A hole is drilled in a copper sheet. The diameter of the hole is 4 cm at 27.0°C. Coefficient of linear expansion of copper is 1.70 x 10 – 5 K – 1. Diameter of the hole when the sheet is heated to 227°C

Engineering

Physics

Thermal Expansion

Question

A hole is drilled in a copper sheet. The diameter of the hole is 4 cm at 27.0°C. Coefficient of linear expansion of copper is 1.70 x 10^{– 5} K^{– 1}. Diameter of the hole when the sheet is heated to 227°C

increases by 0.136 cm

decreases by 0.136 cm

decreases by 0.136 mm

increases by 0.136 mm

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Diameter of hole changes following linear expansion of copper
D' = D(1 + αΔT)
ΔD = D' – D = DαΔT = 4 x 1.7 x 10^{– 5} x (200) (cm)
= 13.6 x 10^{– 3} (cm)
= 0.136 mm