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Iron ball is heated, percentage increase will be largest in
1. Diameter
2. Surface Area
3. Volume
4. Density

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Correct Answer - Option 3 : Volume

CONCEPT:

  • Thermal expansion: When the temperature of any object is changed then the tendency of changing the shape, area, and volume of the body is called the thermal expansion of that object.

There are three types of thermal expansion:

SR.No 1. Linear expansion 2. Areal Expansion 3. Volume expansion
1 When the temperature of anybody is changed then the tendency of changing the length of the body is called a linear thermal expansion of that body. When the temperature of anybody is changed then the tendency of changing the area of the body is called the areal thermal expansion of that body. When the temperature of anybody is changed then the tendency of changing the volume of the body is called a volume thermal expansion of that body.
2

Change in length is defined as:

ΔL = L α Δ T

Where Δ L = changes in length, L = original length, Δ T = changes in temperature of the body, and α = coefficient of linear expansion.

The change in area is defined as:

ΔA = A β Δ T

Where ΔA = changed in the area, A = the original area, β = the coefficient of areal expansion, and ΔT = temperature change.

Change in volume (Δ V) is given by:

Δ V = V γ Δ T

Where V = original volume, γ = the coefficient of volume expansion and ΔT = temperature change.


The relation between α, β, and γ is given by:

β = 2α, and γ = 3α i.e., 1:2:3 = α : β : γ 

  • Density (d): The mass per unit volume is called density.
    • Density (d) = Mass (m)/Volume (V).

EXPLANATION:

  • Since the radius increment is a linear expansion, which is directly proportional to the temperature change. 
  • Similarly, the area change and volume change are directly proportional to the temperature change.
  • Density change (Δ d) = Mass (m)/Change in volume (ΔV)

  • Since the density change is inversely proportional to volume change, so the density will have a minimum percentage increase and volume will have a maximum percentage increase.


The correct option is 3.

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