Answer to Question #161733 in Chemistry for Mazini Casbeth

Question

The Eiffel tower is a steel structure whose height increases by 19.4 cm when the temperature changes from -9 to +42°c. What is the approximate height in meters at the lower temperature?

Answer 1

The dependence of thermal expansion on temperature, substance, and length is summarized in the equation:

ΔL = αLΔT

where ΔL is the change in length L (19.4 cm = 0.194 m), ΔT is the change in temperature, and α is the coefficient of linear expansion (for steel, α = 12 × 10^{– 6} 1/ºC).

From here:

L = ΔL / αΔT = 0.194 m / (12 × 10^{– 6} 1/ºC × [+42°C - (-9 °C) ] ) = 317 m

Answer: 317 m