A brass plug is to be placed in a ring made of iron. At 20 ∘C,...

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A brass plug is to be placed in a ring made of iron. At 20 ∘C,...

A brass plug is to be placed in a ring made of iron. At 20 ∘C, the diameter of the plug is 8.752 cmand that of the inside of the ring is 8.742 cm . They must both be brought to what common temperature in order to fit?

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Answer 1

Answer #1

D_{brass =} D_iron

delta T = (D_0,brass - D_0,iron) / (alpha_iron D_0,iron - alpha_brass D_0,brass)

= (8.752 - 8.742) / ((12 * 10^-6 * 8.742) - (19 * 10^-6 * 8.752))

= -162.9 ⁰C

T_final = 20 - 162.9

= -142.9 ⁰C = -143 ⁰C

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Answer 2

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