Need help on "length change due to temperature change" question

supernovaes

1. The problem statement, all variables and given/known data

The tallest building in the world, according to some architectural standards, is the Taipei 101 in Taiwan, at a height of 1671 feet. Assume that this height was measured on a cool spring day when the temperature was 16.5 . You could use the building as a sort of giant thermometer on a hot summer day by carefully measuring its height. Suppose you do this and discover that the Taipei 101 is 0.465 foot taller than its official height.

What is the temperature, assuming that the building is in thermal equilibrium with the air and that its entire frame is made of steel?


2. Relevant equations

delta L = alpha*(L_0)*delta T (linear thermal expansion)
alpha = coefficient of linear expansion.

3. The attempt at a solution

I converted ft to meter and I looked around for the coefficient of expansion for steel and it was 0.000016 meters per degree Celsius.

(0.465/(0.000016*509.321))+16.5 = T_final
i got 73.56 and it was wrong, can anyone help? thanks!

Chestermiller

The lengths you are using are not in consistent units. Either use ft or meters, but not both. Also, your stated units of the CLTE are not correct. They should be m/(mC), or, equivalently, ft/(ftC).

nlsherrill

Looks like your deltaL is still in feet

SteamKing

Not to mention the temperature of your summer's day was a balmy 73.6 C, which is rather warm (165 F).