11.8 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.

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    Answered by

    Payal Gupta | Contributor-Level 10

    4 months ago

    11.8 Initial temperature, T1 = 27.0 °C, Initial diameter of the hole, d1 = 4.24 cm

    Final temperature, T2 = 227.0 °C, Final diameter of the hole =d2

    Coefficient of linear expansion of copper, αcopper = 1.70 ×10-5 K–1

    We know

    Changeinarea(?A)Originalarea(A) = β? T where β is the coefficient of superficial expansion, β=2αcopper

    (πd224-πd124)πd124 = 2αcopper? T

    d22-d12d12 = 2αcopper? T

    d22d12 - 1= 2αcopperT2-T= 2 × 1.70 ×10-5 (227-27) = 6.8 ×10-3

    d22=1.0068×4.24×4.24

    d2 = 4.2544 cm

    So change in diameter = 4.2544 – 4.24 = 0.01439 cm

    Diameter increase by 1.44 ×10-2 cm

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