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Physical properties of sea water solutions: heat capacity
Desalination -
PHYSICAL HEAT
EIscvrer Publishing Company, Amsterdam - Printed in The Netherlands
PROPERTIES OF SEA WATER
SOLUTIONS:
CAPACITY* l
D. I-. JAMIESON, J. S. TUDHOPE, Natiotd
hginecring
R. MORRIS
AND
G. CARTWRlGHT
Laboratory. E&t Kilbride, Glasgow iSc*orfand)
(Received April 4.1969)
SUMhfARY
The heat capacity of sea water and its concentrates has been measured in the temperature range 80 to 180°C using a differential heating method. An equation is given which tits the measured values of heat capacity, together with those from the literature, to within their various experimental accuracies. t . INTRODtJtIFtON Most distillation plants for desalination purposes have been designed to operaie at temperatures of less than 120°C. This maximum temperature was adopted because it represented the temperature below which calcium sufphate scaling was unimportant. It is likely that research will provide soiutions to this scaling problem and that in these circumstances higher maximum temperatures will be used in flash evaporation plant. In anticipation of this. measurements of vapour pressure, density, viscosity, thermal conductivity and heat capacity are being made in the National Engineering Laboratory at temperatures up to about 180°C for sea water solutions ranging in concentration from I to 5 times that of natural sea water. The present article gives the results of measurements of heat capacity.
2. EXlSnNG DATA The heat capacity of sea water at normal concentration was determined between 0 and 3O’C by Cox (I) and at concentrations of 0.3 to 3.5 times normal sea water between 0 and 80°C by Bromley (2). Both these measurements arc in agreement and are believed to be accurate to within about &- 0.2 per cent. Ponizovskii (3) has also reported data for the heat capacity of various brine solutions at 22S”C. Where the relative composition of the solution is similar to that of sea * Prcsettfcd at PURAQUA-U.S. E?rhibition and lntemational cation and Desalination. held in Rome, Feb. 17-23. 1969.
Conference
on Water Putifi-
f3esahation, 7 (I%F/?O)
23-30
24
D. 1. JAMIESON
et
fff.
water the heat capacity vaiues are within I per cent of Bromley’s data. No measurements at temperatures above 8O’C or with more concentrated sea water solutions are known to the authors. 3.
CHOICE
OF SEA WATER
The salinity of sea water v.ztries from place to piace throughout the world. However. for all practical purposes. the relative composition of the dissolved salts is constant. That is, the only variable is the amount of pure water in which the various sea s&s are dissolved, so a knowledge of the variation of any property with salinity gives the property for any sample of sea water, irrespective of its source. When sea water is concentrated its composition is altered by. for example, the decomposition of bicarbonate and the precipitation of calcium sulphate. For these tests a synthetic sea water from which calcium sulphate had been deliberately omitted was used. This “Ca-free’ sea water is described in (4) and represents sea water from which the calcium sulphate had been removed by precipitation or TABLE I COMPOSITION
OF “CA-FREE”
NaCl MgCIt * 6HzO Mg801.7HzO KC7 KBr HJBOJ NaF
ARTlFlctAL
SEA WATER
26.9 6.83 4.84 0.60 0.10 0.03 0.003
TABLE it REUTIVE
#.XB%iKXXTtOX5
OF NAlUR4L
A?40
ARTIFICIAL
SEA WATER -
NafCt Ca/Cl Mg/Cl K/Cl !SoIlQ B&i SrlCl
Natural sea water
To-free*’
0.5556 0.02to6 0.06694 0.0200 0.1395 O.tlO34 o.ooo7
0.5573
sea water
0.06658 0.0181 0.0925’ 0.0037 -
l The SO*-concentration has been reduad precipitate SU the Cat- as C&301.
by an amount
corresponding
Desdirtatiott.
to that required to
7 (1969f70) 23-30
NEAT CAPACITY OF SEA WATER
pretreatment
as would
be necessary for the operation
25 of an evaporator
at temp-
eratures up to 180°C. The composition
salts are given in Tables
and relative proportions of the constituent I and II. Sea water solutions at other concentrations were
prepared by dissolving the salts listed in Table I in the appropriate amount of distilled water. The composition of a few samples of the artif!cial sea water was confirmed by chemical analyses. The difference between sea water concentrated in this manner and sea water concentrated in another manner is insignificant with respect to such properties as heat capacity. 4. EXPERIMEXTAL
The heat capacity was determined by a differential heating method. This the rates of heating of a test fluid with that of a liquid of
consisted of comparing
known heat capacity under identical conditions. This method was chosen hecauSe it gave values of heat capacity over a wide range of temperature from a single experiment and the expected accuracy of & I per cent was considered to be adequate. The apparatus was arranged as shown in Fig. I. The cylindrical cell was machined from a bar of commercially pure titanium I80 mm long x 70 mm diameter with a wall thickness of 1.75 mm. Titanium was chosen because of its high resistance to corrosion in sea water and also because it has a low product of density
Fig. 1. Apparatus for heat capacity measurement, Desalination.
7 (1969170)
23-30
D. T.
26
JAMIESON
et al.
x heat capacity. The cell was filled with a weighed amount of the test liquid such that at the highest temperature there was still a small air space. A small Platinax magnet was inserted to stir the test liquid and the lid with the platinum resistance ,thermometer was closed. The lid was fitted with a Viton “0” ring seal and the rlbsence of any leakage was always confirmed by weighing before and after each test. The cell was placed in an air bath and located by three centering pins. This was then @aced, as shown, in a constant temperature oil bath. The latter was filled with Arocl~t t24S and its temperature was maintamed at 185 + 0.01 “C. The test liquid was stirred magnetically and its temperature recorded. This was done, as indicated in Fig. 2. by passing a measured current of about 4.3 mA through the resistance thermometer. The voltage drop across the resistance thermometer was converted to a frequency by a Dymec model 2210 voltagefrequency convertor. The frequency was measured and recorded on paper tape at intervals of about I5 seczmds using a Nuclear Enterprise model NE8303 scalertimer-printer circuit, With this equipment the frequency recorded is proportional
Fig. 2 Diagram
of citit
for measuring rate
of hating.
to
the voltage drop across the thermometer, which is proportional to the resistance of the thermometer, which is in turn proportional to the temperature of the test liquid. The variation of frequency with temperature is nearly linear and was determined by calibration. From this data the heat capacity could be calculated since if a cold body is placed in a warm environment its temperature rises and the rate of temperature rise is given by dT AT -=------0) dt WC, where A is constant proportional to the heat transfer coefficient. If the body is a cell containing a liquid then Z3esu&u!ion.7 (1969170)23-30
27
HEAT CAPACITY OF SEA WATER iT
AT
-i-Jr = WC, + K where K is the mass x heat capacity of the cell. dT/dr was recorded every I5 seconds for the duration of the heating period, which, for sea water, was about 6 hours. These vaiues were smoothed by plotting dT/dt versus T using a computer. A quadratic was found to fit the data %ell. This was confirmed by dividing the data into 10 equal parts and fitting each part ’ separately to a quadratic. The smoothed values were not appreciably different from those obtained from a single quadratic. The values of K could be calculated but since the cell is composed of a number of different materials, including a resistance thermometer, it was more convenient to determine this by calibration. In this experiment the values of A and K were determined by calibration with distilled water and heptane. These liquids have been recommended (5) as suitable for calibration purposes and the heat capacity values used were taken from (6) and (5) respectively.
5.
SOURCES OF ERROR
(a) As the test liquid becomes warmer the vapour pressure increases and so liquid must be evaporated. This is most im~rtant at the higher temperatures (above the normal boiling point). The amount of heat required to evaporate enough liquid to keep the vapour space at the saturation vapour pressure can be calculated but this was found to be negligable. This correction was not applied to the experimental data. (b) In Eqs. (I) and (2), A is constant only when the temperature of the test liquid is the same as that of the titanium cell. This condition obtains when the rate of stirring is high and the minimum rate of stirring permissible is claimed (7) to vary slightly according to the liquid being studied. The latter has not been investigated as it is unlikely that sea water will be appreciably different from distilled water. It was found, however, that with low rates of stirring the rate of heating varied with the rate of stirring. This effect tends to disappear as the stirring rate is increased, (c) Errors in the measurement of temperature can be divided into random errors and consistent errors. The latter are not important since the resistance thermometer was calibrated in terms of frequency at fixed temperatures and, in addition, the method is a relative one and these errors will be eliminated during the calibration. Small random errors are smoothed out by the large number of measurements. 6.
ACCURACY
An average of five repeat tests were carried out with heptane,
distilled water
DesaliMrion. 7 (1969170) 23-30
Fig. 3. Rcpcat tests with sea water of I IO.88 g/kg salinity
and each of the four samples of sea water. Between 90 and 1do’C the standard deviation of the individual tests from the average was 1 per cent. That is the reproducibility of the data is about & 2 percent and the reproducibility of the average of five repeat tests is about f: t per cent. At temperatures below 90°C and above 160°C the rates of heating were very high and very low respectively. Accurate temperature measurement was difficult under these conditions and the errors in heat capacity increased from I per cent to about 2 percent at 80 ar4 ! 70°C. Above 170°C even larger errors occurred. Fig. 3 shows the values from three repeat tests carried out with sea water at a salinity of I IO.88 g/kg. These values can be setm to be in agreement with the low temperature values of BromIey and so it can be assumed that the accuracy of the average vaiues is also about & I per cent. 7. REsULls The average experimental values obtained for the heat capacity of sea water solutions are given in Fig. 4. The following equation was fitted to these values CP = (CT~-t- a,S
f aaS*) + (b, + B,S + b&T
+ (ct + c2S i- c3S2)T’
+
+ (d, -#- d2S I- d3S2)T3
where S is the salinity in g/kg and T is the temperature
in “K. Drsalinution, 7 (1%9/70)
23-30
HEAT CAPACITY
OF SEA WATER
29
a, = 5.328 a2 = -9.76 x lo-' a1 = 4.04X IO-'
Fig
TABLE SMOOTHED -___-
4. Avenge
VALUES
Saiinity ‘1 \ &kg Temp_ \
0 20 40 60 80 100 120 140 MO 180
values of heat capacity
rersus temperature.
111
.,
(‘C-I
b, = -6.913 x 1o-3 bz = 7.351x 1o-J b, = 3.15x 1o-6
‘1
OF HEAT
CAPACW -.._
Hcaf cape&y 0
( k J kR -‘K -9
20
35
40
60
80
100
4-079 4.078 4.079 4.085 4.097 4.116 4.144 4.182 4.233 4.297
(normal !ica water) 3.990 3.999 4.006 4.014 4.026 4.044 4.069 4.106 4.157 4.223
3.962 3.973 3.982 3.991 4.003 4.020 4.045 4.082 4.132 4.199
3.854 3.872 3.890 3.901 3.912 3.927 3.950 3.985 4.034 4.102
3.756 3.784 3.EO2 3.814 3.825 3.837 3.859 3.892 3.940 4.009
3.648 3.590 3.699 3.621 3.719 3.640 3.731 3.652 3.741 3.660 3.753 3.671 3.772 . 3.689 3.803 3.718 3.850 3.764 3.919 3.831
120
140
MO
180
3.522 3.550 3.566 3.576 3.583 3.592 3.609 3.637 3.681 3.746
3.464 3.485 3.497 3.504 3sa9 3.517 3.533 3.560 3.6ot 3.664
3.416 3.427 3.433 3.43s 3.438 3.446 3.461 3.487 3.527 3.585
7 (1969j70)
23-30
--
4.207 4.189 4.181 4.183 4.194 4.215 4.246 4.287 4.338 4.399
Des&&z&n.
30 = 9.6 x 1o-6 c2 = -1.927 x 1O-6 cj = 8.23 x 1O-9
Cl
d, = 2.5 x 1o-9 (12 = 1.666 x LO-’ d, = -7.125 x lo-”
The solid lines in Fig. 4 represent this solution. For completeness the low temperature data of Bromley (2) and the literature data (6) for distilled water are also shown on this graph. The equation fits Bromley’s data and the data for distitled water with an average error of 0.1 per cent and a maximum error of 0.28 per cent. At temperaup to 16o’C the equation is within the claimed accuracy of &- I per cent. Smoothed values of the heat capacity of sea water solutions are given in Table III. This was constructed from the above equation. ACKN0WLEffiEMENl-S
This paper is published by permission of the Director of the National Engineering Laboratory. Ministry of Technology. it is Crown copyright and is reproduced by permission of the Controller of H. M. Stationery Office. REFEREIKES
I. 2.
3.
4. 5. 6. 7.
R. A. Cix AND N. D. SWIM, The specific heat of sea water. Proc. Roy. Sot. (London), Ser. A. 252 (1959) 51-62. L. A. BROMEY. V. A. DESACIISURE. J. C. CUPP A!GV 1. S. WRIGHT, Heat capaciria of sea water solutions at salinities of I to I2 percent and temperarums of 2” to 8O’C. 1. Clrrm. Eitg. RUM. 12 ( 1967) 202-206. A. M. Poh~zovs~lr, E. P. MELSHKO AND N. 1.GLOKUNA. Viscosity and specific heat of sea water and natural brines, Trudy Komi filiala, Akad, Nauk. SSSR, 4(l) (1953) 75-80 (in Russian). W. H. EMERSONAND D. T. JAMIMN, Some physical propcrtics of sea water in various conoentrations, Desahation. 3 (1967) 213-224. D. C. GIFZZI~Y;SAIM, G. T_ FLJRUKAWA, Heat capacity standards for the range 14 to 12tXYK. J. Amer. &em. Sot.. 75 (1953) 522-527. Engimtring Sciences Data Unit, Item No. 68008. Specific heat capacity at constant pttZSSUE of water substance. N. H. SPEAR, Mcasudng specific heat of liquids at high temperatures. huf. Cirrm., 24 (1952) 938-941.
Desahtatiott,
7 (1%9/70)
23-30
PHYSICAL HEAT
EIscvrer Publishing Company, Amsterdam - Printed in The Netherlands
PROPERTIES OF SEA WATER
SOLUTIONS:
CAPACITY* l
D. I-. JAMIESON, J. S. TUDHOPE, Natiotd
hginecring
R. MORRIS
AND
G. CARTWRlGHT
Laboratory. E&t Kilbride, Glasgow iSc*orfand)
(Received April 4.1969)
SUMhfARY
The heat capacity of sea water and its concentrates has been measured in the temperature range 80 to 180°C using a differential heating method. An equation is given which tits the measured values of heat capacity, together with those from the literature, to within their various experimental accuracies. t . INTRODtJtIFtON Most distillation plants for desalination purposes have been designed to operaie at temperatures of less than 120°C. This maximum temperature was adopted because it represented the temperature below which calcium sufphate scaling was unimportant. It is likely that research will provide soiutions to this scaling problem and that in these circumstances higher maximum temperatures will be used in flash evaporation plant. In anticipation of this. measurements of vapour pressure, density, viscosity, thermal conductivity and heat capacity are being made in the National Engineering Laboratory at temperatures up to about 180°C for sea water solutions ranging in concentration from I to 5 times that of natural sea water. The present article gives the results of measurements of heat capacity.
2. EXlSnNG DATA The heat capacity of sea water at normal concentration was determined between 0 and 3O’C by Cox (I) and at concentrations of 0.3 to 3.5 times normal sea water between 0 and 80°C by Bromley (2). Both these measurements arc in agreement and are believed to be accurate to within about &- 0.2 per cent. Ponizovskii (3) has also reported data for the heat capacity of various brine solutions at 22S”C. Where the relative composition of the solution is similar to that of sea * Prcsettfcd at PURAQUA-U.S. E?rhibition and lntemational cation and Desalination. held in Rome, Feb. 17-23. 1969.
Conference
on Water Putifi-
f3esahation, 7 (I%F/?O)
23-30
24
D. 1. JAMIESON
et
fff.
water the heat capacity vaiues are within I per cent of Bromley’s data. No measurements at temperatures above 8O’C or with more concentrated sea water solutions are known to the authors. 3.
CHOICE
OF SEA WATER
The salinity of sea water v.ztries from place to piace throughout the world. However. for all practical purposes. the relative composition of the dissolved salts is constant. That is, the only variable is the amount of pure water in which the various sea s&s are dissolved, so a knowledge of the variation of any property with salinity gives the property for any sample of sea water, irrespective of its source. When sea water is concentrated its composition is altered by. for example, the decomposition of bicarbonate and the precipitation of calcium sulphate. For these tests a synthetic sea water from which calcium sulphate had been deliberately omitted was used. This “Ca-free’ sea water is described in (4) and represents sea water from which the calcium sulphate had been removed by precipitation or TABLE I COMPOSITION
OF “CA-FREE”
NaCl MgCIt * 6HzO Mg801.7HzO KC7 KBr HJBOJ NaF
ARTlFlctAL
SEA WATER
26.9 6.83 4.84 0.60 0.10 0.03 0.003
TABLE it REUTIVE
#.XB%iKXXTtOX5
OF NAlUR4L
A?40
ARTIFICIAL
SEA WATER -
NafCt Ca/Cl Mg/Cl K/Cl !SoIlQ B&i SrlCl
Natural sea water
To-free*’
0.5556 0.02to6 0.06694 0.0200 0.1395 O.tlO34 o.ooo7
0.5573
sea water
0.06658 0.0181 0.0925’ 0.0037 -
l The SO*-concentration has been reduad precipitate SU the Cat- as C&301.
by an amount
corresponding
Desdirtatiott.
to that required to
7 (1969f70) 23-30
NEAT CAPACITY OF SEA WATER
pretreatment
as would
be necessary for the operation
25 of an evaporator
at temp-
eratures up to 180°C. The composition
salts are given in Tables
and relative proportions of the constituent I and II. Sea water solutions at other concentrations were
prepared by dissolving the salts listed in Table I in the appropriate amount of distilled water. The composition of a few samples of the artif!cial sea water was confirmed by chemical analyses. The difference between sea water concentrated in this manner and sea water concentrated in another manner is insignificant with respect to such properties as heat capacity. 4. EXPERIMEXTAL
The heat capacity was determined by a differential heating method. This the rates of heating of a test fluid with that of a liquid of
consisted of comparing
known heat capacity under identical conditions. This method was chosen hecauSe it gave values of heat capacity over a wide range of temperature from a single experiment and the expected accuracy of & I per cent was considered to be adequate. The apparatus was arranged as shown in Fig. I. The cylindrical cell was machined from a bar of commercially pure titanium I80 mm long x 70 mm diameter with a wall thickness of 1.75 mm. Titanium was chosen because of its high resistance to corrosion in sea water and also because it has a low product of density
Fig. 1. Apparatus for heat capacity measurement, Desalination.
7 (1969170)
23-30
D. T.
26
JAMIESON
et al.
x heat capacity. The cell was filled with a weighed amount of the test liquid such that at the highest temperature there was still a small air space. A small Platinax magnet was inserted to stir the test liquid and the lid with the platinum resistance ,thermometer was closed. The lid was fitted with a Viton “0” ring seal and the rlbsence of any leakage was always confirmed by weighing before and after each test. The cell was placed in an air bath and located by three centering pins. This was then @aced, as shown, in a constant temperature oil bath. The latter was filled with Arocl~t t24S and its temperature was maintamed at 185 + 0.01 “C. The test liquid was stirred magnetically and its temperature recorded. This was done, as indicated in Fig. 2. by passing a measured current of about 4.3 mA through the resistance thermometer. The voltage drop across the resistance thermometer was converted to a frequency by a Dymec model 2210 voltagefrequency convertor. The frequency was measured and recorded on paper tape at intervals of about I5 seczmds using a Nuclear Enterprise model NE8303 scalertimer-printer circuit, With this equipment the frequency recorded is proportional
Fig. 2 Diagram
of citit
for measuring rate
of hating.
to
the voltage drop across the thermometer, which is proportional to the resistance of the thermometer, which is in turn proportional to the temperature of the test liquid. The variation of frequency with temperature is nearly linear and was determined by calibration. From this data the heat capacity could be calculated since if a cold body is placed in a warm environment its temperature rises and the rate of temperature rise is given by dT AT -=------0) dt WC, where A is constant proportional to the heat transfer coefficient. If the body is a cell containing a liquid then Z3esu&u!ion.7 (1969170)23-30
27
HEAT CAPACITY OF SEA WATER iT
AT
-i-Jr = WC, + K where K is the mass x heat capacity of the cell. dT/dr was recorded every I5 seconds for the duration of the heating period, which, for sea water, was about 6 hours. These vaiues were smoothed by plotting dT/dt versus T using a computer. A quadratic was found to fit the data %ell. This was confirmed by dividing the data into 10 equal parts and fitting each part ’ separately to a quadratic. The smoothed values were not appreciably different from those obtained from a single quadratic. The values of K could be calculated but since the cell is composed of a number of different materials, including a resistance thermometer, it was more convenient to determine this by calibration. In this experiment the values of A and K were determined by calibration with distilled water and heptane. These liquids have been recommended (5) as suitable for calibration purposes and the heat capacity values used were taken from (6) and (5) respectively.
5.
SOURCES OF ERROR
(a) As the test liquid becomes warmer the vapour pressure increases and so liquid must be evaporated. This is most im~rtant at the higher temperatures (above the normal boiling point). The amount of heat required to evaporate enough liquid to keep the vapour space at the saturation vapour pressure can be calculated but this was found to be negligable. This correction was not applied to the experimental data. (b) In Eqs. (I) and (2), A is constant only when the temperature of the test liquid is the same as that of the titanium cell. This condition obtains when the rate of stirring is high and the minimum rate of stirring permissible is claimed (7) to vary slightly according to the liquid being studied. The latter has not been investigated as it is unlikely that sea water will be appreciably different from distilled water. It was found, however, that with low rates of stirring the rate of heating varied with the rate of stirring. This effect tends to disappear as the stirring rate is increased, (c) Errors in the measurement of temperature can be divided into random errors and consistent errors. The latter are not important since the resistance thermometer was calibrated in terms of frequency at fixed temperatures and, in addition, the method is a relative one and these errors will be eliminated during the calibration. Small random errors are smoothed out by the large number of measurements. 6.
ACCURACY
An average of five repeat tests were carried out with heptane,
distilled water
DesaliMrion. 7 (1969170) 23-30
Fig. 3. Rcpcat tests with sea water of I IO.88 g/kg salinity
and each of the four samples of sea water. Between 90 and 1do’C the standard deviation of the individual tests from the average was 1 per cent. That is the reproducibility of the data is about & 2 percent and the reproducibility of the average of five repeat tests is about f: t per cent. At temperatures below 90°C and above 160°C the rates of heating were very high and very low respectively. Accurate temperature measurement was difficult under these conditions and the errors in heat capacity increased from I per cent to about 2 percent at 80 ar4 ! 70°C. Above 170°C even larger errors occurred. Fig. 3 shows the values from three repeat tests carried out with sea water at a salinity of I IO.88 g/kg. These values can be setm to be in agreement with the low temperature values of BromIey and so it can be assumed that the accuracy of the average vaiues is also about & I per cent. 7. REsULls The average experimental values obtained for the heat capacity of sea water solutions are given in Fig. 4. The following equation was fitted to these values CP = (CT~-t- a,S
f aaS*) + (b, + B,S + b&T
+ (ct + c2S i- c3S2)T’
+
+ (d, -#- d2S I- d3S2)T3
where S is the salinity in g/kg and T is the temperature
in “K. Drsalinution, 7 (1%9/70)
23-30
HEAT CAPACITY
OF SEA WATER
29
a, = 5.328 a2 = -9.76 x lo-' a1 = 4.04X IO-'
Fig
TABLE SMOOTHED -___-
4. Avenge
VALUES
Saiinity ‘1 \ &kg Temp_ \
0 20 40 60 80 100 120 140 MO 180
values of heat capacity
rersus temperature.
111
.,
(‘C-I
b, = -6.913 x 1o-3 bz = 7.351x 1o-J b, = 3.15x 1o-6
‘1
OF HEAT
CAPACW -.._
Hcaf cape&y 0
( k J kR -‘K -9
20
35
40
60
80
100
4-079 4.078 4.079 4.085 4.097 4.116 4.144 4.182 4.233 4.297
(normal !ica water) 3.990 3.999 4.006 4.014 4.026 4.044 4.069 4.106 4.157 4.223
3.962 3.973 3.982 3.991 4.003 4.020 4.045 4.082 4.132 4.199
3.854 3.872 3.890 3.901 3.912 3.927 3.950 3.985 4.034 4.102
3.756 3.784 3.EO2 3.814 3.825 3.837 3.859 3.892 3.940 4.009
3.648 3.590 3.699 3.621 3.719 3.640 3.731 3.652 3.741 3.660 3.753 3.671 3.772 . 3.689 3.803 3.718 3.850 3.764 3.919 3.831
120
140
MO
180
3.522 3.550 3.566 3.576 3.583 3.592 3.609 3.637 3.681 3.746
3.464 3.485 3.497 3.504 3sa9 3.517 3.533 3.560 3.6ot 3.664
3.416 3.427 3.433 3.43s 3.438 3.446 3.461 3.487 3.527 3.585
7 (1969j70)
23-30
--
4.207 4.189 4.181 4.183 4.194 4.215 4.246 4.287 4.338 4.399
Des&&z&n.
30 = 9.6 x 1o-6 c2 = -1.927 x 1O-6 cj = 8.23 x 1O-9
Cl
d, = 2.5 x 1o-9 (12 = 1.666 x LO-’ d, = -7.125 x lo-”
The solid lines in Fig. 4 represent this solution. For completeness the low temperature data of Bromley (2) and the literature data (6) for distilled water are also shown on this graph. The equation fits Bromley’s data and the data for distitled water with an average error of 0.1 per cent and a maximum error of 0.28 per cent. At temperaup to 16o’C the equation is within the claimed accuracy of &- I per cent. Smoothed values of the heat capacity of sea water solutions are given in Table III. This was constructed from the above equation. ACKN0WLEffiEMENl-S
This paper is published by permission of the Director of the National Engineering Laboratory. Ministry of Technology. it is Crown copyright and is reproduced by permission of the Controller of H. M. Stationery Office. REFEREIKES
I. 2.
3.
4. 5. 6. 7.
R. A. Cix AND N. D. SWIM, The specific heat of sea water. Proc. Roy. Sot. (London), Ser. A. 252 (1959) 51-62. L. A. BROMEY. V. A. DESACIISURE. J. C. CUPP A!GV 1. S. WRIGHT, Heat capaciria of sea water solutions at salinities of I to I2 percent and temperarums of 2” to 8O’C. 1. Clrrm. Eitg. RUM. 12 ( 1967) 202-206. A. M. Poh~zovs~lr, E. P. MELSHKO AND N. 1.GLOKUNA. Viscosity and specific heat of sea water and natural brines, Trudy Komi filiala, Akad, Nauk. SSSR, 4(l) (1953) 75-80 (in Russian). W. H. EMERSONAND D. T. JAMIMN, Some physical propcrtics of sea water in various conoentrations, Desahation. 3 (1967) 213-224. D. C. GIFZZI~Y;SAIM, G. T_ FLJRUKAWA, Heat capacity standards for the range 14 to 12tXYK. J. Amer. &em. Sot.. 75 (1953) 522-527. Engimtring Sciences Data Unit, Item No. 68008. Specific heat capacity at constant pttZSSUE of water substance. N. H. SPEAR, Mcasudng specific heat of liquids at high temperatures. huf. Cirrm., 24 (1952) 938-941.
Desahtatiott,
7 (1%9/70)
23-30