12.017 7.279 9.353 9.648^ .295 .0006 .4896 .4902 .4894 +. 7.016 4.182 5.417 5.599 .182 .0003 .5006 .5009 .4990 +. 7.279 4.430 5.679 5.854 .176 .0003 .4996 .4999 .4982 +. 4.183 2.327 3.120 3.255 .135 .0003 .5153 .5156 .5101 +. 4.430 2.570 3.374 3.500 .126 .0002 .5096 .5098 .5081 (^) +. 2.327 1.419 1.817 1.873 .056 .0001 .5407 .5408 .5325 (^) +. 2.570 1.614 2.037 2.092 .055 .0001 .5289 .5290 .5261 (^) +. 1.419 .583 .9095 1.001 .092 .0002 .6341 .6343 .6244 (^) +. 1.615 .714 1.074 1.164 .090 .0002 .5903 (^) .5905 .5901 +. .584 .284 .4073 .434 .027 .0001 1. 1078 1. 1079 1. 1059 +. .714 .356 .504j .535 .031 .0001 .8830 .8831 .8966 -^.
Dickinsonl
Osborne J Specific^ Heat^ and^ Heat^ of^ Fusion^ of^ Ice
TABLE 4
Determinations of Specific Heat of Ice
Sample No. 2, Experimental Results
[Mass, 399.8 grams]
65
Date Exp^ energyTotal
Cor- rection for ther-
mal
leak- age
Cor- rected total energy
Initial
tem-
pera- ture 01
Final
tem-
pera- ture
Tem- perature differ-
ence
Total mean heat capacity
^ito^
Mean heat capacity of (^) calo- rimeter By (^) to ^
Mean heat capacity of ice ^lt0^
Mean specific heat dy to (^) $ Sn.
June 12 1
joules
joules
joules 18069
degC -45. (^509)
degC
degC
ildeg
jideg
JIdeg
Ca/
g-deg
2 18060.5 + 4.8 18065 35.094 24.915 10. 178 1774. 1023. 751.4. 3 18042.^ -^ 4.2 18039 24.915 14.974 9.9412 1814. 6 1032. 7 781.9.
4 18035. -11.8^18023 14.974 5.262 9.7118 1855. 1040. 7 815.1.
6 3604.1 -^ 1.1 3603.0 3.344 1.459 1. 8853 1911.1 1046. 864.9. 7 1914. 6 -^ 0.3 1914.3 1.459 .530 .9289 2060. 8 1047. 1013. 7. June 13 1 18352. 7 -^ 9.1 18344 -26. 561 -16.409 10. 152 1807. 1031. 775.7. 2 18311.8 0.0 18312 16.371 6.470 9.9013 1849. 1039. 809.9. 3 5487.6 + 2.6 5490.2 6.470 3.551 2.9189 1880. 1044.7 836.2. 4 5484. -^ 2.2 5482. 7 3.551 .722 2.8286 1938. 1046. 5 891.8. 5 914.7 -^ 4.2 910.5 .722 .352 .3702 2459. 1047. 1412.2. 6 456.3 + 1.0 457.3 .352 .238 .1137 4022. 1047. 5 2974. 1.
TABLE (^5)
Specific Heat of Ice
Sample No. 2, Reduction of Results
Initial
tem-
pera- ture
Final
tempera-
ture ^dA=e 2 ~ d-d'^ K{d-d')
Mean specific heat
5it0^2=
Specific corrected
dobs
S^
(9calc.
^^calc
deoC degC degC degC degC
calv> Q'deg
35.094 24. 915 29.570 30.004 .434 .0008 .4493 .4501 .4507 -. 26.561 16.409 20.877 21.485 .608 .0011 .4639 .4650 .4670 -.
- 915 14.974 19. 315 19.944 .629 .0012 .4676 .4688 .4700 -.
- 371 6.470 10. 292 11.420 1.128 .0021 .4843 .4864 .4874 -.
- 974 5.262^ 8.877^ 10.^118 1.241^ .0023^ .4874^ .4897^ .4904^ -^. 6.470 3.551 4.793 5.010 .217 .0004 .5000 .5004 .5007 -. 3.551 .722^ 1.601^ 2.136^ .535^ .0010^ .5333^ .5343^ .5399^ -^. 3.344 1.459 2.209 2.402 .193 .0004 .5172 .5176 .5212 - , 1.459 .530 .879^ .994^ .115^ .0002^ .6062^ .6064^ .6282^ -^. .722 .352^ .5041^ .537^ .033^ .0001^ .8445^ .8446^ .8812^ -^. .352 .238 .2894 .295 .006 .0000 1.779 1.779 1.6522 +.
Dickinsonl Osborne (^) J Specific^ Heat^ and^ Heat^ of^ Fusion^ of^ Ice^67
TABLE 8
Determinations of Specific Heat of Ice
Sample No. 4, Experimental Results
[Mass, 460.7 grams]
Date Exp^ energyTotal
Cor- rection lor ther-
mal
leak- age
Cor- rected total
energy
Initial
tem-
pera- ture ^
Final
tem-
pera- ture
Tem- perature differ-
ence
di to ^
Total mean heat capacity di to di
Mean heat capacity of calo- rimeter 01 to Si
Mean heat capacity of ice di to di
Mean specific heat
joules joules joules degC
degC
degC JIdeg JIdeg jideg
co/ g-deg
Aug. 5 1 15167.4 +6.2 15174 36. 0626 27.9733 8. 0893 1875.8 1018.5 857.3 0.
2 15156. +2.6 15159 27.9733 20. 0447 7.^9286 1911.9^ 1026.8^ 885.1^.
3 17942.7 -2.2^17941 19. 8574 10.6655 9.^1919 1951.8^ 1033.3^ 918.5^.
8959.0 -1.2^ 8957.8^ 10.6655 6. 1438 4.5217^ 1981.^ 1038.^7 942.4^.
4468.6 +2.9 4471. 6. 1438 3.8982 2.^2456 1991.2^ 1041.^ 950.0^.
4478. -7.2^ 4470.9 3.8982 1.6695 2.2287^ 2006.^ 1042.8^ 963.3^.
1789.7 0.0 1789. 1.6695 .7827 .8868^ 2018.1^ 1043.9^ 974.2^.
Aug. 6 9154. 0.0 9154 40.8110 35. 8648 4.9462^ 1850.^ 1013.^ 837.3^.
18356.7 +3.1 18360 35.8648 26. 1189 9. 7459 1883.^ 1020.2^ 863.6^.
3 18325.1 -1.4 18324 26. 1189 16.6050 9. 5139 1926.0^ 1028.4^ 897.6^.
18313. +1.2 18314 16.6045 7.3042 9.3003^ 1969.2^ 1035.9^ 933.3^.
9159. -3.1 9156 7.3037 2.7250 4. 5787 1999.^7 1041.^ 958.6^.
1836.4 -3.4 1833.0 2. 7236 1.8116 .9119 2010.0^ 1043.^ 966.9^.
Aug. 7 18288.0 -3.3 18285 39.5670 29.7674 9. 7996 1865.9 1016.9 849.0.
68 Bulletin^ of the^ Bureau^ of Standards
TABLE 9
Specific Heat of Ice
Sample No. 4, Reduction of Results
[Vol. (^) Z
Initial
tem-
pera- ture ^
Final
tempera-
ture (^) V^1^2=^
61+62 0^
2 ~^
6-6' (^) A{6-d')
Mean specific heat
Specific corrected
^obs
S^
^calc.
^obs-
\alc
degC degC degC degC deaC
caho
O-deg
39.567 29.^767 34.^319 34.667^ .348^ .0006^ .4405^ .4411^ .4418 -^. 35.865 26.^119 30.^607 30.992^ .385^ .0007^ .4481 .4488^ .4487 +.
36.063 27.^973 31. 761 32.018 .257 .0005 .4449 .4454 .4465 -^.
27.973 20. 045 23. 680 24.009 .329 .0006 .4593 .4599 .4616 -.
- 767 20. 196 24. 519 24.982 .463 .0009 .4596 .4605 .4600 (^) +.
- 196 10.834 14. 792 15. 515 .723 .0013 .4769 .4782 .4781 (^) +. 19.857 10.665 14.552 15.261 .709 .0013 .4766 .4779 .4786 - (^). 16.604 7.304^ 11.012^ 11.954^ .942^ .0018^ .4843 .4861^ .4852 +.
- 665 6.144 8.095 8.404 .309^ .0006^ .4890 .4896 .4907 -^. 10.836 1.674 4.259 6.255 1.996 .0037 .4952 .4989 .4980 +. 7.304 2.725 4.461 5.014 .553 .0010 .4974 .4984 .4976 +. 6.144 3.898 4.894 5.021 .127 .0002 .4930 .4932 .4968 -^. 3.898 1.670 2.552 2.784 .232 .0004 .4999 .5003 .5015 -. 2.724 1.812 2.222 2.268 .046 .0001 .5017 .5018 .5024 -. 1.956 .822 1.268 1.389 .121 .0002 .5051 .5053 .5058 -. 1.812 .903^ 1.279^ 1.358^ .079^ .0001^ .5051^ .5052^ .5057^ -^. 1.669 .783 1.143 1.226 .083^ .0002^ .5055^ .5057 .5066 -^. .903 .340 .554 .622 .068^ .0001^ .5166^ .5167 .5177 -^.
.822 .266 .468 .544 .076 .0001 .5231 .5232 .5234 -^.
.266 .073 .139 .170 .031 .0001 .6759 .6760 .7116 -^.
.073i .045. .057« .059, .OOlr .0000 1.730 1.730 1.7326 -^.
