Difference Between Density and Specific Gravity

Density is defined as the amount of mass in a unit volume of matter. Density is an intrinsic property, as it depends on the internal packing of atoms in the given material and also on the atomic mass of the element or compound. This means that the density of the material will remain the same, irrespective of external conditions. The standard unit of density is Kg/m³.

Mathematically, density is the ratio of mass and volume and it is denoted by the Greek letter roh (ρ).

Density = Mass/Volume

Specific Gravity of a substance is the ratio of its density with another reference substance. It is a unit-less quantity. Specific gravity is an ambiguous term as gravity has nothing to do with it, hence the term relative density is more often used. 

If a substance has a specific gravity less than 1 then it will drown in the reference substance, if the specific gravity is greater than 1 then the substance will float in the reference substance.

For fluids, the reference substance is usually water (10³ kg/m³) and for gases, it’s air at room temperature (1.2 kg/m³).

Specific gravity = ρ_i/ρ_o 

where, 

ρ_i = density of substance,

ρ_o = density of reference substance.

Following is a table of differences between Density and Specific Gravity:

	Density	Specific Gravity
1.	It is the relationship between the mass and volume of a substance.	It is the ratio of the density of a substance and a reference substance.
2.	Density is an absolute quantity.	Specific gravity is a relative quantity.
3.	Density = Mass/Volume	Specific gravity = ρi/ρo
4.	Density is unique for material under a given temperature.	Specific gravity for a single substance can vary depending upon the reference substance used.
5.	It’s unit is Kg/m3	It is unit-less.

Sample Problems

Problem 1: A copper bar has dimensions 1.5cm X 1.0cm X 3.0cm and its mass is 37.5gm. Find its density.

Solution:

Density = Mass/Volume, so in order to calculate density we’ll need the volume of the copper bar.

volume = l x b x h

volume = 1.5 x 1.0 x 3.0 

volume = 4.5 cm³

mass =  37.5 gm

=> density = 40/4.5 = 9.99 gm/cm³

Problem 2: A solid plastic toy displaces 24 cm³ when fully immersed in water, if its mass is 29gm find its density.

Solution:

Density = Mass/Volume, volume of the plastic toy will be equal to the volume of the water

that it displaces.

therefore volume = 24 cm³ 

mass = 29gm

=> density = 24/29 = 0.83 gm/cm³

Problem 3: A football of diameter 80mm and mass 160g lands in the water. Calculate the specific gravity of the football and tell whether it’ll float or sink.

Solution:

A football is a sphere, so it’s volume is 4/3 * π * r³

converting radius from mm to cm and plugging it in the formula we get 

volume of football = 4/3 * π * 4³ = 2144.66 cm³.

mass = 160g

=> density = 160/2144.66 = 0.074 gm/cm³

specific gravity = density of football / density of water

=>specific gravity = 0.074/1 = 0.074

as the specific gravity of football is less than 1 the ball will float on water. 

Problem 4: What is the unit of specific gravity?

Solution:

As specific gravity is a ratio of densities, it doesn’t have any units.

Problem 5: How much water with density 1 gm/cm³ must be added to 200 ml alcohol of density 0.8 gm/cm³ to bring its density up to 0.9 gm/cm³?

Solution:

weight of 200 ml of alcohol = density * volume

weight of 200 ml of alcohol = 0.8 * 200 = 160 gm

let us assume that adding ‘x’ gram of water will bring specific gravity of alcohol to 0.9.

volume of x gram of water = 1 * x = x ml.

=> final mass of the solution (water + alcohol) = 160 + x 

and final volume of the solution = 200 + x.

density of solution = (160 + x) / (200 + x)

=> (160 + x) / (200 + x) = 0.9

=> 160 + x = 180 + 0.9x

=> 0.1x = 20

=> x = 200

therefore 200 gm of water must be added to 200 ml of alcohol to make the alcohol’s density to 0.9.