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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?

Respuesta :

whitneytr12

Answer:

The length at the final temperature is 11.7 cm.

Explanation:

We need to use the thermal expansion equation:

[tex]\Delta L=\alpha L_{0}\Delta T[/tex]

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:

[tex]L_{f}-L_{0}=\alpha L_{0}(T_{f}-T_{0})[/tex]

[tex]L_{f}=L_{0}+\alpha L_{0}(T_{f}-T_{0})[/tex]

[tex]L_{f}=0.115+(12.5*10^{-6})(0.115)(1221-22)[/tex]

[tex]L_{f}=0.117\: m[/tex]

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

I hope it helps you!

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