Need help on length change due to temperature change question

AI Thread Summary
The discussion centers on calculating the temperature change of the Taipei 101 building due to thermal expansion. The user attempts to apply the formula for linear thermal expansion but encounters issues with unit consistency and incorrect coefficients. They initially calculate a temperature of 73.56 degrees Celsius, which is flagged as incorrect by others in the thread. Key corrections include ensuring consistent units and using the proper coefficient of linear thermal expansion for steel. The conversation emphasizes the importance of accurate unit conversion and formula application in physics problems.
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Need help on "length change due to temperature change" question

Homework Statement



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?

Homework Equations



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

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!
 
Last edited by a moderator:
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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).
 
Last edited:


Looks like your deltaL is still in feet
 


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

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