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If a round of solid iron is heated, ____ will have the minimum percentage increase.
1. radius
2. surface area
3. volume
4. All will have equal percentage increase.

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Correct Answer - Option 1 : radius

Concept:

Thermal expansion:

  • Thermal expansion is the tendency of objects to undergo a change in shape, volume, and area due to a change in their temperature.
  • On heating, the average kinetic energy of the molecules increases and they start moving vigorously about their mean position.
  • In the process, the intermolecular spacing increases and the material expands in all directions.
  • Coefficient of thermal expansion: The coefficient of thermal expansion is a property of any material that indicates the extent to which a material expands upon heating.
  • It is the rate of material expansion under a unit temperature increment.
Linear expansion
  • It is the change in one dimension (length) due to a change in temperature (ΔT).
  • The coefficient of linear expansion is α.
Change in length, ΔL = L0αΔT
Superficial expansion
  • It is the change in two dimensions (area) due to a change in temperature (ΔT).
  • The coefficient of linear expansion is β.
Change in area, ΔA = A0βΔT
 
Cubical expansion
  • It is the change in three dimensions (volume) due to a change in temperature (ΔT). It is also called volumetric expansion.
  • The coefficient of linear expansion is γ.
Change in volume, ΔV = V0γΔT
 

 

The relation between α, β and γ is given as

α =  β \ 2 =  γ / 3

So,  γ is having more value than α and β.

Explanation:

Since, α has minimum value as compared to β and γ, so we can say that linear expansion will be minimum as compared to surface area and volume. 

Density is given as mass / volume. As mass is same, volume is decreasing then, we can say density is decreasing and not increasing. So, density cannot be the correct option here. 

So, the minimum increase is of length that is radius in this case.

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