Answer to Question #133836 in Mechanics | Relativity for Jessica

Question

The Eiffel Tower is a steel structure whose height increases by 19.0 cm when the temperature changes from -9 to +42 oC. What is the approximate height (in meters) at the lower temperature?

Answer 1

Explanation:

Given:

Change in Length:

∆L = 19cm = 0.190m

Change in temperature:

∆T = 42 - (-9) = 51°C

Coefficient of linear Thermal expansion of steel:

k = 12 × 10^-6 m/mK

Using the formula for linear expansion:

$\Delta L=Lk\Delta T$

$L= \dfrac{\Delta L}{k\Delta T}$

Substituting the given values into equation 1

$L= \dfrac{0.190}{(12 \cdot 10^{-6})(51)}$

Approximate height at the lower temperature is $L=310.45m$