Question

a cube of side 10cm is heated from 27 c to 227 c the change in its total surface area if coefficient of linear expansion is 2*10^-6 per c
(c is Celsius)

Answer 1

Answer:

4.8 × 10⁻⁵ m²

Explanation:

To find------> Change in total surface area of cube

Solution------> ATQ,

Side of cube = 10 Cm

= 10 × 10⁻² m

= 10⁻¹ m

Change in temperature = 227° - 27°

= 200° C

Coefficient of linear expansion = 2 × 10⁻⁶ / °c

We know that ,

Coefficient of superficial expansion

= 2 × Coefficient of linear expansion

=> β = 2 α

=> β = 2 × ( 2 × 10⁻⁶ )

=> β = 4 × 10⁻⁶ / °c

Initial surface area = 6 ( side )²

= 6 ( 10⁻¹ )²

= 6 × 10⁻² m²

We know that ,

β = Δ A / ( A × Δ T )

Where , ΔA = Change in surface area

A = Initial surface area

Δ Τ = Change in temperature

4 × 10⁻⁶ = Δ A / 6 × 10⁻² × 200

=> 4 × 10⁻⁶ × 6 × 10⁻² × 200 = Δ A

=> 4800 × 10⁻⁸ = Δ Α

=> Δ A = 4800 × 10⁻⁸

=> Δ Α = 4.8 × 10⁻⁵ m²