As part of a project for the General Physics III course, a group of students must carry out the following experiment: i.

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As part of a project for the General Physics III course, a group
of students must carry out the following experiment:
i. Immerse an aluminum sphere whose diameter is d = 2.54533 cm in a
container containing boiling water.
ii. Place a ring with a mass of 21.6 g and D = 2.54000 cm in
internal diameter in a container in which water and ice
coexist.
iii. After waiting a few minutes, the sphere and the ring are
removed from their respective containers and the sphere is placed
on the ring.
IV. Wait until the sphere and ring reach equilibrium.
Once the experiment has been carried out, as part of the
analysis, the group of students must answer some questions. Suppose
you are part of that group, and you have to answer the following
questions from the experiment described above:
A. If once equilibrium is reached the sphere passes through the
ring, and considering that there is no exchange of energy in the
form of heat with the surroundings, what is the equilibrium
temperature of the ring-sphere system? Explain
B. What is the mass of the sphere? Explain
C. What must be the temperature of the sphere so that the
density is 0.15% higher compared to when it was immersed in the
container of boiling water? Explain
D. Explain extensively, qualitatively why the temperature
of a sphere must be increased to decrease its density.
Note: for the resolution of this exercise it is
essential to maintain the number of decimals given in the values
​​of the diameters "d" and "D" in the calculations that involve
these magnitudes.
𝑐𝐴𝑙uminum = 910 J kg∙K
𝛼𝐴𝑙uminum= 2,4 × 10−5 K −1
𝑐𝐶𝑢 = 390 J kg∙K
𝛼𝐶𝑢 = 1,7 × 10−5 K −1