Accuracy of density determination by specific gravity method
Answers
Density and Specific Gravity.
The terms density and specific gravity are not strictly speaking
synonymous, although they are often taken as being so for the reason
that will be explained presently. Density is the mass of unit volume
of substance, and is therefore an absolute value independent of the
gravitating force at the part of the earth at which its determination
is made. Specific gravity, on the other hand, is relative value
being as usually determined the weight of definite volume of
substance at known temperature compared with the weight of
similar volume of some other substance also at known temperature;
it is therefore ratio* In the case of liquids, the standard substance
universally adopted for the ratio is water. Now the distinction
between mass and weight is that the latter is less by some 0*5 per
cent, at the equator than at the pool-cerise caribous. Since on the
metric system the unit of volume has been fixed at c.c, the volume
occupied by gram of water at 4° G, its maximum density, the
specific gravity of substance at definite temperature if we make
the comparison with water at 4° C, also represents the weight of
cubic centimeter of the substance in grams. For very exact measure ments the weights must be corrected for the buoyancy of air and
also to the mean gravitating force. When this is done, specific
gravity and density (the latter expressed on the metric units) are
represented by the same value. For practical work it is convenient
to regard specific gravity as the weight of known volume of
substance at some such temperature as 60° F. compared with that of
an equal volume of water at the same temperature.
Methods of Determining Specific Gravity of Liquids.
There are two methods in common use for this purpose. The first consists in weighing equal volumes of the liquid at known temperature and of water at this or some other known temperature, and calculating the ratio between these two weights, denoting the weight of water as or as 1,000. Taking the latter standard, which is the one usually adopted in brewing, the results are calculated by the formula -*—£, where is the specific gravity of the liquid, the weight of the liquid, and the weight of an equal volume of water. This is the more accurate method of determining specific gravity. The second method depends on the use of floating spindle, and is based on the principle that body floating in liquid displaces volume of that liquid equal to its own weight. To calibrate the spindle it is placed in water at known temperature, and the point on the stem noted to which it sinks. It will then be found to sink to another point in some other liquid of higher or lower specific gravity. In the former case it will not sink so far, whilst in the latter case it will sink farther. In other words, the volume of given weight of liquid of higher specific gravity than water will be less than that of the same weight of water, and it will be more in the case of liquid of lower specific gravity than water. The results are calculated by the formula ,—, in which is the volume of water (the mark on the stem to which the spindle sinks ( in water), and the volume of the liquid (the mark on the stem to which the spindle sinks in that liquid). In commercial Saccharomyces used for determining the specific gravity of wort, it is found convenient to mark the scale in reciprocals of the values obtained from the above observations, so that the higher values increase from the top of the spindle towards the lower end. Instruments used in practice are, as is well known, graduated in various scales according to the particular requirements they are designed to fulfill, whilst in order to extend the scale of short instruments, use is made of counterpoises. Apart from the fact that spindle instruments can never be made so sensitive as the chemical balance, there is another source of error inherent in them, namely, that the capillarity, surface tension and viscosity of water are not the same as those of other liquids, so that the construction of an accurate scale—more especially for liquids of high and low specific gravitates—e.g., strong worth or strong solutions of alcohol in water is very difficult. However, for all practical purposes these instruments are of sufficient accuracy. We may deduce the principle of the two methods of determining specific gravity from the above observations. The gravity method depends on the comparison of the weights of equal volumes of liquid and of water, whilst the spindle method depends on the comparison of the volumes of equal weights of liquid and of water.