Question

A piece of steel is 11.5cm long at 22C. It is heated to 1221C, close to its melting point. How long is it, in cm, at the high temperature?

Answer 1

The length at the final temperature is 11.7 cm.

Step-by-step explanation:

We need to use the thermal expansion equation:

`\Delta L=\alpha L_(0)\Delta T`

Where:

• L(0) is the initial length
• ΔT is the differential temperature, final temperature minus initial temperature (T(f)-T(0))
• ΔL is the final length minus the initial length (L(f)-L(0))
• α is the coefficient of linear expantion of steel (12.5*10⁻⁶ 1/°C)

So, we have:

`L_(f)-L_(0)=\alpha L_(0)(T_(f)-T_(0))`

`L_(f)=L_(0)+\alpha L_(0)(T_(f)-T_(0))`

`L_(f)=0.115+(12.5*10^(-6))(0.115)(1221-22)`

`L_(f)=0.117\: m`

Therefore, the length at the final temperature is 11.7 cm.

I hope it helps you!