Solved Problem in Thermal Expansion
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An iron rod, average linear coefficient of expansion 12 × 10−6 °C−1, has a length of 15 m at 20 °C if the bar is heated to 150 °C find:
ä) The expansion of the bar;
b) The final length of the bar.

Problem data
• coefficient of linear expansion of iron:     α = 12 × 10−6 °C−1;
• initial length of the bar:     L0 = 15 m;
• initial bar temperature:     ti = 20 °C;
• final bar temperature:     tf = 150 °C.
Problem diagram

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
$\bbox[#99CCFF,10px] {\Delta L=L-L_{0}}$
$L=L_{0}+\Delta L\\ L=15+0.02$
$\bbox[#FFCCCC,10px] {L=15.02\;\text{m}}$