Question

What is the coefficient of linear expansion of a rod if its found to be 100m long
at 20 e and 100. 14 m long
at 100°c ?​

Answer 1

Given

Length of a rod = l = 100 m (at T = 20° C)

Length at $T_{o}$ = 100°C = 100.14 m

To Find

Coefficient of linear expansion of the rod.

Formula

$\boxed{\Delta l\:=\:l \alpha \Delta T }$

Calculations

Here,∆l = 100.14 - 100 = 0.14 m.

∆T = 100 - 80 = 20 m.

Using the formula

∆l = l × $\alpha$ × ∆T

=> 0.14 = 100 × $\alpha$ × 80

=> $\alpha \:=\: \dfrac{0.14}{8000}$

=> $\alpha \:=\: 1.75\times 10^{-5}$

Answer 2

Given

Length of a rod = l =

$100 m (at T = 20° C)$

Length at T_{o}T

o

$= 100°C = 100.14 m$

To Find

Coefficient of linear expansion of the rod.

Formula

$\boxed{\Delta l\:=\:l \alpha \Delta T } </p><p>$

Calculations

Here

$,∆l = 100.14 - 100 = 0.14 m.$

$∆T = 100 - 80 = 20 m.$

Using the formula

$∆l = l × \alphaα × ∆T \\ </p><p></p><p>=> 0.14 = 100 × \alphaα × 80</p><p>$

$=> \alpha \:=\: \dfrac{0.14}{8000}</p><p>$

$=> \alpha \:=\: 1.75\times 10^{-5}$