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Derive the relation of coefficient of linear expansion (α).

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"When a solid  heated and its length increases, then the expansion is called linear expansion."

Consider a rod whose the rod is length is L0. when the rod is directly heated, the increase in its length ΔL is proportional to (i) its Original length L0 and (ii) change in temperature ΔT is in°C or Kelvin).

where 'α' is called the coefficient of linear expansion.

Definition of α : " It is defined as the increase in length per unit length per unit rise in temperature," Unit of α is °C or K-1.

Length of the rod after heating : Since ΔL = L - L0. where L is the length after heating the rod. Hence, eqn. (i) can be written as

L - L0 = α L0 ΔT

or L = L0 (1 + αΔT)

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