Question

At 22°C, a rod is exactly 24.49 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 230°C, where the rod now measures 24.60 cm on the same ruler. What is the coefficient of thermal expansion for the material of which the rod is made? The linear expansion coefficient of steel is 11 x 10^-6 1/C°.

Answer 1

given

initial temp of rod = 22 C

initial length of rod Li = 24.49 cm

final length of rod = Lf = 24.60 cm

initial length of steel ruler Ls = 24.49 cm

final temp = 230C

s = 11 x10^-6 / C

for steel

s = Ls / Ls x T

11 x10^-6 =  Ls / 24.49 x(230-22)

Ls = 0.056 cm

now for rod

the change in length of rod will be = L = ( 24.60 - 24.49 ) + Ls

  L = ( 24.60 - 24.49 ) + 0.056

L = 0.166 cm'

so now

r = L / Li x T

r = 0.166 / 24.49 x (230-22)

r = 3.25 x 10^-5 /C