Question

What is specific gravity? How is it related to density?

Short answer

Answer: The specific gravity of the substance is 0.6.

Step-by-step solution

Define Specific Gravity

Specific gravity is a dimensionless unit, and it is the ratio of the density of a substance to the density of a reference substance. In most cases, the reference substance is water (which has a density of \(1000 \frac{kg}{m^3}\) at \(4^\circ C\)).

Define Density

Density (\(\rho\)) is the mass (\(m\)) per unit volume (\(V\)) of a substance. Mathematically, density can be expressed as: $$\rho = \frac{m}{V}$$ The units of density are typically kilograms per cubic meter (\(\frac{kg}{m^3}\)) in the SI system or grams per cubic centimeter (\(\frac{g}{cm^3}\)) in the CGS system.

Relate Specific Gravity to Density

To relate specific gravity to density, we need to express it in terms of the density of the given substance and the density of the reference substance. Let the density of the given substance be \(\rho_{substance}\), and the density of the reference substance be \(\rho_{ref}\). The formula for specific gravity (\(SG\)) can then be expressed as follows: $$SG = \frac{\rho_{substance}}{\rho_{ref}}$$ For objects that are less dense than water, the specific gravity will be less than 1, while for objects denser than water, the specific gravity will be greater than 1.

Calculate Specific Gravity from Density

Suppose the density of a substance is given and we need to find its specific gravity. Let's say the density of the substance is \(600 \frac{kg}{m^3}\), and the density of the reference substance (i.e., water) is \(1000 \frac{kg}{m^3}\). Using the specific gravity formula: $$SG = \frac{600 \frac{kg}{m^3}}{1000 \frac{kg}{m^3}} = 0.6$$ The specific gravity of the substance is 0.6 (i.e., it is less dense than the reference substance, water).