WAEC 2016 Physics · Question 35

An aluminium rod of length 1.8m at 10°C is heated to proceed produce a difference in length of 0.007m…

Question

An aluminium rod of length 1.8m at 10°C is heated to proceed produce a difference in length of 0.007m. Calculate the temperature to which it is heated. (Linear expansivity of aluminium = 2.3 x 10 $^{-5}$ K $^{-1}$

A.155oC
B.160oC
C.169oC
D.179oC

Answer: D. 179oC

Explanation written with AI and checked against the answer key

Analyze the question: A rod of length 1.8 m at 10°C expands by 0.007 m. We need the final temperature, using the linear expansivity α = 2.3 × 10⁻⁵ K⁻¹. Concept: Linear expansion is given by ΔL = L₀ α Δθ so Δθ = ΔL / (L₀ α) Solution: Δθ = 0.007 / (1.8 × 2.3 × 10⁻⁵) Denominator: 1.8 × 2.3 × 10⁻⁵ = 4.14 × 10⁻⁵ Δθ = 0.007 / 4.14 × 10⁻⁵ = 7 × 10⁻³ / 4.14 × 10⁻⁵ ≈ 169.08 K Final temperature = 10 + 169.08 ≈ 179°C Check: 169 is the rise in temperature, not the final temperature. Option C (169°C) is the trap for students who forget to add the starting 10°C. The question asks for the temperature to which the rod is heated, so we add the initial temperature. Answer: D. 179°C. Tip: When a question asks "the temperature to which it is heated", always compute Δθ first and then add the initial temperature. Check whether the question asks for the change or the final value.

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