A rod of length 1.000 m expands by ΔL = α L0 ΔT with α = 1.2 × 10^-5 /°C and ΔT = 30°C. What is ΔL?

• A. 0.00036 m
• B. 0.0036 m
• C. 0.000036 m
• D. 0.036 m

Answer: (A)

When a solid heats up, it expands in proportion to its length, the temperature change, and its coefficient of linear expansion. The change in length is given by ΔL = α L0 ΔT.

Plugging in the values: α = 1.2 × 10^-5 /°C, L0 = 1.000 m, ΔT = 30°C, we get ΔL = (1.2 × 10^-5) × (1.000) × (30) = 3.6 × 10^-4 m, which is 0.00036 m (about 0.36 mm).

This small expansion makes sense for typical materials under a moderate temperature rise. The other numbers would require tenfold or hundredfold changes in either α or ΔT (for example, a result of 0.0036 m would come from a tenfold larger product αΔT, 0.000036 m from a tenfold smaller product, and 0.036 m from a thousandfold larger product).