A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27 °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 °C-1.
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Given: d1 = 4.24 cm, ∆T = 227 – 27 = 200 °C,
α = 1.70 × 10-5 °C-1
To find: Change in diameter (∆d)
Formula: α = \(\frac{d_2-d_1}{d_1\triangle T}=\frac{\triangle d}{d_1 \triangle T}\)
Calculation: From formula.
∆d = α x d1 x αT
= 1.70 × 10 × 4.24 × 200
∴ ∆d = 1.44 × 10-2 cm
The change in diameter of the hole is 1.44 × 10-2 cm.
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