A brass cube of side 10cm is heated through 30°C. If the linear expansivity of brass is 2.0 × I0$^{-5}$ K-1 , what is the increase in its volume?

Analyze the question: A brass cube with side 10 cm is heated by 30°C. We are given the linear expansivity α = 2.0 × 10⁻⁵ K⁻¹ and must find the increase in volume.

Concept: For solids, the cubic (volume) expansivity is about three times the linear expansivity:

γ = 3α

The increase in volume is:

ΔV = γ V₀ Δθ = 3α V₀ Δθ

Solution:

1. Initial volume: V₀ = 10³ = 1000 cm³
2. Cubic expansivity: γ = 3 × 2.0 × 10⁻⁵ = 6.0 × 10⁻⁵ K⁻¹
3. Temperature change: Δθ = 30 K

ΔV = 6.0 × 10⁻⁵ × 1000 × 30 ΔV = 6.0 × 10⁻⁵ × 30000 ΔV = 1.8 cm³

Answer: The increase in volume is 1.80 cm³, which is option E.

Tip: Remember the pattern: area expansivity = 2α and volume expansivity = 3α. In exam questions like this, always compute the initial volume first, then multiply by 3α and the temperature rise. A common mistake is to use α instead of 3α, which gives 0.60 cm³ (option C), so watch out for that trap.