[ \Delta L = \alpha , L_0 , \Delta T ]
✅ Compare to known values: This is likely aluminum or brass. Question: An aluminum rod (α = 2.3 × 10⁻⁵ /°C, Y = 7.0 × 10¹⁰ Pa) is 1.000 m at 20°C. It is fixed between two rigid walls. If the temperature rises to 50°C, what is the thermal stress?
ΔL = 1.504 – 1.500 = 0.004 m ΔT = 85 – 15 = 70°C α = ΔL / (L₀ ΔT) = 0.004 / (1.500 × 70) = 3.81 × 10⁻⁵ /°C linear thermal expansion problems and solutions pdf
However, many students struggle to apply the formula correctly. If you are searching for a — you are likely looking for a structured, step-by-step resource to practice and master this topic.
Introduction Linear thermal expansion is a fundamental concept in physics and engineering. It describes how solid materials change in length as their temperature changes. Understanding this principle is critical for designing bridges, railway tracks, pipelines, and even精密机械. [ \Delta L = \alpha , L_0 ,
ΔT = 60.0 – 20.0 = 40.0°C ΔL = (1.2 × 10⁻⁵)(2.000)(40.0) = 9.6 × 10⁻⁴ m = 0.00096 m Final length = 2.000 + 0.00096 = 2.00096 m
ΔT = 30°C Strain if free = α ΔT = (2.3e-5)(30) = 6.9e-4 But walls prevent expansion → compressive stress: Stress = Y × (α ΔT) = (7.0e10)(6.9e-4) = 4.83 × 10⁷ Pa If the temperature rises to 50°C, what is
✅ Key takeaway: Expansion is small but critical in precision work. Question: A metal bar is 1.500 m at 15°C and 1.504 m at 85°C. Find α.