Thermal Expansion (Area Expansion) problem help

In summary, thermal expansion is the process by which a material expands in size when its temperature increases. This can cause structural damage and other issues in various applications. Thermal expansion affects area expansion by increasing the dimensions of a material in all directions, resulting in an increase in the total area. The coefficient of thermal expansion is a measure of how much a material expands or contracts in response to a change in temperature. To solve thermal expansion problems, one must determine the change in temperature and the coefficient of thermal expansion, and use a formula to calculate the new area, taking care to use consistent units and consider the direction of expansion.
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queennicolee
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Homework Statement


A steel ring with a hole having area of 3.990 cm2 is to be placed on an aluminum rod with crosssectional area of 4.000 cm2. Both rod and ring are initially at a temperature of 35.0°C. At what common temperature can the steel ring be slipped onto one end of the aluminum rod?

Homework Equations


delta A = yAodelaT

T = To + deltaT

The Attempt at a Solution

 
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  • #2
Please show an attempt that you made at solving the problem.
 

1. What is thermal expansion?

Thermal expansion is the tendency of a material to expand or contract in response to changes in temperature. This phenomenon occurs because as the temperature increases, the particles in the material vibrate more and take up more space, causing the material to expand.

2. How does thermal expansion affect area?

Thermal expansion can affect the area of a material by causing it to expand or contract in the direction of its surface. This is known as area expansion. When a material expands, its area increases, and when it contracts, its area decreases. This can be observed in objects such as bridges and railroad tracks, which have expansion joints to allow for thermal expansion and prevent damage.

3. What factors affect thermal expansion?

The degree of thermal expansion in a material depends on several factors, including the material's coefficient of thermal expansion, the change in temperature, and the shape and size of the material. Different materials have different coefficients of thermal expansion, which is a measure of how much they expand or contract per degree of temperature change.

4. How is thermal expansion calculated?

The amount of thermal expansion in a material can be calculated using the formula: 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. This formula can also be used to calculate the change in area due to thermal expansion.

5. How can thermal expansion be managed or controlled?

Thermal expansion can be managed or controlled by using materials with low coefficients of thermal expansion, incorporating expansion joints in structures, and designing structures to allow for expansion and contraction. It is also important to consider the temperature changes that a material may experience in its intended environment when selecting materials for a project.

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