Question 1

How do you calculate linear thermal expansion?

Accepted Answer

Linear thermal expansion is calculated using ΔL = α · L₀ · ΔT, where α is the coefficient of linear thermal expansion (1/K), L₀ is the initial length, and ΔT is the temperature change. For example, a 1 m steel bar (α = 11.7×10⁻⁶ /K) heated by 100 K expands by ΔL = 11.7×10⁻⁶ × 1 × 100 = 1.17 mm. Area expansion uses 2α and volume expansion uses 3α for isotropic materials.

Question 2

What is thermal stress in a constrained member?

Accepted Answer

When a member is fully constrained from expanding, the prevented thermal strain generates a thermal stress σ = E · α · ΔT, where E is Young's modulus. For example, steel (E = 206 GPa, α = 11.7×10⁻⁶ /K) constrained over a 100 K temperature rise develops σ = 206×10⁹ × 11.7×10⁻⁶ × 100 ≈ 241 MPa compressive stress. This is critical for piping systems, bridges, railway tracks and precision machinery.

Question 3

How does a bimetallic strip deflect with temperature?

Accepted Answer

A bimetallic strip is made of two metals with different thermal expansion coefficients bonded together. When temperature changes, the difference in expansion causes the strip to curve — the material with higher α expands more and becomes the convex side. The radius of curvature is approximately ρ ≈ t / (3(α₁ − α₂)ΔT), where t is the total thickness. The tip deflection of a strip of length L is δ ≈ L² / (2ρ). Bimetallic strips are used in thermostats, circuit breakers and temperature-activated switches.

Question 4

Why is Invar used in precision instruments?

Accepted Answer

Invar (Fe-36%Ni alloy) has an exceptionally low coefficient of thermal expansion of approximately 1.2×10⁻⁶ /K — about 1/10th that of ordinary steel. This makes it ideal for precision measurement instruments, optical components, clock parts and precision molds where dimensional changes due to temperature variation cannot be tolerated. In FEA (finite element analysis), material selection between Invar and standard steel can make the difference of an order of magnitude in thermal deformation.

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