Thermal Expansion Aluminium Problem

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SUMMARY

The discussion centers on calculating the temperature required to separate a brass ring from an aluminum rod due to thermal expansion. The coefficients of linear expansion for brass (19 x 10^-6) and aluminum (24 x 10^-6) are critical in determining the necessary cooling temperature. The formula used is T = Initial temperature - (10.00 - 10.01) / [(10 x 19 - 10.01 x 24) x 10^-6]. This equation effectively accounts for the expansion differences between the two metals, allowing for precise temperature calculations.

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  • Understanding of thermal expansion principles
  • Familiarity with coefficients of linear expansion
  • Basic algebra for manipulating equations
  • Knowledge of temperature measurement in Celsius
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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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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.
 

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