Engineering & design · Grades 9–12
Linear thermal expansion
Assume a constant expansion coefficient and small strain over the temperature range.
Method and conditions
Assume a constant expansion coefficient and small strain over the temperature range.
ΔL = αL₀ΔT
Worked examples
A rod has L₀=10 m and α=3×10⁻⁶ K⁻¹. For temperature rise 29 K, find length increase in mm. Round the final result to 4 decimal places if needed. Answer in mm.
Use ΔL=(3×10⁻⁶)(10)(29) m, then convert metres to millimetres.
0.87 mm
A rod has L₀=4 m and α=9×10⁻⁶ K⁻¹. For temperature rise 52 K, find length increase in mm. Round the final result to 4 decimal places if needed. Answer in mm.
Use ΔL=(9×10⁻⁶)(4)(52) m, then convert metres to millimetres.
1.872 mm
Try it
A rod has L₀=6 m and α=3×10⁻⁶ K⁻¹. For temperature rise 53 K, find length increase in mm. Round the final result to 4 decimal places if needed. Answer in mm.
A rod has L₀=3 m and α=2×10⁻⁶ K⁻¹. For temperature rise 33 K, find length increase in mm. Round the final result to 4 decimal places if needed. Answer in mm.
Check your work
Answers and marking notes
- 0.954 mm
Use ΔL=(3×10⁻⁶)(6)(53) m, then convert metres to millimetres.
- 0.198 mm
Use ΔL=(2×10⁻⁶)(3)(33) m, then convert metres to millimetres.
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