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)

1 Answer

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

Original length #(L_o)# = 300.0 m
Coefficient of Linear expansion of steel #(alpha) = 11 x 10^6 ^oC^-1#
Temperature change #(Delta T) = 40-22 = 18.0 ^oC#

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 x 10^6 ^oC^-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.