Thermal Expansion Aluminium Problem

In summary, to separate a heated brass ring with a diameter of 10.00 cm at 19.9°C from an aluminum rod with a diameter of 10.01 cm at 19.9°C, the combination must be cooled to a temperature calculated using the equation T = initial temperature - (10.00 - 10.01) / [(10 x 19 - 10.01 x 24) x 10^-6]. This equation takes into account the average coefficients of linear expansion for both metals.
  • #1
smashbrohamme
97
1
A brass ring of diameter 10.00 cm at 19.9°C is heated and slipped over an aluminum rod of diameter 10.01 cm at 19.9°C. Assume the average coefficients of linear expansion are constant.
(a) To what temperature must the combination be cooled to separate the two metals?



Brass=19 x 10^-6
Aluminum=24 x 10^-6

(Change)A=γ x Ao x (change)Temperature.

This is the equation for one instance.

What is a conveniant equation to solve for both at the same time? I am stuck and I feel if I keep using that top equation I will just be guessing all day.
 
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  • #2
I came across a equation that works, but I am not sure with the theory behind it..maybe someone can explain it for me.

T= Initial temperature - (10.00-10.01)/[(10x19-10.01x24)10^-6]

Proofing equations is probably my weakest area in academia.
 

1. What is thermal expansion and how does it relate to aluminum?

Thermal expansion is the tendency of a material to expand or contract when its temperature changes. This is especially relevant for aluminum because it has a high coefficient of thermal expansion, meaning it expands significantly when heated and contracts when cooled.

2. What is the problem with thermal expansion in aluminum?

The problem with thermal expansion in aluminum is that it can cause structural instability or damage to objects made from this material. When aluminum is exposed to high temperatures, it can expand and contract at different rates, leading to warping, cracking, or even failure of the object.

3. How does the coefficient of thermal expansion affect aluminum?

The coefficient of thermal expansion (CTE) is a measure of how much a material expands or contracts when its temperature changes. Aluminum has a relatively high CTE, which means it will expand and contract more than other materials when exposed to temperature changes. This can lead to dimensional changes and potential problems with the stability of structures made from aluminum.

4. How can the thermal expansion problem be addressed in aluminum?

There are a few ways to address the thermal expansion problem in aluminum. One solution is to use alloys with lower coefficients of thermal expansion, such as aluminum-silicon alloys. Another option is to design structures with built-in allowances for thermal expansion, such as using flexible joints or gaps between components. Proper insulation and ventilation can also help minimize the effects of temperature changes on aluminum objects.

5. Are there any other factors that can exacerbate the thermal expansion problem in aluminum?

Yes, there are other factors that can worsen the thermal expansion problem in aluminum. These include high temperatures, rapid temperature changes, and repeated heating and cooling cycles. Additionally, the shape and size of the aluminum object can also impact its susceptibility to thermal expansion, as well as the materials it is in contact with.

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