Question

a piece of steel expands 10 cm when it is heated from 20 to 40 deg C. How much would it expand if it was heated from 20 to 60 deg.C?

Answer 1

20 cm

Step-by-step explanation

Given:

• The change in length of a piece of steel, ΔL = 10 cm, when its temperature change is ΔT = 20°C

Find:

• The change in length of the same piece of steel, ΔL, when its temperature is changed ΔT = 40°C

The change in length of a solid material is,

`\Delta L=\alpha\cdot L_o\cdot\Delta T`

Where L₀ is the original length, α is the linear expansion coefficient and ΔT is the change in temperature.

In this case, we know how much is the piece of steel expanded when the temperature change is 20°C, so we can find the product αL₀,

`\alpha L_o=(\Delta L)/(\Delta T)`

Replace the known values and solve,

`\alpha L_o=\frac{10\text{ }cm}{20\degree C}=0.5cm/\degree C`

If the temperature change now is 40°C,

`\Delta L=\alpha L_o\Delta T=0.5cm/\degree C\cdot40\degree C=20cm`

Hence, when the piece of steel is heated from 20°C to 60°C it will expand 20 centimeters.