Density

Define density.

Density refers to the measure of how closely the particles are packed in a body. By definition, it is the mass of the body per unit of its volume. We represent it by \(\rho\).

If \(M\) represents mass and \(V\) represents its volume, then \[\rho = \frac{M}{V}\]

Density is a scalar quantity and intrinsic property. SI unit of density is \(Kg \cdot m^{-3}\).

Its dimensional formula is \([M^{1}L^{-3}T^{0}]\).

Density of water is maximum at 4° Celsius. It is \(1000 Kg \cdot m^{-3}\) = \(1 Kg \cdot L^{-1}\)= \(1 g \cdot cm^{-3}\) = \(1 g \cdot ml^{-1}\).

Specific Gravity

Specific gravity is the measure of how heavier an object is in comparison with a reference substance. The reference substance is usually water for solids and liquids, and air for the gases. Mathematically, it is the ratio of the densities of the substance one is interested and the reference substance.
Another name for specific gravity is relative density.

\[\textbf{Specific Gravity}=\frac{\textbf{Density of Substance}}{\textbf{Density of Water}}\]

Being a ratio, specific gravity is unit-less and dimensionless quantity.

Comparison of densities of liquids and gases

Liquids are normally in-compressible and there is no effect of change in pressure on their densities. However, gases are highly compressible. Their densities vary with pressure. High pressure compresses the gases and increase its densities. Thus, densities of gases increase with increase in the pressure.