RELATIVE DENSITY: CALCULATION, EXAMPLES, EXERCISES - PHYSICAL - 2025

The relative density is the dimensionless relationship between the density of a substance and a reference which is usually water at 4 ° C (39.2 ° F) for liquids and solids, while for gases dry air is used.

In some texts it is also called specific gravity (literal translation of specific gravity in English), but it is the same concept. Both densities must be in the same system of units and have been measured under equal conditions of pressure and temperature.

Floating objects have a lower relative density than water. Source: PIxabay.

Relative density is calculated mathematically as follows:

Although the density of any substance depends on the pressure and temperature conditions in which it is measured, especially when it comes to gases, the relative density is a very useful concept to quickly characterize diverse materials.

This can be seen immediately, since the density of water is approximately 1 gram for each cubic centimeter: 1 g / cc or 1000 kg / m ³, at atmospheric pressure and in a good range of temperatures (from 0 to 15 º C).

Giving the relative density of a substance it is immediately known how light or heavy it is with respect to water, the universal substance.

In addition, the relative density is an easy value to remember since it is measured with small and easy-to-handle numbers, as will be seen in the next section, in which the values ​​of the relative densities for some known substances are mentioned.

Examples

The relative density of water is obviously 1, since as said at the beginning, it is the reference standard for liquids and solids. Liquids such as coffee, milk or soft drinks have relative densities very close to that of water.

As for oils, there is no single relative density value applicable to all, since it depends on their origin, composition and processing. Most of the relative densities for oils are in a range between 0.7 and 0.95.

Gases are much lighter, so in many applications the reference that is taken is the density of the air, in such a way that the relative density indicates how light or heavy a gas is compared to air. Compared to water, the relative density of air is 0.0013.

Let's look at some relative density values ​​for known substances and materials.

Relative density of some known substances

- Human body: 1.07.

- Mercury: 13.6.

- Glycerin: 1.26.

- Gasoline: 0.68.

- Sea water: 1,025.

- Steel: 7.8.

- Wood: 0.5.

- Ice: 0.92.

The relative density value provides immediate information on whether a substance or material floats in water or sinks.

In view of this, a layer of oil will remain on top of a layer of water, since almost all oils have a lower specific gravity than this liquid. A cube of wood in water may have a portion out of it, just like ice.

Difference with absolute density

The absolute density is the quotient between the mass of a substance and the volume it occupies. As volume in turn depends on temperature (most substances expand when heated) and pressure, density in turn depends on these two magnitudes. Mathematically we have:

Where ρ is the density, whose units in the International System are Kg / m ³, m is the mass and V is the volume.

Due to the relationship that volume has with temperature and pressure, the density values ​​that appear in the tables are usually specified at atmospheric pressure and in certain temperature ranges.

Thus, under normal conditions for gases: 1 atmosphere of pressure and 0º C of temperature, the density of the air is set at 1,293 Kg / m ³.

Despite the fact that its value experiences these variations, it is a very appropriate quantity to determine the behavior of substances, especially in media considered continuous.

The difference with relative density is that absolute density does have dimensions, in which case its values ​​depend on the selected unit system. In this way, the density of water at a temperature of 4º C is:

ρ _water = 1 g / cm ³ = 1000 Kg / m ³ = 1.94 slug / ft ³

Solved exercises

-Exercise 1

Find the volume occupied by 16 grams of oil whose specific gravity is 0.8.

Solution

First we find the absolute density ρ _oil of the oil. Denoting its relative density as s _g, we have:

ρ _oil = 0.8 x Density of water

For the density of water, the value given in the previous section will be used. When the relative density is known, the absolute density is immediately recovered by multiplying this value by the density of the water. So:

Material density = Relative density x Density of water (under normal conditions).

Therefore, for the oil in this example:

ρ _oil = 0.8 x 1 g / cm ³ = 0.8 g / cm ³

Since density is the quotient between mass m and volume V, it will be as follows:

-Exercise 2

A rock has a specific gravity of 2.32 and a volume of 1.42 x 10 ^-4 m ³. Find the weight of the rock in units of the International System and in the technical system.

Solution

The value of the density of water will be used as 1000 Kg / m ³:

ρ _rock = 2.32 x 1000 Kg / m ³ = 2.32 x 10 ³ Kg / m ³

The mass m of the rock is in kilograms:

The weight in units of the technical system is 0.33 Kilogram-force. If it is preferred in the international system, then the unit is Newton, for which the mass is multiplied by the value of g, the acceleration of gravity.

-Exercise 3

A pycnometer is a container with which the relative density of a substance can be determined at a certain temperature.

Pycnometer. Source: Wikipedia.org.

To determine the density of an unknown liquid in the laboratory, this procedure was followed:

- The empty pycnometer was weighed and the reading was 26.038 g

- Then the pycnometer was filled with water at 20º C (water density 0.99823 g / cc) and weighed, obtaining a value of 35.966 g.

- Finally, the pycnometer filled with the unknown liquid was weighed and the reading obtained was 37,791 g.

It is asked to deduce an expression to calculate the density of the liquid and apply it with the data obtained.

Solution

The mass of both the water and the fluid are determined by subtracting the full pycnometer reading from the empty pycnometer:

mass _H2O = 35.966 g - 26.038 g = 9.928 g; _fluid mass = 37.791 g - 26.038 g = 11.753 g

Finally it is substituted in the expression that was deduced:

_fluid ρ = (11.753 g / 9.928 g). 0.99823 g / cc = 1.182 g / cc.

References

1. Encyclopedia Britannica. Specific gravity. Recovered from: britannica.com.
2. Giancoli, D. 2006. Physics: Principles with Applications. 6 ^th.. Ed Prentice Hall.
3. Mott, R. 2006. Fluid Mechanics. 4th. Edition. Pearson Education. 12-21.
4. Valera Negrete, J. 2005. Notes on General Physics. UNAM. 44-45.
5. White, F. 2004. Fluid Mechanics. 5th Edition. Mc Graw Hill. 17-18.