Thermal Expansion Aluminium Problem

AI Thread Summary
To separate a brass ring from an aluminum rod due to thermal expansion, one must determine the cooling temperature required. The coefficients of linear expansion for brass and aluminum are 19 x 10^-6 and 24 x 10^-6, respectively. The equation T = Initial temperature - (10.00 - 10.01) / [(10 x 19 - 10.01 x 24) x 10^-6] can be used to find the necessary temperature for separation. The discussion highlights the challenge of applying the correct equations and understanding the underlying theory. Clarification on the equations and their proofs is sought to aid in solving the problem effectively.
smashbrohamme
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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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