Question

At 17°C, a rod is exactly 20.10 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 261°C, where the rod now measures 20.21 cm on the same ruler. What is the coefficient of linear expansion for the material of which the rod is made?

Answer 1

Given

   rod

initial

   T1 = 17 0C, l1 = 20.10 cm = 0.2010 m
final
   T2 = 261 0C, l2 = 20.21 cm = 0.2021 m

change in length is Dl = l2-l1 =0.2021 - 0.2010 = 0.0011 m

change in temperature is DT = T2-T1 = 261-17 = 244 0C

now the linear thermal expansion is Dl = l1*alpha(DT)

   now the coefficient of linear expansion alpha = Dl/(l1*DT)

   alpha = 0.0011/(0.2010*244)
   alpha = 2.24288394*10^-5 / 0C

the coefficient of linear expansion for the material of which the rod is made alpha = 2.24288394*10^-5 / 0C