Question

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 is 1.70 x 10${}^{-5}$

• A. $1.44\times {10}^{-2}$ cm
• B. $2.44\times {10}^{-3}$ cm
• C. $1.44\times {10}^{-2}$mm
• D. $2.44\times {10}^{-3}$ mm

Answer 1

The correct option is A $1.44\times {10}^{-2}$ cm

$D_2=4.24cm$

Initial Area of the hole $\left(A_0\right)=\pi r^2=22/7(4.24/2{)}^2=4.494\pi c{m}^2$

Initial temp. $\left(T_1\right)=27°=27+273=300K$

Final temp. $\left(T_2\right)=227°=227+273=500K$

Coefficientof linear exp. $\left(O\right)=1.7\times {10}^{-5}/°C$

Superficial expansion $\left(b\right)=2\times$ Linear expansion

$=2\times 1.7\times {10}^{-5}°C=3.4\times {10}^{-5}°C$

Use formula

$A=A_0(1+b\Delta T)A=4.49\pi [1+3.4\times {10}^{-5}\times (500-300\left)\right]A=4.494\pi [1+0.0068]A=4.525c{m}^2=\pi D{2}^2/$\\B2^2=4.523\times4\\ D2=4.2544cm$

Change in diameter $=\Delta D=D_2-D_1=4.2544-4.24=0.0144cm$