First slide

Thermal expansion

Question

Coefficient of linear expansion of brass and steel rods are ( $α_{1}$ and $α_{2}$ . Lengths of brass and steel rods are l₁ and l₂, respectively. If $(l_{2} - l_{1})$ is maintained same at all temperatures, which one of the following relations holds good? [NEET 2016]

Moderate

A

$α_{1} l_{2}^{2} = α_{2} l_{1}^{2}$
B

$α_{1}^{2} l_{2} = α_{2}^{2} l_{1}$
C

$α_{1} l_{1} = α_{2} l_{2}$
D

$α_{1} l_{2} = α_{2} l_{1}$

Solution

According to question,
Coefficient of linear expansion of brass = $α_{1}$
Coefficient of linear expansion of steel = $α_{2}$
Length of brass and steel rods are l₁ and l₂ respectively.
As the increase in length $(l'_{2} - l'_{1})$ is same for all temperatures.
So, $l'_{2} - l'_{1} = l_{2} - l_{1}$
$\Rightarrow l_{2} (1 + α_{2} Δ t) - l_{1} (1 + α_{1} Δ t) = l_{2} - l_{1} \Rightarrow l_{2} α_{2} = l_{1} α_{1}$

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