Thermal Properties of Matter – Rankers Physics

Uncategorized: Practice Problem & Solution

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? (2016 - I)
$\alpha_1 l_2 = \alpha_2 l_1$
$\alpha_1 l_2^2 = \alpha_2 l_1^2$
$\alpha_1^2 l_2 = \alpha_2^2 l_1$
$\alpha_1 l_1 = \alpha_2 l_2$

Solution Explained:

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

If the difference in lengths remains the same, the change in their lengths for a given temperature change must be equal. Therefore, $\Delta l_1 = \Delta l_2 \Rightarrow l_1 \alpha_1 \Delta T = l_2 \alpha_2 \Delta T \Rightarrow \alpha_1 l_1 = \alpha_2 l_2$.

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