First we have to dig up the equation we are going to use:
is the change in length
is the coefficient for linear expansion
is the length of the material
is the change is temperature
Now we know
and the length (height) of the structure in question (Willamette Hall).
To be able to use this equation we have to change the temperatures to either Celsius or Kelvin to find the temperature difference (remember that when using a change in temperature, one Kelvin is equal to one degree Celsius).
You could either change both the temperatures to Celsius and then find the change in temperature from those two temps, but there is a trick you can use to shorten the math a bit. The temperature change is
. If comparing just temperature change, we know that one degree Celsius is equal to 9/5 of a degree Fahrenheit, so we can just multiply the 68 times 5/9 to get 37.8 degrees Celsius.
Let's see the Math of this little trick:
(subscipts 1 and 2 refer to the low and high temps respectively, and the C and F are celsius and fahrenheit)
So we know that the change in temperature is (37.8K).
Now we plug in the values we know to find the change in length.