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Seawater densities intercompared dilatometrically
Deep-SeaResearch,Vol. 35, No. 9, pp. 1673--1675,1988.
0198-0149/88$3.00 + 0.00 ~) 1988PergamonPress plc.
Printed in Great Britain.
NOTE
Seawater densities intercompared dilatometrically GERALDA.
BOT]?OMLEY*
(Received 22 January 1988; in revised form 27 April 1988; accepted 10 May 1988) A b s t r a e t - - S e a w a t e r s at 25°C and four salinities were each diluted s o m e 4% by quantitative addition of distilled water in a precision dilatometer. T h e observed small volume changes agree well with those deduced from the MILLERO and POlSSON (1981) International one-atmosphere equation of state which is based on absolute density m e a s u r e m e n t s .
INTRODUCTION
THE International one-atmosphere equation of state of seawater given by MILLEROand POlSSON (1981) depends on the highest quality absolute density determinations at specified temperatures and salinities through which a polynomial surface has been fitted. An account is given here of dilatometric measurements which test at high precision the density-salinity function between the discrete points at 25°C. Should new absolute seawater densities of even higher precision be needed in future then the dilatometer method offers convenient and speedy interpolation between directly measured density data points. The dilatometric method may also have considerable application in density studies on bitterns and other waters of non-standard composition. EXPERIMENTAL
Measurements were made with a special dilatometer which, when given a temporary tilt, permits a known volume of distilled water to be mixed with a defined mass of seawater. The volume change between the original state and the final state is deduced from the level change in a fine-bore capillary. The dilatometric technique is similar in its details to that used by BO~OMLEV and GLOSSOP(1979) for determining limiting apparent molar volumes of electrolytes in solution except for a slight apparatus modification appropriate to injecting the less dense distilled water into denser seawater. At fixed temperature and pressure a mass M of seawater is mixed in the dilatometer with a mass W of distilled water. The volume change on mixing is V C = ( M + W ) / D 2 - M / D 1 - W/DO,
(1)
where DO, D 1 and D2 are the densities, respectively, of pure water, the original seawater and the resulting seawater of known dilution by mass. The numerical densities of ? D e p a r t m e n t of Physical and Inorganic Chemistry, University of W e s t e r n Australia, Nedlands, 6009, Australia. 1673
1674
G . A . Bo'rrOMLEY
seawater adopted at various salinities followed exactly the recommendations of MILLERO and POISSON (1981). The seawater of salinity 35.25, from which other dilutions were made, was an Indian Ocean sample whose density was compared with that of an I.A.P.S.O. Standard using a 50 ml pyknometer. RESULTS
The dilatometer experiments were all done at a temperature controlled to better than 1 mK within 20 mK of 25°C on four widely different initial salinities of seawater with volumes within 1% of 591 c m 3. The relevent quantities as given in Table 1 have been scaled up to an initial seawater volume, DV, of 1000 c m 3. The calculated volume changes are those deduced from equation (1) with the density-salinity formulations noted above, and with an extra significant figure retained for the purpose of error analysis. The potential impact of observational errors on the corresponding volume changes can be assessed most directly by recalculating at high precision the volume change for the dilution in Line 1 but using deliberately maladjusted input data as in Table lb. One sees that barely feasible errors in salinity or distilled water mass affect the volume change by perhaps 2%, but that only a crude knowledge of the dilatometer volume and temperature is needed. The S.M.O.W. entry refers to artificially changing the reference density of pure water by 1 in 10,000. (The lowest salinity experiment has a 4% discrepancy when tl~e salinity is changed as above but otherwise gives similar adjustments.) The negative volume changes predicted from the International one-atmosphere equation of state are larger than the observed ones by only 1.9, 1.9, 3.0 and 2.8%. Earlier formulations for the equation of state of seawater gave discrepancies up to 50%. The most critical feature of the present experiment is the mercury thread calibration of the narrow capillary tube, nominal bore 0.05 cm. The linear movement of the seawater boundary meniscus was more than 5 cm in the first three experiments in Table 1, easily measureable to 0.02 cm, but one might allow something for "drainage errors" and suggest a limit of 1% accuracy. Setting the overall error in the dilatometrically determined volume change at 2% corresponds to an uncertainty of four in seventh place in the comparative density of seawater after dilution. MILLERO and PoIssoN (1981) assess the standard deviation of their 476 experimental density determinations (but 0-40°C) from the fitting equation Table 1. (a) Volume change produced by stated dilution. (b) Re-calculation of 35.25 salinity dilution Salinity (per mille) (a)
35.25 33.23 30.94 17.88
(b)
New New New New New
S W
= = DV = Temp. = S.M.O.W. =
Seawater (cm 3) 1000 1000 1000 1000 34.75 36.00 1050 24°C (see main text)
Water added (g) 36.65 45.22 47.23 35.02 New New New New New
volume volume volume volume volume
Volume change (cm 3) Observed Calculated -0.01812 -0.02026 -0.01872 -0.00600 change change change change change
= = = = =
-0.01848 -0.02066 -0.01929 -0.00617 -0.01807 -0.01816 -0.01850 -0.01835 -0.01848
Seawater densities intercompared dilatometrically
1675
as 3.66 in sixth place. The dilatometric evidence is that where one is making a relatively small change in salinity at 25°C and chiefly concerned about changes in density rather than the absolute density value, then the recommended equation of state may be relied upon to considerably finer limits than the quoted standard deviation. This observation is of potential importance in studies of salt-fingers. REFERENCES BOTTOMLEY G. A. and L. G. GLOSSOP (1979) Dilatometer studies of the apparent molar volume limiting law for high charge electrolytes. Australian Journal of Chemistry, 32, 699-708. MILLERO F. J. and A. Polssot~ (1981) International one-atmosphere equation of state of seawater. Deep-Sea Research, 28, 625-629.
0198-0149/88$3.00 + 0.00 ~) 1988PergamonPress plc.
Printed in Great Britain.
NOTE
Seawater densities intercompared dilatometrically GERALDA.
BOT]?OMLEY*
(Received 22 January 1988; in revised form 27 April 1988; accepted 10 May 1988) A b s t r a e t - - S e a w a t e r s at 25°C and four salinities were each diluted s o m e 4% by quantitative addition of distilled water in a precision dilatometer. T h e observed small volume changes agree well with those deduced from the MILLERO and POlSSON (1981) International one-atmosphere equation of state which is based on absolute density m e a s u r e m e n t s .
INTRODUCTION
THE International one-atmosphere equation of state of seawater given by MILLEROand POlSSON (1981) depends on the highest quality absolute density determinations at specified temperatures and salinities through which a polynomial surface has been fitted. An account is given here of dilatometric measurements which test at high precision the density-salinity function between the discrete points at 25°C. Should new absolute seawater densities of even higher precision be needed in future then the dilatometer method offers convenient and speedy interpolation between directly measured density data points. The dilatometric method may also have considerable application in density studies on bitterns and other waters of non-standard composition. EXPERIMENTAL
Measurements were made with a special dilatometer which, when given a temporary tilt, permits a known volume of distilled water to be mixed with a defined mass of seawater. The volume change between the original state and the final state is deduced from the level change in a fine-bore capillary. The dilatometric technique is similar in its details to that used by BO~OMLEV and GLOSSOP(1979) for determining limiting apparent molar volumes of electrolytes in solution except for a slight apparatus modification appropriate to injecting the less dense distilled water into denser seawater. At fixed temperature and pressure a mass M of seawater is mixed in the dilatometer with a mass W of distilled water. The volume change on mixing is V C = ( M + W ) / D 2 - M / D 1 - W/DO,
(1)
where DO, D 1 and D2 are the densities, respectively, of pure water, the original seawater and the resulting seawater of known dilution by mass. The numerical densities of ? D e p a r t m e n t of Physical and Inorganic Chemistry, University of W e s t e r n Australia, Nedlands, 6009, Australia. 1673
1674
G . A . Bo'rrOMLEY
seawater adopted at various salinities followed exactly the recommendations of MILLERO and POISSON (1981). The seawater of salinity 35.25, from which other dilutions were made, was an Indian Ocean sample whose density was compared with that of an I.A.P.S.O. Standard using a 50 ml pyknometer. RESULTS
The dilatometer experiments were all done at a temperature controlled to better than 1 mK within 20 mK of 25°C on four widely different initial salinities of seawater with volumes within 1% of 591 c m 3. The relevent quantities as given in Table 1 have been scaled up to an initial seawater volume, DV, of 1000 c m 3. The calculated volume changes are those deduced from equation (1) with the density-salinity formulations noted above, and with an extra significant figure retained for the purpose of error analysis. The potential impact of observational errors on the corresponding volume changes can be assessed most directly by recalculating at high precision the volume change for the dilution in Line 1 but using deliberately maladjusted input data as in Table lb. One sees that barely feasible errors in salinity or distilled water mass affect the volume change by perhaps 2%, but that only a crude knowledge of the dilatometer volume and temperature is needed. The S.M.O.W. entry refers to artificially changing the reference density of pure water by 1 in 10,000. (The lowest salinity experiment has a 4% discrepancy when tl~e salinity is changed as above but otherwise gives similar adjustments.) The negative volume changes predicted from the International one-atmosphere equation of state are larger than the observed ones by only 1.9, 1.9, 3.0 and 2.8%. Earlier formulations for the equation of state of seawater gave discrepancies up to 50%. The most critical feature of the present experiment is the mercury thread calibration of the narrow capillary tube, nominal bore 0.05 cm. The linear movement of the seawater boundary meniscus was more than 5 cm in the first three experiments in Table 1, easily measureable to 0.02 cm, but one might allow something for "drainage errors" and suggest a limit of 1% accuracy. Setting the overall error in the dilatometrically determined volume change at 2% corresponds to an uncertainty of four in seventh place in the comparative density of seawater after dilution. MILLERO and PoIssoN (1981) assess the standard deviation of their 476 experimental density determinations (but 0-40°C) from the fitting equation Table 1. (a) Volume change produced by stated dilution. (b) Re-calculation of 35.25 salinity dilution Salinity (per mille) (a)
35.25 33.23 30.94 17.88
(b)
New New New New New
S W
= = DV = Temp. = S.M.O.W. =
Seawater (cm 3) 1000 1000 1000 1000 34.75 36.00 1050 24°C (see main text)
Water added (g) 36.65 45.22 47.23 35.02 New New New New New
volume volume volume volume volume
Volume change (cm 3) Observed Calculated -0.01812 -0.02026 -0.01872 -0.00600 change change change change change
= = = = =
-0.01848 -0.02066 -0.01929 -0.00617 -0.01807 -0.01816 -0.01850 -0.01835 -0.01848
Seawater densities intercompared dilatometrically
1675
as 3.66 in sixth place. The dilatometric evidence is that where one is making a relatively small change in salinity at 25°C and chiefly concerned about changes in density rather than the absolute density value, then the recommended equation of state may be relied upon to considerably finer limits than the quoted standard deviation. This observation is of potential importance in studies of salt-fingers. REFERENCES BOTTOMLEY G. A. and L. G. GLOSSOP (1979) Dilatometer studies of the apparent molar volume limiting law for high charge electrolytes. Australian Journal of Chemistry, 32, 699-708. MILLERO F. J. and A. Polssot~ (1981) International one-atmosphere equation of state of seawater. Deep-Sea Research, 28, 625-629.