Question

37. A hole is drilled in a steel sheet. The diameter of the hole is 4.24 cm at 27.0 degree
celcius. What is the change in the diameter of the hole when the sheet is heated to 227
degree celcius? The coefficient of linear expansion of steel is 1.20x10-5/C.
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Answer 1

Answer:

0.0144 cm

Explanation:

Here, diameter of hole ( D1) = 4.24 cm

So, initial area of hole (Ao)= πr² = 22/7 ( 4.24/2)²

= 4.494π cm²

intial temperature ( T1) = 27°C = 27+ 273 = 300 K

Final temperature ( T2) = 227°C = 227+ 273 = 500K

coefficient of linear expansion (a) = 1.7 × 10^-5/°C

coefficient of superficial expansion (b) = 2× linear expansion

= 2 × 1.7 × 10^-5/°C

= 3.4 × 10^-5 /°C

Use formula,

A = Ao( 1 + b∆T)

A = 4.494π [1 + 3.4 × 10^-5 × (500-300)]

= 4.494π[ 1 + 3.4 × 10^-5 × 200]

= 4.494π [ 1 + 6.8 × 10^-3 ]

= 4.494π [ 1 + 0.0068]

= 4.494π × 1.00068

= 4.525π cm² = πD2²/4

D2² = 4.525 × 4

D2 = 4.2544 cm

Change in diameter (∆D) = D2 - D1

= 4.2544 - 4.24

= 0.0144 cm

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