# calculus

posted by
**stan**
.

A 20.0 g copper ring at 0.000°C has an inner diameter of D = 2.54000 cm. An aluminum sphere at 108.0°C has a diameter of d = 2.54508 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, and the coefficients of linear expansion of aluminum and copper are αAl = 23*10^-6/C° and αCu = 17*10^-6/C°, respectively. . What is the mass of the sphere?