Solved Problem on Thermal Expansion

Bandeira do Brasil  Portugu√™s    Flag of the United Kingdom  English
An iron rod, average linear coefficient of expansion \( 12 \times 10^{-6}\;^{\text{o}}\text{C}^{-1} \), has a length of 15 m at 20 ° C, if the bar is heated to 150 ° C, determine
ä) The expansion of the bar; b) The final length of the bar.

Problem data
Problem sketch

Iron bar at the temperature of 20 degrees with 15 meters of lengths and at the temperature of 150 degrees expanded of delta L.
figure 1

Solution

(a) The expansion of the bar
\[ \bbox[#99CCFF,10px] {\Delta L=\alpha L_{0}\Delta t} \]
\[ \Delta L=\alpha L_{0}(\;t_{\text{f}}-t_{\text{i}}\;)\\ \Delta L=12 \times 10^{-6} \times 15 \times(\;150-20\;)\\ \Delta L=180 \times 10^{-6} \times 130\\ \Delta L=23400 \times 10^{-6} \]
\[ \bbox[#FFCCCC,10px] {\Delta L=0.02\;\text{m}} \]

b) The final length of the bar
\[ \bbox[#99CCFF,10px] {\Delta L=L-L_{0}} \]
\[ L=L_{0}+\Delta L\\ L=15+0.02 \]
\[ \bbox[#FFCCCC,10px] {L=15.02\;\text{m}} \]


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