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Question

# Calculate the increase in length of a zinc rod $50.0 \mathrm{~m}$ long at $15.0{\degree} \mathrm{C}$ when it is heated to $130.0{\degree} \mathrm{C}$.

Solution

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$\textbf{Given:}$

$l=50 \text{ m}$

$T_1=15 ^\circ \text{C}$

$T_2=130 ^\circ \text{C}$

$\alpha= 2.6 \times 10^{-5} \dfrac{\text{ }}{^\circ\text{C}}$

The change in the length of the material under the influence of the change in temperature is given by the formula:

$\Delta l=\alpha \cdot l \cdot \Delta T$

By including the given data in the formula we get:

\begin{align*} \Delta l&=\alpha \cdot l \cdot (T_2-T_1) \\ &=2.6 \times 10^{-5} \cdot 50 \cdot (130-15)\\ &\boxed{\Delta l=0.15 \text{ m} } \end{align*}

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