Hence, masses of equal volumes are directly proportional to their densities, and volumes of equal masses are inversely proportional to their densities. The relative density of a substance is the ratio of its density to the density of pure water at a temperature of 4°C. If we assume the quantity of matter in 1 cc. of pure water at 4°C. as a unit of density, the density of the water will be 1, and the quantity of matter in 1 cc. of any other substance will measure its relative density. The density of water varies with its temperature as well as with its purity. The temperature 4°C. is taken for the standard density because the density of water is greatest at that temperature. In order to get the most accurate results in the following experiments, distilled water at 4° C. must be used. 151. Specific Gravity. Since the ratio between the weights of equal volumes of substances in the same place is the same as the ratio of their masses, we can use the term specific gravity in place of relative density. Since, also, pure water is taken as the standard in specific gravity, we may express it by the following formula : Weight of the body in air Sp. gr. = or Sp. gr. = In this expression W is the weight of the body in air, and W' its apparent weight in water. Since there are different systems of weights and measures it is evident that the number representing the density of a substance will depend upon the system of units used, while its relative density or its specific gravity will be the same in all systems. For example, the density of wrought iron in the C. G. S. system is 7.85, which means that it has a mass of 7.85 g. per c. c. In the F. P. S. system its density is 489, which means that its mass is 489 lb. per cubic foot. In both systems its specific gravity is 7.85, which means that its weight is 7.85 times that of an equal volume of water. The density of a substance depends upon its physical condition. If the substance is a mineral, its density depends upon its purity. If the substance is a metal, its density is affected by the treatment received in the process of manufacture; for instance, whether it is cast, or drawn into wire. The density of an alloy depends upon the proportional parts of the metals composing it. The accompanying table of densities and specific gravities is made by taking the average of results found by different observers. With slight exception they are as reported in the Physical Tables published by the Smithsonian Institution. 152. To find the Specific Gravity of a Body Heavier than Water. Tie a light cord about the body, suspend it from one arm of a balance, and weigh it; call this weight FIG. 134 = 146 g. = 94 g. - The weight of a stone in air (W) Since the specific gravity is the weight of the stone divided by the weight of an equal volume of water and since the difference between the weight of the stone in air and in water is the buoyant force of the water, or the weight of a volume of water equal to that of the stone: 153. To find the Specific Gravity of a Body Lighter than Water. Since the buoyant force of the water is greater than the weight of the body, it will float, and it must be fastened to a heavy body in order to submerge it. The specific gravity can be found as follows: Weigh the body in air (W), then weigh a heavy sinker in water and call its apparent weight S. Tie the sinker to the body and weigh them both in water. Call the apparent weight W". Compute the specific gravity from the form EXAMPLE. Suppose a piece of wood weighs 40 g. in air (W), a sinker registers 50 g. in water (S), and the two when tied together and submerged register 30 g. (W"). It is evident that the wood not only displaces its own weight of water, but buoys up 20 g. of the weight of the sinker; therefore the wood displaces 40 + 20 g. of water, hence its specific gravity is 40 40 60 = .67. (a) By the 154. To find the Specific Gravity of Liquids. Specific Gravity Bottle. Any bottle with a small neck having a fixed mark around the neck can be used in this method. Weigh the bottle when empty (a). Fill with water to the fixed mark and weigh (b). The difference gives the weight of water (b − a). Fill with the required liquid and weigh (c). The difference (c − a) gives the weight of the same volume of the liquid. Then the specific gravity Weight of liquid will be Weight of equal volume of water EXAMPLE. Weight of the empty bottle (a) Weight of the bottle filled with water (b) Weight of the bottle filled with the liquid (c) = C a 198.25 = Sp. gr. = .793. = b a = Specific gravity bottles are usually made to hold a certain number of grams of water at a stated temperature, and are so marked. If the bottle holds 1000 g. of water, the specific gravity can be obtained directly. For example, if a thousand-gram bottle holds 1240 g. of hydrochloric acid, then the specific gravity of the acid is 1.240. (b) By the Method of Balancing Columns. A good form of apparatus for this method is that of Hare, shown in Fig. 135. A and B are glass tubes joined at the R upper ends to the branches of a Y tube. The other end of the Y is joined to a rubber tube R. The lower end of each tube dips into a liquid in a beaker. C is a clamp and M a meter stick. When pressure is reduced in R the liquids rise to heights that are inversely proportional to their specific gravities. If water is in A and alcohol in B, the specific gravity of the alcohol will be as follows: Sp. Gr. = Height of A the heights to be measured from the surface of (c) By the Hydrometer. A B FIG. 135 are sealed. Either mercury or small shot are put into the lower bulb in order to keep the stem of the instrument vertical. For liquids heavier than water the unit mark is placed at the upper end of the stem, which is graduated decimally. This instrument (Fig. 136) is used by floating it in FIG. 136 the liquid in a hydrometer jar, and reading the height to which the liquid stands on the stem. Special forms of hydrometers are used for special liquids. |