Matter exists in three states solid, liquid and gas. Any state of matter that can flow is a fluid. Liquids and gases are therefore, referred to as fluids.

__Density :__

Density of a substance is the mass per unit volume. Homogenous bodies have uniform density:

ρ = M/V

The unit of density is kg/m3 in S.I. system. Dimension of density is given by [ρ] = = [M] [L^{-3}].

__Relative Density or Specific Gravity :__

Relative density of a substance is the ratio of the density of the substance to the density of pure water (ρ_{w} = 1000 kg/m3) at 4°C.

ρ_{r} = ρ/ρ_{w}.

Relative density is dimensionless

**Illustration :** A hollow metallic sphere has inner and outer radii respectively as 5 cm and 10 cm. If the mass of the sphere is 2.5 kg, find (a) density of the material (b) relative density of the material of the sphere.

**Solution:** The volume of the material of the sphere is

V = 4/3 π(r_{2}^{3} – r_{1}^{3})

= (4/3)x 3.14 x 0.000875 m^{3}

= 0.00367 m^{3}

(a) Therefore, density of the material of the sphere is

ρ= M/V = 2.5/0.00367 kg/m^{3}

= 681.2 kg/m^{3}

(b) ρ_{r} = 681.2/1000 = 0.6812

__Density of a mixture__

Let a number of substances of masses M1, M2, M3 etc., and densities ρ_{1}, ρ_{2}, ρ_{3}, etc. respectively be mixed together. The total mass of the mixture is M_{1} + M_{2} + M_{3} + ….

The total volume is M_{1}/ ρ_{1} + M_{2}/ρ_{2} + M_{3}/ρ_{3} + …. , provided that the substances retain their individual states within the mixture.

Therefore, the density of the mixture is

The same expression may written in terms of the volumes:

The density of the mixture is

where V_{1}, V_{2}, V_{3} … represent the volumes of substances of densities ρ_{1}, ρ_{2}, ρ_{3} . . . in the mixture

**Illustration :** Two liquids of densities 2.5 gm/cm^{3} and 0.8 gm/cm^{3} are taken in the ratio of their masses as 2:3 respectively. Find the average density of the liquid combination.

**Solution:** Let the masses be ‘ 2 m ‘ gm and ‘ 3 m ‘ gm respectively. Therefore, the volume of the first liquid of density 2.5 gm/cm^{3} is V_{1} = 2m/2.5 cm^{3}

That of the second liquid is V_{2} = 3m/0.8 cm^{3}

Total volume V = V_{1} + V_{2} = 2m/2.5 + 3m/0.8 cm^{3}

Total mass = 2m + 3m = 5 m gm

Therefore, the average density

= 10/9.1

= 1.09 gm/cm^{3}

**Exercise :** Two miscible liquids of densities 1.2 gm/cc and 1.4 gm/cc are mixed with a proportion ratio of their volumes equal to 3:5. What is the density of resulting liquid?