Question

The length of a steel beam increases by 0.75 mm when its temperature is raised from 22∘C to 35∘C. What is the length of the beam at 22∘C? Please help me out with explanation. Trying to learn as much as I can!

Answer 1

The change in the linear dimension can be estimated to be:

\(\frac{\Delta L}{L}=\alpha_{L} \Delta T\)

where alpha is linear-expansion coefficient \(=12^{*} 10^{\wedge}-6\) for steel, \(\mathrm{dL}\) OR delta \(\mathrm{L}\) is change in length, \(\mathrm{dT} \mathrm{OR}\) delta \(\mathrm{T}\) is change in temp, \(\mathrm{L}\) is original length at initial temp

\(=>0.75=L^{*} 12^{*} 10^{\wedge}-6^{*}(35-22)\)

\(\Rightarrow \mathrm{L}=4807.69 \mathrm{~mm}\) OR \(4.8 \mathrm{~m}\)