First slide

Thermal expansion

Question

Two rods of lengths L₁ and L₂ are made of materials whose coefficient of linear expansion are $α_{1}$ and $α_{2}$ . If the difference between the two lengths is independent of temperature :

Moderate

A

$(L_{1} / L_{2}) = (α_{1} / α_{2})$
B

$(L_{1} / L_{2}) = (α_{2} / α_{1})$
C

$L_{1}^{2} α_{1} = L_{2}^{2} α_{2}$
D

$α_{1}^{2} L_{1} = α_{2}^{2} L_{2}$

Solution

$L_{2}' - L'_{1} = L_{2} - L_{1} \Rightarrow L_{2} (1 + α_{2} ∆ T) - L_{1} (1 + α_{1} ∆ T) = L_{2} - L_{1} \Rightarrow (L_{2} α_{2} - L_{1} α_{1}) ∆ T = 0 \Rightarrow \frac{L_{1}}{L_{2}} = \frac{α_{2}}{α_{1}}$

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