Question

At 22°C, a rod is exactly 23.45 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 23.70 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

Thermal length expansion: ∆L = αLo∆T
∆L = (11×10^-6)*23.45*(240-22) = 0.05623 cm
New length of ruler at the 23.45 mark: 23.45 + 0.05623 = 23.51 cm

After the expansion, the actual length is 23.51 cm, but the scale
still reads 23.45 cm there. "One cm" on the ruler after the expansion
corresponds to: 23.51/23.45 = 1.0026 cm

So when the rod reads 23.7 cm, it's actual length is 23.7*1.0026 = 23.76 cm
That means it has expanded by 23.76 - 23.45 = 0.31 cm

α = ∆L/Lo∆T = 0.31 / 23.45*(240-22) = 6.064×10^-5 /C°