Need help on length change due to temperature change question

In summary, the conversation discusses the concept of length change due to temperature change, specifically in the context of the tallest building in the world, Taipei 101 in Taiwan. The problem involves using the building as a "giant thermometer" to measure the temperature on a hot summer day and calculating the temperature based on its measured height. The equation for linear thermal expansion is mentioned, along with the coefficient of expansion for steel. However, the solution provided by the person asking for help is incorrect due to inconsistent units and an incorrect value for the temperature.
  • #1
supernovaes
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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!
 
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  • #2


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).
 
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  • #3


Looks like your deltaL is still in feet
 
  • #4


Not to mention the temperature of your summer's day was a balmy 73.6 C, which is rather warm (165 F).
 
  • #5
please help...from which book is this problem
 

1. How does temperature affect the length of an object?

Temperature affects the length of an object through thermal expansion or contraction. When an object is heated, its molecules vibrate faster and take up more space, causing the object to expand. When an object is cooled, the molecules slow down and the object contracts.

2. What is the coefficient of thermal expansion?

The coefficient of thermal expansion is a measure of how much a material expands or contracts with a change in temperature. It is expressed as a fractional change in length or volume per unit temperature change.

3. How do you calculate the change in length due to a temperature change?

The change in length due to a temperature change can be calculated using the equation: ΔL = αLΔT, where ΔL is the change in length, α is the coefficient of thermal expansion, L is the original length, and ΔT is the change in temperature.

4. Can temperature changes cause structural damage to objects?

Yes, temperature changes can cause structural damage to objects. If an object is exposed to extreme temperature changes, it can experience thermal stress, which can lead to cracks or warping. This is why it is important to consider thermal expansion when designing structures or choosing materials.

5. How does the coefficient of thermal expansion vary between different materials?

The coefficient of thermal expansion varies between materials and can even vary within the same material depending on its composition. Generally, materials with weaker bonds between molecules tend to have a higher coefficient of thermal expansion, while materials with stronger bonds have a lower coefficient of thermal expansion.

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