Thermal expansion (Simple) (attempt posted)

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SUMMARY

The discussion centers on calculating the increase in interior space of a geodesic dome made of aluminum due to thermal expansion. The dome has a diameter of 55.0 meters at -18°C in winter and is analyzed for its volume change when the temperature rises to 30°C. Key equations referenced include Delta L = alpha (L initial) (Delta T) for length and Delta V = Beta (V initial) (Delta T) for volume. The participant, Bjorn, struggles with determining the coefficients necessary for these calculations, indicating a need for clarity on how to approach the problem correctly.

PREREQUISITES
  • Understanding of thermal expansion concepts, specifically linear and volumetric expansion.
  • Familiarity with the equations for thermal expansion, including Delta L and Delta V.
  • Knowledge of geodesic dome geometry and volume calculations.
  • Ability to interpret and apply coefficients of thermal expansion for materials, particularly aluminum.
NEXT STEPS
  • Research the coefficients of thermal expansion for aluminum to apply in calculations.
  • Learn how to calculate the volume of a hemisphere and the effects of temperature changes on it.
  • Explore practical examples of thermal expansion in architectural structures.
  • Study the relationship between temperature changes and material properties in engineering contexts.
USEFUL FOR

Students studying physics or engineering, particularly those interested in thermal dynamics and material properties, as well as architects and builders involved in geodesic dome construction.

Bjorn J
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Homework Statement


I'm looking for a good explanation, not interested in the answer.

A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 on a winter day at a temperature of -18 C.

How much more interior space does the dome have in the summer when the temperature is 30 C?

Relevant equations:
1. For length: Delta L = alpha (L initial) ( Delta T)
2. For Volume: Dela V = Beta (V initial) ( Delta T)

Attempt:

I attempted to calculate the surface area of the hemisphere by dividing the surface area of a sphere by 2.
= 6361m
Coming to calculate the area of increase, this is where I got stuck. I was not given any coefficients, and from my knowledge they are obtained experimentally.

I'm guessing I'm approaching this problem incorrectly.

Thanking you in advance for a detailed explanation of how to obtain how much the dome increased.

Bjorn.

Homework Equations

The Attempt at a Solution

 
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Bjorn J said:
I attempted to calculate the surface area
Why are you calculating surface area? The question asks about interior space.
 

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