Coefficient of linear expansion of brass and | vedclass

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(C) Let the lengths of the brass and steel rods at temperature $T$ be $L_1$ and $L_2$ respectively.After a change in temperature $\Delta T$,the new le

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$\alpha_1 l_1 = \alpha_2 l_2$

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(C) Let the lengths of the brass and steel rods at temperature $T$ be $L_1$ and $L_2$ respectively.After a change in temperature $\Delta T$,the new lengths are:$L_1' = l_1(1 + \alpha_1 \Delta T)$$L_2' = l_2(1 + \alpha_2 \Delta T)$Given that the difference $(L_2' - L_1')$ remains constant and equal to $(l_2 - l_1)$ at all temperatures:$L_2' - L_1' = l_2 - l_1$$l_2(1 + \alpha_2 \Delta T) - l_1(1 + \alpha_1 \Delta T) = l_2 - l_1$$l_2 + l_2 \alpha_2 \Delta T - l_1 - l_1 \alpha_1 \Delta T = l_2 - l_1$$(l_2 - l_1) + \Delta T(l_2 \alpha_2 - l_1 \alpha_1) = l_2 - l_1$For this to hold for any $\Delta T$,the coefficient of $\Delta T$ must be zero:$l_2 \alpha_2 - l_1 \alpha_1 = 0$$\alpha_1 l_1 = \alpha_2 l_2$

Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $(l_2 - l_1)$ is maintained same at all temperatures,which one of the following relations holds good?

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