A 27.0 g copper ring at 0°C has an inner diameter of D = 3.04591 cm. A hollow aluminum sphere at 87.0°C has a diameter of d = 3.05180 cm. The sphere is placed on top of the ring, and the two are allowed to come to thermal equilibrium, with no heat lost to the surroundings. The sphere just passes through the ring at the equilibrium temperature. What is the mass of the sphere?
The linear expansion coefficient of aluminum is 23.0 x 10^-6 /C°, and the linear expansion coefficient of copper is 17.0 x 10^-6 /C°, the specific heat of aluminum is 900 J/kg·K, and the specific heat of copper is 386 J/kg·K.