Question

The coefficient of linear expansion of iron is 1.0 x 10-5 per oC. The surface area of an. iron cube, with an edge length of 5.0 cm, will increase by what amount if it is heated. from 10 oC to 60 oC?

Answer 1

Er:  Heating increases the volume of a body … formula for change in volume … 
… ΔV = 3 α V₀ ΔT … V₀ = ( 5.0 cm ) ³ = 125cm ³ … α = 1.0 × 10 ⁻⁵ °C ⁻¹ … 
… ΔT = T ‒ T₀ = ( 60-10) °C = 50 °C … it follows that … 
… ΔV = 3 α V₀ ΔT = 3 (1.0 × 10 ⁻⁵ °C ⁻¹ ) (125 ) ( 50 °C ) = 0.1875 cm ³ 
… final volume V = V₀ + ΔV = 125 cm ³ + 0.1875cm ³ = 125.1875cm ³ 
… V = L ³ … --> … L = ∛ V = ∛ [ 125.1875 cm ³ ] = 5.0024
… A = L ² = (5.0024 cm ) ² =25.024 cm ² … 
… A₀ = L₀ ² = ( 5.0 cm ) ² =  25cm ² … 
… ΔA = A ‒ A₀ =  25.024cm -25.cm ² =  …0.024 
The area of the iron cube increases by0.024   cm ².