Thermal expansion (Simple) (attempt posted)

AI Thread Summary
The discussion centers on understanding thermal expansion in the context of a geodesic dome made of aluminum, specifically how temperature changes affect its interior volume. The user seeks a detailed explanation rather than a direct answer, noting the initial dimensions of the dome and the temperature difference between winter and summer. They attempted to calculate the surface area but became confused about how to determine the increase in interior space, realizing they need coefficients for thermal expansion. The response clarifies that the focus should be on volume rather than surface area, emphasizing the importance of using the correct equations for volume expansion. The conversation highlights the need for a clear understanding of thermal expansion principles to solve the problem effectively.
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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