Supplement
This supplement should help you to better understand how the formulas and
allowance factors used have been derived.
Fundamental Principles
Mass (g)
Density =
Volume (cm
3
)
The Archimedean Principle:
A solid immersed in a liquid is exposed to the force of buoyancy (G). This value
is the same as that of the weight of the liquid displaced by the volume of the solid.
The volume of an immersed solid V (s) equals the volume of the displaced
liquid V (fl).
The following are determined:
1. The weight of the sample in air: W (a)
2. The buoyancy of the solid in liquid: G
The specific gravity of a solid is:
sample mass
ρ ===
sample volume
If the density ρ (fl) of the displaced liquid is known, then
Mass (fl)
V (fl) = =
ρ (fl)
Therefore:
W (a) · ρ (fl)
ρ =
G
Calculation
The specific gravity of a solid is calculated from the ratio
ρ : W (a) = ρ (fl) : W (a) – W (fl),
where:
W (a) · ρ (fl)
ρ =
W (a) – W (fl)
W (a) – W (fl) = G = buoyancy of the sample
G
ρ (fl)
W (a)
V (fl)
W (a)
V (s)
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