The linear expansivity of brass is 2 x 10$^{-5}$  $^oC^{-1}$. If the volume of piece of brass is 10cm$^3$ at 0$^o$C. What will be its volume at 100$^o$C?

Analyze the question: We're given the linear expansivity (α) of brass and need the new volume. So we must convert α to the cubical (volume) expansivity first.

Concept:

• Cubical expansivity γ ≈ 3α
• Volume at temperature θ: V₂ = V₁(1 + γΔθ)

Solution:

1. α = 2 × 10⁻⁵ °C⁻¹, so γ = 3α = 6 × 10⁻⁵ °C⁻¹
2. ΔV = V₁γΔθ = 10 × 6 × 10⁻⁵ × 100 = 0.06 cm³
3. V₂ = 10 + 0.06 = 10.06 cm³

Tip: If a question gives the linear expansivity but asks about area or volume, remember the factors: area β = 2α, volume γ = 3α. The most common mistake is using α directly. That would give 10.02 cm³ (option C), which is a trap.