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Variations
Things are complicated by the variation of the density of water with temperature, and also by the
confusion that gave us the distinction between cc and ml. The milliliter is the volume of 1.0 g of
water at 4°C, by definition. The actual volume of 1.0 g of water at 4°C is 0.999973 cm3 by
measurement. Since most densities are not known, or needed, to more than three significant
figures, it is clear that this difference is of no practical importance, and the ml can be taken
equal to the cc. The density of water at 0°C is 0.99987 g/ml, at 20° 0.99823, and at 100°C
0.95838. The temperature dependence of the density may have to be taken into consideration
in accurate work. Mercury, while we are at it, has a density 13.5955 at 0°C, and 13.5461 at
20°C.
The basic idea in finding specific gravity is to weigh a sample in air, and then immersed in
water. Then the specific gravity is W/ (W - W'), if W is the weight in air, and W' the weight
immersed. The denominator is just the buoyant force, the weight of a volume of water equal to
the volume of the sample. This can be carried out with an ordinary balance, but special
balances, such as the Jolly balance, have been created specifically for this application. Adding
an extra weight to the sample allows measurement of specific gravities less than 1.
Pycnometer
A pycnometer is a flask with a close-fitting ground glass stopper with a fine hole through it, so a
given volume can be accurately obtained. The name comes from the Greek word meaning
"density." If the flask is weighed empty, full of water, and full of a liquid whose specific gravity is
desired, the specific gravity of the liquid can easily be calculated. A sample in the form of a
powder, to which the usual method of weighing cannot be used, can be put into the pycnometer.
The weight of the powder and the weight of the displaced water can be determined, and from
them the specific gravity of the powder.
The specific gravity of a liquid can be found with a collection of small weighted, hollow spheres
that will just float in certain specific gravities. The closest spheres that will just float and just sink
put limits on the specific gravity of the liquid. This method was once used in Scotland to
determine the amount of alcohol in distilled liquors. Since the density of a liquid decreases as
the temperature increases, the spheres that float are an indication of the temperature of the
liquid. Galileo's thermometer worked this way.
Hydrometer
A better instrument is the hydrometer, which consists of a weighted float and a calibrated stem
that protrudes from the liquid when the float is entirely immersed. A higher specific gravity will
result in a greater length of the stem above the surface, while a lower specific gravity will cause
the hydrometer to float lower.
The small cross-sectional area of the stem makes the instrument very sensitive. Of course, it
must be calibrated against standards. In most cases, the graduations ("degrees") are arbitrary
and reference is made to a table to determine the specific gravities. Hydrometers are used to
determine the specific gravity of lead-acid battery electrolyte, and the concentration of antifreeze
compounds in engine coolants, as well as the alcohol content of whiskey.
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