Some iron has a coefficient of linear expansion of 12 x 10-6 K-1. A 100mm length of iron piping is heated through 20 K. The pipe extends by:

Question

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We start by identifying the formula for linear thermal expansion: ΔL = α × L0 × ΔT, where α is the coefficient of linear expansion, L0 is the original length, and ΔT is the temperature change.

Option 1: 2.4 mm. If we test this value, we would need ΔL = 2.4 mm. Using the given α = 12 × 10^-6 K^-1 and L0 = 100 mm with ΔT = 20 K, the computed ΔL is ΔL = (12 × 10^-6) × 100 × 20 = 12 × 10^-6 × 2000 = 24 × 10^-3 = 0.024 mm. This is far from 2.4 mm, so this option is too large by a factor of 100.

Option 2: 0.0024 mm. Here ΔL would be 0.0024 mm. Comparing with the calculation ΔL = 0.024 mm, this value is smaller by a factor of 10, indicating a misplacement of a decimal point in the computation or a misunderstanding of units. It does not match the expected result from the standard formula.

Option 3: 0.24 mm. This option suggests a tenfold increase over the correct calculation. If ΔL were 0.24 mm, the implied computation would be ΔL = 0.24 mm, which equals 0.24 mm / (12 × 10^-6 × 100 × 20) ≈ 1000,000 times larger than the actual factor, so this is inconsistent with the given values.

Option 4: 0.024 mm. This aligns with the core calculation: ΔL = α × L0 × ΔT = (12 × 10^-6) × (100) × (20) = 12 × 10^-6 × 2000 = 24 × 10^-3 = 0.024 mm. The units are consistent (mm), and the arithmetic matches the standard expansion formula using the provided coefficient, length, and temperature change.

In this kind of problem, the key is to keep track of units and multiply the three factors together in the correct order. Mistakes typically come from misplacing decimal points or confusing the scale of α. By plugging in the numbers step by step, you can verify whether a proposed option follows from the formula ΔL = α L0 ΔT and the given data.

SPHY001 Practice Quiz - Unit 13 | LA053

Some iron has a coefficient of linear expansion of 12 x 10-6 K-1. A 100mm length of iron piping is heated through 20 K. The pipe extends by:

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