The Eiffel Tower in Paris stands 300.0 m tall on a day of average temperature, 22.0°C. How much taller is the steel tower on a hot summer day (T = 40°C) in centimeters? (αsteel = 11 x 10-6 °C-1)

Let's use the GRASS method to solve this problem.

Given: Original length ##(L_o)## = 300.0 m Coefficient of Linear expansion of steel ##(alpha) = 11 \times 10^{6 \circ}C^-1## Temperature change ##(Delta T) = 40-22 = 18.0 ^\circC##

Required to find: Change in length ##(Delta L)##

Analysis: The formula for figuring out this question is

##Delta L = alpha L_o Delta T##

The unknown value is already isolated, so we do not need to manipulate the formula.

Solve and Significant Figures:

##Delta L = (11 \times 10^6 ^o C^-1) (300.0 m) (18^oC)## ##Delta L = 0.0594 m##

Convert to centimeters by multiplying by 100: ##Delta L = 5.94 cm##

This means the Eiffel Tower is 5.94 cm taller on a hot day of 40 degrees than it is at 22 degrees.