Question

At 23°C, a rod is exactly 20.06 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 240°C, where the rod now measures 20.24 cm on the same ruler. What is the coefficient of linear expansion for the material of which the rod is made?

___ (°C)⁻¹

Answer 1

here,

the coefficient of linear expansion of steel , alpha1 = 12 * 10^-6 per degree C

let the actual expanded length of rod be L

for ruler

L = L0 * ( 1 + alpha1 * dT)

L = 20.24 * ( 1 + 1.2 * 10^-6 * (240 - 23))

solving for L

L = 20.2453 cm

let the coefficient of linear expansion for the material of which the rod is made be alpha2

for rod

L = L0 * ( 1 + alpha2 * dT)

20.2453 = 20.06 * ( 1 + alpha2 * (240 - 23))

alpha2 = 4.26 * 10^-5 per degree C

the coefficient of linear expansion for the material of which the rod is made is 4.26 * 10^-5 per degree C