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.
Initial temperature, T1=27.0oC Diameter of the hole at T1,d1=4.24cm Final temperature, T2=227oC Diameter of the hole at T2=D2 Co-efficient of linear expansion of copper, αCu=1.70×10−5K−1 For co-efficient of superficial expansion β,and change in temperature △T, we have the relation: Change in area (△) / Original area (A) = β△T [(πd22/4)−(πd22/4)]/(πd11/4)=△A/A ∴△A/A=(d22−d12)/d12 But β=2α ∴(d22−d12)/d12=2α△T (d22/d12)−1=2α(T2−T1) d22/4.242=2×1.7×10−5(227−27)+1 d22=17.98×1.0068=18.1 ∴d2=4.2544cm Change in diameter =d2−d1=4.2544−4.24=0.0144cm Hence, the diameter increases by 1.44×10−2cm
