An aluminum measuring rod, which is correct at 5^oC measures the length of a line as 80 cm at 45^oC.If thermal coefficient of linear expansion of aluminum is $2.50\times {10}^{-5}{/}^{\circ }\mathrm{C}\text{, }$ the correct length of the line is:

The 80 cm mark on the aluminum rod is really at a greater distance from the zero position than indicated because of the increase in temperature$\mathrm{\Delta \theta }={40}^{\circ }\mathrm{C}$. The increased length is

$\begin{array}{l}\mathrm{\Delta L}={\mathrm{\alpha }}_{\mathrm{A}1}{\mathrm{L}}_{\mathrm{A}1}\mathrm{\Delta \theta a}\\ =\left(2.50\times {10}^{-5}\right)\left(80\right)\left(40\right)=0.08\mathrm{cm}\end{array}$

The correct length of the line is

$\mathrm{L}=80+0.08=80.08\mathrm{cm}$