Density

Definition:  

Density is the amount of  (mass) present per unit volume.It is a scalar quantity and depends on mass and volume to measure it. Its symbol is , a greek letter, rho.  It is typically measured in g/cm3 and its SI unit is kg/m3.

Explanation:

 If there is a wooden block, its density could be easily calculated by measuring its mass(in grams) in unit volume (in cm3 ). The diagram represents the mass present in   1cm 3 of wooden block. Density is a key concept that determines how much mass (stuff) is present in the unit volume of the given object.   

Analogy:

Imagine two school gyms:

Gym A (box A) starts with a few students. Gym B (box B) starts with more students, so it’s already denser. As more students come, both gyms get more crowded with students. This shows how packing more students into the same gym space is like increasing the density of objects or substances by adding more mass into the same volume.

Formula:

Density is a fundamental property of matter that explains matter present per unit volume. 

Mathematically, density (ρ) of an object  is defined as the ratio of mass (m) to  its volume (V), and the formula is given by:

= mV

This formula highlights that density measures how much mass is concentrated in a given volume. Objects with higher density have more mass per unit volume than objects with lower density. 

Unit and SI unit of Density: 

Though the SI unit of density is kg/m³, for convenience we use g/cm³ for solids, g/ml for liquids, and g/L for gases.

Effect of mass and volume on Density

According to formula,

= mV

1. Relation of Mass with Density (When Volume is Constant)

Relation: Density (ρrho) is directly proportional to mass (m) when volume (V) is constant

Scenario: Comparing the densities of two different materials, iron and aluminium, each occupying a volume of 1 cubic metre.

• Object A: Iron block with a mass of 10 kilograms (mA​= 10kg).
• Object B: Aluminium block with a mass of 20 kilograms (mB​=20kg).

Therefore,

• The density of the iron block (ρA) is 10 kg/m3
• The density of the aluminium block (ρB​) is 20 kg/m3

Aluminium has a higher density compared to iron when they occupy the same volume.

2. Relation of Volume with Density (When Mass is Constant)

Relation: Density (ρrhoρ) is inversely proportional to volume (V) when mass (m) is constant. 

Scenario: Comparing the densities of two different gases, helium and nitrogen, each contained in cylinders with a mass of 5 kilograms.

• Object A: Helium gas in a cylinder with a volume of 100 cubic metres (VA=100 m3)
• Object B: Nitrogen gas in a cylinder with a volume of 50 cubic metres (VB=50 m3)