THE PRACTICE STUDIO
Go slowly. Ask why. Make it yours.
PRACTICE / Thermal expansion
Count the three directional changes
A free rectangular anisotropic solid has linear expansion coefficients 10, 20 and −5 in units of 10⁻⁶ K⁻¹ along its three perpendicular edges. It warms uniformly by 100 K with no mass loss.
What is its first-order fractional volume increase?
Organize the givens & assumptions
- αx = 10 × 10⁻⁶ K⁻¹
- αy = 20 × 10⁻⁶ K⁻¹
- αz = −5 × 10⁻⁶ K⁻¹
- ΔT = 100 K
Uniform temperatures and the stated expansion coefficients; small thermal strains and first-order expansion unless a retained ratio is explicitly requested. Free expansion except for the named axial constraints. Constrained rods remain straight and linearly elastic; no buckling, yielding or moving supports.
- A
- B
- C
- D
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