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Question
A circular hole of diameter 2.00 cm is made in an aluminium plate at 0°C. What will be the diameter at 100°C? α for aluminium = 2.3 × 10–5 °C–1.
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Solution
Given:
Diameter of a circular hole in an aluminium plate at 0°C, d1 = 2 cm = 2 × 10–2 m
Initial temperature, t1 = 0 °C
Final temperature, t2 = 100 °C
So, the change in temperature, (Δt) = 100°C - 0°C = 100°C
The linear expansion coefficient of aluminium, αal = 2.3 × 10–5 °C–1
Let the diameter of the circular hole in the plate at 100oC be d2 , which can be written as
d2 = d1(1+αΔt)
⇒ d2 =2 × 10-2(1+2.3×10-5×102)
⇒ d2 = 2×10-2(1+2.3×10-3)
⇒ d2 = 2×10-2+2.3×2×10-5
⇒ d2 = 0.02 +0.000046
⇒ d2 =0.020046 m
⇒ d2 ≈ 2.0046 cm
Therefore, the diameter of the circular hole in the aluminium plate at 100oC is 2.0046 cm.
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