Relative Density - Measurement

Measurement

Relative density can be calculated directly by measuring the density of a sample and dividing it by the (known) density of the reference substance. The density of the sample is simply its mass divided by its volume. Although mass is easy to measure, the volume of an irregularly shaped sample can be more difficult to ascertain. One method is to put the sample in a water-filled graduated cylinder and read off how much water it displaces. Alternatively the container can be filled to the brim, the sample immersed, and the volume of overflow measured. The surface tension of the water may keep a significant amount of water from overflowing, which is especially problematic for small samples. For this reason it is desirable to use a water container with as small a mouth as possible.

For each substance, the density, ρ, is given by

\rho = \frac{\text{Mass}}{\text{Volume}} = \frac{\text{Deflection} \times \frac{\text{Spring Constant}}{\text{Gravity}}}{\text{Displacement}_\mathrm{Water Line} \times \text{Area}_\mathrm{Cylinder}}\,

When these densities are divided, references to the spring constant, gravity and cross-sectional area simply cancel, leaving

RD=\frac{\rho_\mathrm{object}}{\rho_\mathrm{ref}} = \frac{\frac{\text{Deflection}_\mathrm{Obj.}}{\text{Displacement}_\mathrm{Obj.}}}{\frac{\text{Deflection}_\mathrm{Ref.}}{\text{Displacement}_\mathrm{Ref.}}} = \frac{\frac{3\ \mathrm{in}}{20\ \mathrm{mm}}}{\frac{5\ \mathrm{in}}{34\ \mathrm{mm}}}=\frac{3\ \mathrm{in} \times 34\ \mathrm{mm}}{5\ \mathrm{in} \times 20\ \mathrm{mm}} = 1.02\,

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