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  4. An aluminium measuring rod, which is correct at 5° C measures the length of a line as 80 cm at 45° C. If thermal coefficient of linear expansion of aluminium is 2.50 × 10-5 / ° C, the correct length of the line is:

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

Thermal Properties of Matter

Solution:

The $80\, cm$ mark on the aluminium rod is really at a greater distance from the zero position than indicated because of the increase in temperature $\Delta \theta=40^{\circ} C$. The increased length is
$\Delta L =\alpha_{A l} L_{A l} \Delta \theta $
$=\left(2.50 \times 10^{-5}\right)(80)(40)=0.08 \,cm$
The correct length of the line is
$L=80+0.08=80.08\, cm$