At 20 ◦C, a rod is exactly 20.05 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 270 ◦C, where the rod now measures 20.11 cm on the same ruler. What is the coefficient of linear expansion for the material of which the rod is made? Take αsteel = 1.2 * 10-5 K-1.

The coefficient of expansion is

∝=1.56*10^-5/C

Explanation:

The problem is based on linear expansivity

The linear expansivity of a solid is the fractional increase in length per unit degree rise in temperature.

It is given as

∝=ΔL/ΔT

Given L1=20.5cm to m = 20.5/100

=0.205m

L2=20.11cm to m = 20.11/100

= 0.2011nlm

T1=20°c

T2=270°c

∝=0.2011-0.205/270-20

∝=0.0039/250

∝=0.0000156

∝=1.56*10^-5/C