Fig. 82.—Balance and Westphal Sinker.
When great delicacy of manipulation is desired, combined with rapid work, an analytical balance and westphal sinker may be used conjointly.[235] In this case it is well to have two or three sinkers graduated for 20°, 25°, and 40°, respectively. Nearly all fats, when melted and cooled to 40°, remain in a liquid state long enough to determine their density. The sinkers are provided with delicate thermometers, and the temperature, which at the beginning is a little above the degree at which the sinker is graduated, is allowed to fall to just that degree, when the equilibrium is secured in the usual manner. The sinker is conveniently made to displace just five grams of distilled water at the temperature of graduation, but it is evident that a round number is not necessary, but only convenient for calculation.
286. Expression of Specific Gravity.—Much confusion arises in the study of data of densities because the temperatures at which the determinations are made are not expressed. The absolute specific gravity would be a comparison of the weight of the object at 4°, with water at the same temperature. It is evident that such determinations are not always convenient, and for this reason the determinations of density are usually made at other temperatures.
In the case of a sinker, which at 35° displaces exactly five grams of water, the following statements may be made: One cubic centimeter of water at 35° weighs 0.994098 gram. The volume of a sinker displacing five grams of water at that temperature is therefore 5.0297 cubic centimeters. This volume of water at 4° weighs 5.0297 grams. In a given case the sinker placed in an oil at 35° is found to displace a weight equal to 4.5725 grams corresponding to a specific gravity of 35°/35° = 0.9145. From the foregoing data the following tabular summary is constructed:
| Weight | of | 5.0287 | cubic | centimeters | of | oil | at 35°, | 4.5725 | grams. |
| ” | ” | 5.0297 | ” | ” | ” | water | at 35°, | 5.0000 | ” |
| ” | ” | 5.0297 | ” | ” | ” | ” | ” 4°, | 5.0297 | ” |
| Relative | weight | of | oil | at | 35°, | to | water | at | 35°, | 0.9145 | grams. |
| ” | ” | ” | ” | ” | 35°, | ” | ” | ” | 4°, | 0.9092 | ” |
287. Coefficient of Expansion of Oils.—Oils and fats of every kind have almost the same coefficient of expansion with increasing temperature. The coefficient of expansion is usually calculated by the formula
| δ = | D₀ - D₀ʹ |
| (tʹ - t)D₀ |
in which δ represents the coefficient of expansion, D₀ the density at the lowest temperature, D₀ʹ the density at the highest temperature, t the lowest, and tʹ the highest temperatures.