Question

The coefficient of linear expansion of iron is 1.0 × 10−5 per C◦ . 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◦ C to 60◦ C?

Answer 1

The linear expansion of iron is a = 1× 10∧ -5 /°C
Length edge is 5cm
Initial surface area of cube A = 6L ∧²
 = 150cm∧²
The edge length of cube after being heated from 
10°C to 60°C is
L = L[I +a dt] where the dt is = 60-10 = 50°C
5.0025cm
A surface area of the cube after heated is 
A' = 6L' ∧²
= 150.1500375 cm∧²
The increased area is = A' -A = 0.15cm∧²

Answer 2

Based on the linear expansion of iron, the increase in area is 0.15cm²

What is linear expansivity?

Linear expansivity is the increase in length per unit length of a material for every degree rise in temperature.

The linear expansion of iron is α = 1 × 10⁻⁵/°C

Length edge of the iron cube is 5cm

the surface area of cube A = 6L²

Initial surface area = 6 * 5² = 150cm²

The edge length of cube, L₂ after being heated from

10°C to 60°C is calculated using the formula below:

• L₂ = L[I + α*dt]

where

• α is the linear expansion of iron
• dt is the temperature difference

dt = 60-10 = 50°C

L₂ = 5(1 + 1 × 10⁻⁵ * 50)

5.0025cm

The surface area of the cube after heated A' is

A' = 6 * 5.0025²

A' = 150.1500375 cm²

The increased area,  A' -A = (150 -  150.1500375) cm²

The increase in area is 0.15cm²

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