Density & Relative Density

Density and relative density is considered to be the comparison of the density of the substances with that of water. Relative density is a ratio so it has no unit. The value of density of petrol or diesel, which is written on petrol dispensers, indicates the quality of fuel available at the petrol pump. It also tells us the adulteration limit of petrol or diesel. The density of a substance gives an idea of purity. Different materials have different densities. The mass per unit volume concentration is a fixed value for a pure substance.

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Density and Relative Density: Details

there are times when iron is considered to be heavier than cotton. This statement can be simplified by stating that the density of iron is more than the density of cotton. The density of a substance simply tells how heavy or light that substance is. It measures the amount of matter present in the unit volume of a substance. Different substances have different densities.

Definition: The density of a substance is defined as the mass per unit volume of substance. In other words, density of a substance tells how close the particles of a substance are packed. For example, the particles in a unit volume of iron are more closely packed than in the same volume of wood. The amount of mass in the given volume of iron is considered to be greater than the mass for the same volume of wood.

We can also say that an equal amount of mass for iron and wood will occupy different amounts of space or volume.

Density: Formula

The density is defined as the mass per unit volume of a substance. It is represented by \(‘ \rho^{\prime}\). If the mass of the substance is \(M\) and the volume of the substance is \(V\), then the density of the substance is given by

\(\rho=\frac{M}{V}\)

The SI unit of density is kilogram per cubic meter \(\left( {{\rm{kg}}\,{{\rm{m}}^{ – 3}}} \right).\)

Density: Variation in Terms of Temperature

For a fixed mass of a substance, if the volume is increased, the density decreases and if the volume decreases, the density of the substance increases. Substances expand on heating, so on increasing the temperature of a substance, the volume of the substance increases, and it reduces the density of the substance and vice versa. Liquids and gases can undergo significant expansion on heating, so we can easily change their densities by providing heat. In the case of a solid, the change in density on heating or cooling is negligible.

Relative Density: Definition

The relative density of a substance is defined as the ratio of the density of the substance to the density of water at \(4\,^\circ {\rm{C}}.\)It is also known as the specific gravity of a substance.

Relative Density: Formula

Relative density \((R D)\) of a substance is given by the following formula:

\(RD\, = \,\frac{{{\rm{Density}}\,{\rm{of}}\,{\rm{the}}\,{\rm{substance}}}}{{{\rm{Density}}\,{\rm{of}}\,{\rm{water}}\,4\,^\circ {\rm{C}}}}\)

By using the formula of density, for an equal volume of water and the substance, we get

\(RD{\rm{ = }}\frac{{{\rm{Mass}}\,{\rm{of}}\,{\rm{the}}\,{\rm{substance}}}}{{{\rm{Volume}}\,{\rm{of}}\,{\rm{the}}\,{\rm{substance}}}}{\rm{ \times }}\left( {\frac{{{\rm{Volume}}\,{\rm{of}}\,{\rm{the}}\,{\rm{water}}}}{{{\rm{Mass}}\,{\rm{of}}\,{\rm{the}}\,{\rm{water}}}}} \right)\,{\rm{at}}\,{\rm{4}}{\,^{\rm{^\circ }}}{\rm{C}}\)

If volumes substance and water are same, \(RD{\rm{ = }}\frac{{{\rm{Mass}}\,{\rm{of}}\,{\rm{the}}\,{\rm{substance}}}}{{{\rm{Mass}}\,{\rm{of}}\,{\rm{the}}\,{\rm{water}}\,{\rm{4}}{\,^{\rm{^\circ }}}{\rm{C}}}}\)

From equation \((1)\), we can say that the relative density of a substance is the ratio of the mass of the substance to the mass of water of equal volume at \(4\,^\circ {\rm{C}}.\) The density of pure water at \(4\,^\circ {\rm{C}}\) is maximum, and it is equal to \(1000 \mathrm{~kg} \mathrm{~m}^{-3}\) or \(1 \mathrm{~g} \mathrm{~cm}^{-3}\).

The relative density of a substance is dimensionless because it is the ratio of two similar physical quantities.

Density and Relative Density: Relationship

In the SI system, the relative density of a substance is obtained by dividing the density of the substance by \(1000 .\)

\(RD\, = \,\,\frac{{{\rm{ Density}}\,{\rm{of}}\,{\rm{the}}\,{\rm{substance}}\,{\rm{in}}\,{\rm{kg}}\,{{\rm{m}}^{{\rm{ – 3}}}}}}{{{\rm{1000\;kg\;}}{{\rm{m}}^{{\rm{ – 3}}}}}}\)

\({\rm{Density}}{\mkern 1mu} \,{\rm{of}}\,{\mkern 1mu} {\rm{a}}{\mkern 1mu} \,{\mkern 1mu} {\rm{substance}}\,{\rm{ = }}\,\left( {RD{\rm{ \times 1000}}} \right)\,{\rm{kg}}\,{{\rm{m}}^{{\rm{ – 3}}}}\)

In the CGS system, the density of a substance is given by
\({\rm{Density}} = (RD \times 1)\,{\rm{g}}\,{\rm{c}}{{\rm{m}}^{ – 3}}\)

Relative Density of Liquids: Devices to Measure

The relative density of a liquid is measured using a hydrometer device. This device follows the principle of Archimedes’, which states that when a body is immersed fully or partially in a liquid, it experiences an upward force that is equal to the weight of the fluid displaced by it.

A hydrometer is made of glass, and it consists of a stem and a bulb. The bulb of the hydrometer is filled with mercury or lead shot. This makes it float in the upright position. The hydrometer gently lowered into the liquid until it floatsly to measure its relative density. The point at which the surface of the liquid touches the stem of the hydrometer gives the liquid’s relative density. The hydrometer, which is used to measure the purity of milk, is called a lactometer.

Difference Between Relative Density and Density?

Floating and Sinking

When an object is immersed in a liquid, it may float or sink in the liquid depending on its density. If the density of the object is more than the density of the liquid, the object will sink in the liquid. If the density of the liquid is more than the density of the object, then the object will float on the liquid. For example, if we immerse a steel spoon in a bucket full of water, the spoon will sink in the water because its density is more than the density of water, whereas when will immerse a plastic ball in the same bucket of water, the plastic ball will float on the surface of the water because its density is less than the density of water.

A substance whose relative density is less than \(1\) will float on the surface of the water. For example, wood and kerosene. Substances having relative density more than \(1\) will sink in water. For example, iron and aluminium.

Summary

From this article, we can conclude that density is the property of a substance that tells how close the particles are packed in the given volume of the substance. The heavier the object, the more will be its density. The density of a substance decreases by increasing the temperature of the substance, and it increases when the temperature is decreased.

The relative density of a substance is usually used to compare its density with the density of water at \(4\,^\circ {\rm{C}}.\) It also helps in verifying the purity of a substance.

Solved Examples

Q.1. A solid ball has a mass of \(50 \mathrm{~g}\) and a volume of \(20\;{\rm{c}}{{\rm{m}}^3}.\) What is the density of the ball?
Sol: Given, the mass of the ball, \(M=50 \mathrm{~g}\)
The volume of the ball, \(V=20 \mathrm{~cm}^{3}\)
The density of the ball, \(\rho=\frac{M}{V}=\frac{50}{20}=2.5 \mathrm{~g} \mathrm{~cm}^{-3}\)
Therefore, the density of the ball is \(2.5\;{\rm{g}}\;{\rm{c}}{{\rm{m}}^{ – 3}}.\)

Q.2. What is the mass of a body whose volume is \({\rm{2}}\,{{\rm{m}}^{\rm{3}}}\) and relative density is \(0. 52 ?\)
Sol: Given, the volume of the body, \(V=2 \mathrm{~m}^{3}\)
The relative density of the body, \(R D=0.52\)
Let \(M\) be the mass of the body.
The density of the body is given by
\(\rho=R D \times 1000 \mathrm{~kg} \mathrm{~m}^{-3}\)
\(\Rightarrow \frac{M}{V}=0.52 \times 1000\)
\(\Rightarrow M=V \times 0.52 \times 1000\)
\(\Rightarrow M=2 \times 0.52 \times 1000=1040 \mathrm{~kg}\)
Therefore, the mass of the body is \(1040 \mathrm{~kg}.\)

Frequently Asked Questions

Q. What is the SI unit of density and relative density?
Ans: The SI unit of density is kilogram per cubic meter \(\left( {{\rm{kg}}\,{{\rm{m}}^{ – 3}}} \right).\)
\({\rm{Density}} = \frac{{{\rm{ Mass }}}}{{{\rm{ Volume }}}}\)
\({\rm{Unit}}\,{\rm{of}}\,{\rm{Density}}\,{\rm{ = kg}}\,{{\rm{m}}^{{\rm{ – 3}}}}\)
The relative density has no unit because it is the ratio of identical physical quantities.

Q. What is relative density in physics?
Ans: The relative density of a substance is defined as the ratio of the density of the substance to the density of water at \(4\,^\circ {\rm{C}}.\)

Q. How do you find density from relative density?
Ans: The value of the density of a substance can be calculated easily by multiplying the value of relative density with the density of water at \(4\,^\circ {\rm{C}}.\)
\({\rm{Density}}\,\,{\rm{of }}\,{\rm{a }}\,{\rm{substance = }}\left( {RD \times {\rm{1000}}} \right){\rm{ kg}}{\mkern 1mu} \,{{\rm{m}}^{{\rm{ – 3}}}}\) Or
\({\rm{Density}}\,{\rm{of}}\,{\rm{a}}\,{\rm{substance}} = \left( {RD \times 1} \right)\,{\rm{g}}\,{\rm{c}}{{\rm{m}}^{{\rm{ – 3}}}}\)
For example, if the relative density of mercury is \(13.6\), then the density of mercury in the CGS system will be \(13.6 \mathrm{~g} \mathrm{~cm}^{-3}\), and its density in the SI system will be \(13.6 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}\).

Q. What is the difference between density and relative density?
Ans: Density is referred to as the mass per unit volume where as relative density is the density of a substance with respect to the density of water.

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