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Answer :
The relationship L = L_i + α L_i ΔT is a valid approximation when αΔT is small.
When αΔT is large, one must integrate the relationship dL= α LdT to determine the final length.
The linear thermal expansion is given by the relationship[tex]L = L_i + α L_i ΔT[/tex], which is a valid approximation when αΔT is small.
When αΔT is large, one must integrate the relationship[tex]dL= α LdT[/tex]
to determine the final length, given that
α = 2.00 × 10⁻⁵ °C⁻¹ (a typical value for a metal).
If αΔT is small, the above relationship ([tex]L = L_i + α L_i ΔT)[/tex] is valid.
The variation in length is directly proportional to the temperature change, and the constant of proportionality is the coefficient of linear thermal expansion.
This proportionality does not hold true for all materials but is valid only for a few.
The coefficient of linear thermal expansion is represented by the symbol α, which is defined as the fractional change in length per unit change in temperature (⁰C) per unit original length.
Mathematically, it can be represented as [tex]α = (L - L_i)/(L_i × ΔT).[/tex]
The SI unit for the coefficient of linear thermal expansion is K⁻¹ or °C⁻¹.
Therefore, the relationship L = L_i + α L_i ΔT is a valid approximation when αΔT is small.
When αΔT is large, one must integrate the relationship dL= α LdT to determine the final length.
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