Question

A metal cube has edges of length a=10 cm, at a temperature of 0°C. When heated to 100°C, the volume of the cube is 1005.1 cm³. Determine the coefficient of linear expansion of the metal.​

Answer 1

Step-by-step explanation:

Given:

a = 10 cm

t₀ = 0°C

t = 100°C

V = 1005.1 cm³

____________

α - ?

V₀ = a³ = 10³ = 1000 cm³

Δt = t - t₀ = 100 - 0 = 100°C

ΔT = Δt = 100 K

V = V₀·(1 + γ·ΔT)

1 + γ·ΔT = V / V₀

γ·ΔT = V / V₀ - 1

γ = ( V / V₀ - 1 ) / ΔT

The coefficient of volumetric expansion of the metal.​

γ = ( 1000.5/1000 - 1 ) / 100 = 5·10⁻⁶ K⁻¹

The coefficient of linear expansion of the metal

α = γ / 3 = 5·10⁻⁶/3 K⁻¹ ≈ 1.67·10⁻⁶ K⁻¹

Answer 2

SolutionVerified by TopprCorrect option is D) Here percentage change in volume is given as, ΔV=γ×t×100where, γ=3αSo, ΔV=3α×(T1​−T2​)×100ΔV=3×2×10−5×(473−273)×100=1.2

Step-by-step explanation: