The temperature of a metal strip having coefficient of linear expansion is increased from to resulting in increase of its length by

Question

The temperature of a metal strip having coefficient of linear expansion $α$ is increased from $T_{1}$ to $T_{2}$ resulting in increase of its length by $Δ L_{1}$ . The temperature is further increased from $T_{2}$ to $T_{3}$ such that the increase in its length is $Δ L_{2}$ .

Given $T_{3} + T_{1} = 2 T_{2}$ and $T_{2} - T_{1} = Δ T$ , the value of $Δ L_{2}$ is ______. [2026]

Smart Achievers · Accepted Answer

(4)

$Δ L_{1} = α L_{1} Δ T$

$Δ L_{2} = (L_{1} + Δ L_{1}) (T_{3} - T_{2})$

$Δ L_{2} = (L_{1} + Δ L_{1}) Δ T$

$Δ L_{2} = (\frac{Δ L_{1}}{α Δ T} + Δ L_{1}) α Δ T$

$Δ L_{2} = Δ L_{1} [1 + α Δ T]$

Solution

1 $Δ L_{1} [1 + 2 α^{2} {(Δ T)}^{2}]$

2 $Δ L_{1} [1 + α^{2} {(Δ T)}^{2}]$

3 $Δ L_{1} [1 + 2 α Δ T]$

4 $Δ L_{1} [1 + α Δ T]$

Ans.
(4)

$Δ L_{1} = α L_{1} Δ T$

$Δ L_{2} = (L_{1} + Δ L_{1}) (T_{3} - T_{2})$

$Δ L_{2} = (L_{1} + Δ L_{1}) Δ T$

$Δ L_{2} = (\frac{Δ L_{1}}{α Δ T} + Δ L_{1}) α Δ T$

$Δ L_{2} = Δ L_{1} [1 + α Δ T]$

Want Us to Email you About Special Offers & Updates?

Solution

1 ΔL1[1+2α2(ΔT)2]

2 ΔL1[1+α2(ΔT)2]

3 ΔL1[1+2αΔT]

4 ΔL1[1+αΔT]