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

Answer:

The length at the final temperature is 11.7 cm.

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!