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A hole is drilled in a copper sheet. The diameter of the hole is 4.24cm at 27°C. What is the change in the diameter of the hole when the steel is heated at 227°C ? (Coefficient of linear expansion of copper=1.70×10^-5 /°C)

A hole is drilled in a copper sheet. The diameter of the hole is 4.24cm at 27°C. What is the change in the diameter of the hole when the steel is heated at 227°C ? (Coefficient of linear expansion of copper=1.70×10^-5 /°C)

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear Preeti
 
 
Initial temperature, T1 = 27.0°C
Diameter of the hole at T1d1 = 4.24 cm
Final temperature, T2 = 227°C
Diameter of the hole at Td2
Co-efficient of linear expansion of copper, αCu= 1.70 × 10–5 K–1
For co-efficient of superficial expansion β,and change in temperature ΔT, we have the relation:
Change in area (∆)  /  Original area (A)  =  βT
[ (πd22/ 4) – (πd12 / 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 = 4.2544 cm
Change in diameter = d2 – d= 4.2544 – 4.24 = 0.0144 cm
Hence, the diameter increases by 1.44 × 10–2cm.
 
 
 
 
Regards
Arun (askIITians forum expert)

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