Problem 8: A steel rod has a length of exactly 0.2cm at 30^oC. What will be its length at 60^oC?

Solution:

Step: 1 Overview

Linear Expansion:
Every solid undergoes change when its temperature changes, so change in length of solid due to rise in temperature known as linear expansion.
Now how much a solid expands by heating depends upon two factors, first one is the original length and another one is change in temperature. If a solid has initially large length, then after heating it expands more, and also if we give more heat to a solid, it again expands more.
So equation of change in length of a solid due to change in temperature is given below:

ΔL=αLΔT

And final length of Solid after heating is given below:

L'=L(1+αΔT)

Step: 2 Calculation

Given:

T₁=30^oC
T₂=60^oC
ΔT=60-30=30^oC
α (for steel)= 1.1x10^-5L = 0.2cm

Solutions:

From above equation:
L'=L(1+αΔT)
L'=(0.2cm)(1+(1.1x10^-5)(30))
L'=(0.2cm)(1+0.00033)
L'=(0.2cm)(1.00033)
L'=0.200066cm (Ans)