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# The coefficient of linear expansion of copper is $17 \times {10^{ - 6}}$ C. A copper statue is 93 m tall on the summer morning of temperature ${25^0}C$. What is the maximum order of increase in magnitude of the height in the statue (maximum temperature of day is ${45^0}C$ ).

Last updated date: 18th Jun 2024
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Hint: The expansion means, change or increase in length. If the change in length is along one dimension (length) over the volume, then it is called linear expansion. Now, we will assume that the effect of pressure is negligible, then the coefficient of linear expansion is the rate of change of unit length per unit degree change in temperature. The coefficient of linear expansion can be mathematically written as:
$\Delta l = l\alpha \Delta T$
where,
$\alpha$ is the coefficient of linear expansion.
$\Delta l$ is the unit change in length.
$\Delta T$ is the unit change in temperature.

Here, first we will use the formula $\Delta l = l\alpha \Delta T$ to calculate the change in length of the copper statue.
$\Delta l = 93 \times 17 \times {10^{ - 6}} \times (45 - 25)$
$\Delta l = 100mm$