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  • A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 degree C?

Q. 11.8 A hole is drilled in a copper sheet. The diameter of the hole is 4.24\; cm at 27.0^{\circ}C. What is the change in the diameter of the hole when the sheet is heated to 227^{\circ}C\; ? Coefficient of linear expansion of copper =1.70\times 10^{-5}K^{-1}.

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Coefficient of linear expansion of copper \alpha=1.70\times 10^{-5}K^{-1}.

Coefficient of superficial expansion of copper is \beta

\\\beta =2\alpha \\ \beta =2\times 1.7\times 10^{-5}\\ \beta =3.4\times 10^{-5}K^{-1}

Diameter of the hole at 27 oC (d1) = 4.24 cm 

Area of the hole at 227 oC is

\\A_{2}=A_{1}(1+\beta \Delta T)\\ A_{2}=\pi \left ( \frac{4.24}{2} \right )^{2}(1+3.4\times 10^{-5}(227-27))\\ A_{2}=14.215\ cm^{2}

Let the diameter at 227 oC be d2

\\\pi \left ( \frac{d_{2}}{4} \right )^{2}=14.215\\ d_{2}=4.254cm

Change in diameter is d2 -d1 = 4.24 -4.254 = 0.014 cm.

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