Thermal Expansion - Long Question Answer | Physics Grade 11 Solution

Long Question Solution

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Thermal Expansion - Long Question Answer | Physics Grade 11 Solution

Thermal Expansion - Long Question Answer 4

Question: Does cubical expansivity depends upon the initial volume of a solid? Write the unit of this expansivity. Also derive its relation with superficial expansivity.

Ans: No, the cubical expansivity of solid does not depend upon initial volume of solid. The cubical expansivity of a solid is given as
γ = ∆V/V(θ2-θ1)
The ratio of ∆V/V is same in each case for a solid so, the coefficient of cubical expansion is same for all volume of a solid and does not depend on the volume. The unit of this expansivity is per kelvin (K-1).
 
Relation between β and γ: Let us consider a cube whose sides having length l0 and area of each face A0 at temperature 0oC and volume is V0. If the cube is heated, then the side of cube becomes lθ, area Aθ, and volume Vθ. If γ be the coefficient of cubical expansion then,
Vθ = V(1 + γ ∆θ) ……...(1)
Again,
Vθ Aθ lθ
or, Vθ A(1 + β∆θ) l(1 + αθ)
or, Vθ Al(1 + αθ + β∆θ + αβθ2)
 
Since the value of α and β is very small their product with θ2 can be neglected so the above equation can be written as:
Vθ = V0 {1 + (α + β)∆θ} ……....(2)
Comparing equation 1. and 2.
γ = α + β
or, γ = β/2 + β  [since β = 2α]
.: γ/3 = β/2
This is the required relation between γ and β.

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