Relative density
Relative Density
Relative density, also known as specific gravity, is a dimensionless quantity that represents the ratio of the density of a substance to the density of a reference substance, typically water for liquids and solids, and air for gases. It provides a way to compare the densities of different materials without the need for units.
Understanding Relative Density
Relative density (RD) is expressed mathematically as:
$$ RD = \frac{\rho_{substance}}{\rho_{reference}} $$
where:
- $\rho_{substance}$ is the density of the substance in question,
- $\rho_{reference}$ is the density of the reference substance.
Since relative density is a ratio of two densities, it has no units.
Water as a Reference Substance
For most purposes, water at 4°C (the temperature at which it has its maximum density) is used as the reference substance for liquids and solids, and its density is approximately $1 \, \text{g/cm}^3$ or $1000 \, \text{kg/m}^3$.
Air as a Reference Substance
For gases, dry air at standard temperature and pressure (STP) is often used as the reference substance. Its density under these conditions is about $1.225 \, \text{kg/m}^3$.
Table of Differences and Important Points
| Property | Density | Relative Density |
|---|---|---|
| Definition | Mass per unit volume of a substance. | Ratio of the density of a substance to the density of a reference substance. |
| Symbol | $\rho$ | RD or SG (Specific Gravity) |
| Units | $\text{kg/m}^3$, $\text{g/cm}^3$ | Dimensionless (no units) |
| Reference | N/A | Water (for liquids and solids), Air (for gases) |
| Temperature | Depends on the temperature of the substance. | Typically compared at 4°C for water and STP for air. |
| Measurement | Measured using a balance and a volume measuring device. | Measured using a hydrometer, pycnometer, or calculated from density. |
Formulas Involving Relative Density
Relative density can be used to calculate the density of a substance if the density of the reference substance is known:
$$ \rho_{substance} = RD \times \rho_{reference} $$
For example, if the relative density of a liquid is 0.8 with respect to water, its density is:
$$ \rho_{liquid} = 0.8 \times 1000 \, \text{kg/m}^3 = 800 \, \text{kg/m}^3 $$
Examples to Explain Important Points
Example 1: Determining Whether a Substance Will Float
If the relative density of a substance is less than 1, it will float in water. For instance, if a piece of wood has a relative density of 0.6, it will float because its density is less than that of water.
Example 2: Using Relative Density to Find Density
A metal has a relative density of 7.5 with respect to water. To find the density of the metal:
$$ \rho_{metal} = 7.5 \times 1000 \, \text{kg/m}^3 = 7500 \, \text{kg/m}^3 $$
Example 3: Relative Density of a Gas
Helium has a relative density of about 0.14 compared to air. Since the density of air at STP is $1.225 \, \text{kg/m}^3$, the density of helium can be calculated as:
$$ \rho_{helium} = 0.14 \times 1.225 \, \text{kg/m}^3 \approx 0.1715 \, \text{kg/m}^3 $$
Example 4: Using a Hydrometer
A hydrometer is a device used to measure the relative density of liquids. It floats in the liquid, and the level to which it sinks corresponds to the relative density. For example, if a hydrometer sinks to a level marked 1.2 in a liquid, the liquid has a relative density of 1.2 compared to water.
Conclusion
Relative density is a useful concept in physics and engineering for comparing the densities of different materials without the need for specific units. It is particularly important in applications involving buoyancy, material selection, and quality control in manufacturing processes. Understanding how to measure and calculate relative density is essential for students and professionals working with fluids and materials.