A copper ring has a diameter of exactly 25 mm at its temperature of 0 ∘ C . An aluminum sphere has a diameter of exactly 25.04 mm at its temperature of 10 0 ∘ C . The sphere is placed on top of the ri

Question

A copper ring has a diameter of exactly 25 mm at its temperature of $0^{\circ} C$ . An aluminum sphere has a diameter of exactly 25.04 mm at its temperature of $10 0^{\circ} C$ . The sphere is placed on top of the ring, and the two are allowed to come to thermal equilibrium, with no heat being lost to the surroundings. The sphere just passes through the ring at the equilibrium temperature. Find the ratio of the mass of the sphere to the mass of the ring, $\frac{m _{s p h ere}}{m _{r in g}}$ .

Given:

$α_{C u} = 6.96 \times 1 0^{- 6} /^{\circ} C$

$α_{A l} = 2.5 \times 1 0^{- 5} /^{\circ} C$

Specific heat of Cu $= 0.092 C a l / g^{\circ} C$

Specific heat of Al $= 0.230 C a l / g^{\circ} C$

Symbols have their usual meanings.

TestHub · Accepted Answer

25 ( 1 + 6.96 × 1 0 − 6 T ) = 25.04 [ 1 − 2.5 × 1 0 − 5 ( 100 − T ) ] ​ ⇒ T = 5 0 ∘ C ​ m sphere ​ × 0.230 × ( 100 − 50 ) = m Ring ​ × 0.092 × ( 50 − 0 ) ​ ​ ⇒ m r in g ​ 10 m s p h ere ​ ​ = 4

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