A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is: (αCu = 1.7 × 10⁻⁵ K⁻¹ and αAl = 2.2 × 10⁻⁵ K⁻¹)

Question

Accepted Answer

113.9 cm. For the increase in length to be independent of temperature, the product of the coefficient of linear expansion (α) and the length (L) must be the same for both rods. Using the relation αCu × LCu = αAl × LAl, we substitute αCu = 1.7 × 10⁻⁵, LCu = 88 cm, and αAl = 2.2 × 10⁻⁵. Solving for LAl gives LAl = (αCu × LCu) / αAl = (1.7 × 10⁻⁵ × 88) / (2.2 × 10⁻⁵) = 113.9 cm.

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is: (αCu = 1.7 × 10⁻⁵ K⁻¹ and αAl = 2.2 × 10⁻⁵ K⁻¹)

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