Solve Thermal Expansion: Floating Glass Block in Methyl Alcohol

[chantalprince]

Homework Statement

A hollow glass block is floating in a container of methyl alcohol. Initially, everything is at a temperature of 20 degrees C, and just 7% of the block is above the suface of the alcohol. If you heat the container (gently and evenly- so that everything warms up together), at what temperature will the block sink to the bottom?

Homework Equations

So far, I think I need these:

V = V initial (1+Beta x change in Temp)


Beta = Coefficient of Thermal expansion (volume)

Buoyant force = rho x V x g (but I am not given the density of methyl alcohol in my book)


Coef for Therm Exp. for Methyl alcohol = 1200 x 10^-6

The Attempt at a Solution

I am pretty sure I will use the first equation, I just don't know how yet... I don't know any volumes,and I don't have any dimensions to get there, so I don't know how to begin. The 93% submerged tidbit has got to be useful, but I don't see how to use it :( Something to do with buoyant force...?

Thank you ahead of time for any help!

 

[Kurdt]

The buoyant force depends on the density of a substance which is inversely proportional to its volume. You know the buoyant force must support the weight of the sphere as well.