Question
Asked Dec 24, 2019
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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 the combination be cooled to separate the two metals? Is that temperature attainable? (b) What if the aluminum rod were 10.02 cm in diameter?

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Expert Answer

Step 1

(a) For the ring to be removed from the rod, the diameters of the brass and the aluminium is same at the final temperature.

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d = d, [1]

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Step 2

The expression for the diameter of the brass and the aluminium is

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d, = d? [1+ a, (T - T,)] [2] d̟ = d [1+a, (T – T,)] 3) [3]

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Step 3

Use equation (2) and (3) in (1) to sol...

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d [1+cz (T = T,)]= d[1+a,(T - T,)] da – d? a,d, - a,d T=T, +• 0, (10.01cm)-(10.00 cm) (19×10*/°C)(10.00 cm)– (24×10´/°C)(10.01cm) = (20°C) + = -199°C The temperature T is –199°C is not attainable.

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