Question

The height of the Eiffel tower is 324 m, and let's assume it's made completely of steel, which has a thermal coefficient of 1.20 × 10-5/°C.How much taller, in meters, does the Eiffel Tower become at the end of a day when the temperature has increased by 19.5A????1C?

Answer 1

To solve this problem we will apply the concept of linear thermal spacing which expresses the relationship between the change in length through the coefficient of thermal expansion, the total change in temperature and the initial length of the body. Our values are given as

Height of the Eiffel Tower, $L_0 = 324m$

Increase in temperature, $\Delta T = 19.5\°C$

Coefficient of linear thermal expansion of steel, $\alpha = 12*10^{-6} \°C^{-1}$

Replacing,

$\Delta L = L_0\alpha \Delta T$

$\Delta L = (324)(12*10^{-6})(19.5)$

$\Delta L = 0.075816m$

Therefore the Eiffel tower will become taller at the end of a day around to 0.075m

Answer 2

The Eiffel tower, with a height of 324 m, becomes 0.0758 m taller at the end of one day in which the temperature has increased by 19.5 °C.

The height of the Eiffel tower is 324 m (L₀). When the temperature has increased by 19.5 °C (ΔT), it experiences a linear thermal expansion.

Given the thermal coefficient for steel (α) is 1.20 × 10⁻⁵/°C, we can calculate the change in the height (ΔL) of the Eiffel tower using the following expression.

$\Delta L = L_o \times \alpha \times \Delta T = 324 m \times (1.20 \times 10^{-5}/\° C ) \times (19.5 \° C ) = 0.0758 m$

The Eiffel tower, with a height of 324 m, becomes 0.0758 m taller at the end of one day in which the temperature has increased by 19.5 °C.

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