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 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 (ρw = 1000 kg/m3) at 4°C.
ρr = ρ/ρw.
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(r23 – r13)
= (4/3)x 3.14 x 0.000875 m3
= 0.00367 m3
(a) Therefore, density of the material of the sphere is
ρ= M/V = 2.5/0.00367 kg/m3
= 681.2 kg/m3
(b) ρr = 681.2/1000 = 0.6812
Density of a mixture
Let a number of substances of masses M1, M2, M3 etc., and densities ρ1, ρ2, ρ3, etc. respectively be mixed together. The total mass of the mixture is M1 + M2 + M3 + ….
The total volume is M1/ ρ1 + M2/ρ2 + M3/ρ3 + …. , 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 V1, V2, V3 … represent the volumes of substances of densities ρ1, ρ2, ρ3 . . . in the mixture
Illustration : Two liquids of densities 2.5 gm/cm3 and 0.8 gm/cm3 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/cm3 is V1 = 2m/2.5 cm3
That of the second liquid is V2 = 3m/0.8 cm3
Total volume V = V1 + V2 = 2m/2.5 + 3m/0.8 cm3
Total mass = 2m + 3m = 5 m gm
Therefore, the average density
= 1.09 gm/cm3
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?