 # Unit of Density

The density of a substance is the measure of how much stuff an object has in a unit volume. The symbol ρ represents it or it can also be represented by letter D.

## What is Density?

The density of material shows the denseness of that material in a specific given area. A material’s density is defined as its mass per unit volume. Density is essentially a measurement of how tightly matter is packed together. It is a unique physical property for a particular object. The principle of density was discovered by the Greek scientist Archimedes.  It is easy to calculate density if you know the formula and understand its related units.

### Examples

Iron, platinum, and lead are examples of dense materials. Many types of rock and minerals are examples of dense material. Materials that are dense are most likely to ‘feel’ heavy or hard. The opposite of dense is sparse and a few examples of sparse material are glass, bamboo, aluminum, and styrofoam.

In general, liquids are less dense than solids and gases are less dense than liquids. This is due to the fact that solids have densely packed particles, liquids are materials where particles can slide around one another, and gases have particles that are free to move all over the place.

## How is Density Calculated?

Mathematically, the density of an object is expressed as follows:

$Density= \frac{Mass}{Volume}$ $\rho = \frac{m}{v}$

Where,

• ρ is the density
• m is the mass
• V is the volume

## Unit of Density

• Though SI unit of density is kg/m³, for convenience we use g/cm³ for solids, g/ml for liquids, and g/L for gases.
• Density can be explained as the relationship between the mass of the substance and the volume it takes up.
• In a qualitative term, it shows how much heavy an object is at constant volume.
• Different substances have different density, which means for the same volume of different substances weigh differently.

## SI Unit of Density

Each substance has a specific density. Generally, the density of water (which is approximately about 1 gram/cubic centimeter) is taken as the standard value for calculating the density of substances. However, the SI unit of Density is measured using kilograms per cubic meter (kg/m3).

### Other Density Units

Talking about other density units, metric tons and liter are also used even though they are not part of the SI. Some other units include:

• gram per milliliter (g/mL)
• metric ton per cubic meter (t/m3)
• kilogram per liter (kg/L)
• megagram (metric ton) per cubic meter (mg/m3)
• gram per cubic centimeter (g/cm3)
1 g/cm3 = 1000 kg/m3
• kilogram per cubic decimetre (kg/dm3)

In addition to this, in the cgs system density is measured in gram per cubic centimeter (g/cm3).

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## Applications of Density in Real Life

Many applications of density are there in our real-life like a few examples are in pipe design, shipbuilding, helium balloons, weight distribution in the airplane, and the fact that ice floats on water.

• The knowledge of the densities of two substances helps you in separation techniques. For example, separation of oil from water. Leakage of an oil tank in the ocean then oil drops start to float on the water due to their less density in the water.
• Another well-known application of density is determining whether an object will float on water or not. The floating of ships and diving of submarines are due to their density difference.

## Solved Examples

### Question 1:

Take two boxes that have the same volume. Fill the first box with x balls and the second box with 6x balls. If the mass of each ball is the same, which box would weigh more?

Solution:

The box that has more balls has more mass per unit of volume.

Here the first box contains x number of balls and the second box contains a 6x number of balls. Since the number of balls in the second box is 6 times the first box, the second box would weigh more. This property of matter is called density.

### Question 2:

Calculate the density of water if it has a mass of 1160 Kg and a volume of 1 m3?

Solution:

Given,

Mass = 1160 Kg

Volume = 1 m3

Density is given by the formula:

Density = Mass/Volume

ρ = 1160/1 = 1160 kg/m3

### Questions 3:

If you find a shiny rock, a carbon allotrope with a volume of 0.042 cm³ and a mass of 0.14 g, is it graphite or diamond? The density of graphite is 2.266 g/cm3 and the density of diamond is 3.51g/cm3.

Solution:

Given,

Volume of the shiny rock =0.042 cm³

Mass of the shiny rock = 0.15 g

Density of graphite = 2.266 g/cm3

Density of diamond = 3.51g/cm3

Use the density equation to solve for m, mass of graphite and for the mass of a diamond.

ρ = m/V

m = ρV

m = 2.266 g/cm³ x 0.042 cm³ = 0.0951g for graphite

m = 3.51g/cm3 x 0.042 cm³ = 0.1474 g for diamond

The mass of the shiny rock you found is identical with the mass of diamond.