How Does Temperature Affect the Fit Between a Brass Ring and an Aluminum Rod?

In summary, the conversation discusses the thermal expansion of metals, specifically a brass ring and aluminum rod that are initially at the same temperature and have different diameters. The question is raised about the necessary temperature for the two metals to separate, and whether this is attainable. The concept of linear expansion and its equation is also mentioned. There is a debate about whether heating or cooling the metals would be the better approach for separation, and the importance of having the same diameter for both metals is emphasized. The meaning of Lfrod = Lfring is also discussed, indicating that for the two metals to separate, they must have the same length.
  • #1
whitehorsey
192
0
1.A brass ring of diameter 10.00 cm at 20.0°C is heated and slipped over an aluminum rod of diameter 10.01 cm at 20.0°C. Assuming the average coefficients of linear expansion are constant, (a) to what temperature must this combination be cooled to separate them? Is this attainable? (b) What if the aluminum rod were 10.02 cm in diameter?
Lfrod = Lfring


2. Linear expansion of solids Δl = l0αΔT



3. Shouldn't the temperature be heated instead to separate the ring and the rod because then it would expand? Also why is Lfrod = Lfring?
 
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  • #2
If you heat the combined metals, both expand - what is the thermal expansion of aluminium, compared to the expansion of brass? Does heating (both together) work then?

What does Lfrod = Lfring mean?
To find the point where they get separable, both should have the same diameter.
 

Related to How Does Temperature Affect the Fit Between a Brass Ring and an Aluminum Rod?

1. What is thermal expansion of solids?

Thermal expansion of solids is the phenomenon where the size, shape, and volume of a solid material changes in response to changes in temperature. This is due to the individual particles in the material vibrating faster and taking up more space as the temperature increases.

2. How does thermal expansion affect everyday objects?

Thermal expansion can cause everyday objects to expand or contract with changes in temperature. This can be seen in objects such as metal bridges, where the expansion and contraction due to temperature changes can cause stress and even damage over time.

3. What factors affect the amount of thermal expansion in a solid?

The amount of thermal expansion in a solid is affected by the type of material, its dimensions, and the change in temperature. Some materials, such as metals, have a higher coefficient of thermal expansion and will expand more with temperature changes compared to other materials.

4. Can thermal expansion be controlled or prevented?

Thermal expansion can be controlled or prevented through the use of materials with low coefficients of thermal expansion, or through the use of expansion joints in structures. In some cases, precise calculations and measurements can also be used to compensate for thermal expansion in a design.

5. How is thermal expansion measured and expressed?

Thermal expansion is typically measured using a coefficient of thermal expansion, which is the amount of linear or volume change per unit change in temperature. It is expressed in units of length per temperature, such as meters per degree Celsius (m/°C) or inches per degree Fahrenheit (in/°F).

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