Chapter 18 - Temperature, Heat, and the First Law of Thermodynamics - Problems - Page 541: 21

7.5 cm

$L_{f}=L_{0}+\Delta L= L_{0}+L_{0}\alpha \Delta T=$ $=L_{0}(1+\alpha \Delta T)$ $=3.77\,m(1+25\times10^{-6}/C^{\circ}\times32^{\circ}C)$ $=3.773\,m$ Using hypotenuse theorem, we have $x=\sqrt {(\frac{L_{f}}{2})^{2}-(\frac{L_{0}}{2})^{2}}$ $=\sqrt {(\frac{3.773\,m}{2})^{2}-(\frac{3.77\,m}{2})^{2}}= 0.075=7.5\,cm$