A metal rod of length 2.0 m has a linear expansivity of 1.2 × 10⁻⁵ K⁻¹. Compute its expansion in mm when heated by 50 K, to one decimal place.

Physics II / The Zeroth Law and Thermodynamic Coefficients

Practice question · Numerical answer

A metal rod of length 2.0 m has a linear expansivity of $1.2 \times 10^{-5}$ K $^{-1}$ . Compute its expansion in mm when heated by 50 K, to one decimal place.

Hints

Expansion is the original length times the expansivity times the temperature rise.
Compute 2.0 x 1.2e-5 x 50, then convert metres to millimetres.

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1.2 (answers within ±0.05 count)

Why

$\Delta L = L\alpha\Delta T = 2.0 \times 1.2\times10^{-5} \times 50 = 1.2 \times 10^{-3}$ m $= 1.2$ mm. Small, but bridges and rails are built with expansion joints for exactly this.

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A metal rod of length 2.0 m has a linear expansivity of 1.2×10−51.2 \times 10^{-5}1.2×10−5 K−1^{-1}−1. Compute its expansion in mm when heated by 50 K, to one decimal place.

Practise The Zeroth Law and Thermodynamic Coefficients

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A metal rod of length 2.0 m has a linear expansivity of $1.2 \times 10^{-5}$ K $^{-1}$ . Compute its expansion in mm when heated by 50 K, to one decimal place.