Question

A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C? Coefficient of linear expansion of copper = 1.70 × 10^–5 K^–1.

Answer 1

Initial temperature, T₁ = 27.0°C

Diameter of the hole at T₁, d₁ = 4.24 cm

Final temperature, T₂ = 227°C

Diameter of the hole at T₂ = d₂

Co-efficient of linear expansion of copper, α_Cu= 1.70 × 10^–5 K^–1

For co-efficient of superficial expansion β,and change in temperature ΔT, we have the relation:

Change in diameter = d₂ – d₁ = 4.2544 – 4.24 = 0.0144 cm

Hence, the diameter increases by 1.44 × 10^–2 cm.