Need help on length change due to temperature change question

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Homework Help Overview

The discussion revolves around a problem involving thermal expansion, specifically calculating the change in length of a building due to temperature changes. The context is set with the Taipei 101 building and its height measurement under varying temperatures.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply the linear thermal expansion formula but encounters issues with unit consistency and incorrect values for coefficients. Some participants question the units used and suggest ensuring consistency in measurements.

Discussion Status

Participants are actively engaging in clarifying the original poster's approach, pointing out potential errors in unit conversion and the coefficient of linear thermal expansion. There is a focus on correcting assumptions rather than reaching a consensus on the solution.

Contextual Notes

There are indications of confusion regarding the units of measurement and the coefficient of linear thermal expansion, which are critical to solving the problem accurately. The original poster's temperature conversion also appears to be under scrutiny.

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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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