A rod is 5 m long at 10°C. At 110°C its length is 5.0167 m. What is its coefficient of linear expansion?

Correct answer: d 0.0000334 K⁻¹

α = (5.0167 − 5)/(5 × 100) = 0.0167/500 = 3.34 × 10⁻⁵ K⁻¹ = 0.0000334 K⁻¹.

Why the other options are wrong

• a 29940 K⁻¹: This is the inverse of the right value (1/3.34 × 10⁻⁵ ≈ 29940). The formula is α = (L₂ − L₁)/(L₁ΔT) and the division has been turned upside down.
• b 0.33 K⁻¹: 0.33 comes from (0.0167/5) × 100, multiplying by ΔT; the formula divides by ΔT.
• c 0.000835 K⁻¹: 0.000835 needs 20 in the denominator. But L₁ = 5 m and ΔT = 100 K, so the denominator is 500.