A copper ring (with mass of 25.0 g, coefficient of linear expansion of 1.70 X 10-5 (°C)-1, and specific heat of 9.24 X 10-2 cal/g °C) has a diameter of 5.00 cm at its temperature of 15.0°C. A spherical aluminum shell (with mass 10.9 g, coefficient of linear expansion 2.40 X 10-5 (°C)-1, and specific heat 0.215 cal/g °C) has a diameter of 5.01 cm at a temperature higher than 15.0°C. The sphere is placed on top of the horizontal ring, and the two are allowed to come to thermal equilibrium without any exchange of energy with the surroundings. As soon as the sphere and ring reach thermal equilibrium, the sphere barely falls through the ring. Find (a) the equilibrium temperature, and (b) the initial temperature of the sphere.
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