# Thermal expansion (Simple) (attempt posted)

• Bjorn J
In summary, the question is asking for the increase in interior space of a geodesic dome with an aluminum framework when the temperature changes from -18 C to 30 C. The relevant equations for calculating length and volume changes due to temperature are provided, but the asker is unsure of how to apply them without coefficients. They are seeking a detailed explanation on how to calculate the increase in interior space.
Bjorn J

## 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.

## The Attempt at a Solution

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

## What is thermal expansion and how does it occur?

Thermal expansion is the tendency of matter to increase in volume when heated and decrease in volume when cooled. This occurs because when a substance is heated, its molecules have more energy and move around more, causing them to take up more space.

## What are some real-life examples of thermal expansion?

One common example of thermal expansion is when a metal object, such as a railroad track, expands in hot weather and causes the track to become longer. Another example is when a glass jar breaks when hot water is poured into it. This is because the glass expands faster than the water, causing it to crack.

## How is thermal expansion measured and expressed?

Thermal expansion is measured using a coefficient of thermal expansion (CTE), which is a unit that represents the amount of expansion or contraction of a material per degree change in temperature. It is typically expressed in units of length per length per degree Celsius (or Fahrenheit).

## What factors affect thermal expansion?

The main factors that affect thermal expansion are the type of material, its initial temperature, and the change in temperature. Different materials have different CTE values, and materials with higher initial temperatures or larger changes in temperature will experience greater expansion or contraction.

## Can thermal expansion be prevented or controlled?

Thermal expansion can be minimized by using materials with low CTE values, such as ceramics or certain alloys. It can also be controlled by designing structures with room for expansion, using expansion joints, or utilizing materials with different expansion rates in specific areas.

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