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.

Answer 1

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, α_al​ = 2.3 × 10^–5 °C^–1 
Let the diameter of the circular hole in the plate at 100^oC 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 100^oC is ​2.0046 cm.