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.

 

[Moetasim]

I would approach this problem by first identifying the key variables and equations involved. The key variables in this problem are the initial volume of the glass block, the coefficient of thermal expansion of methyl alcohol, and the change in temperature. The equations that can be used are the volume change equation (V=Vinitial(1+Beta x change in Temp)) and the buoyant force equation (Buoyant force = rho x V x g).

To solve the problem, we need to first find the initial volume of the glass block. This can be done by using the fact that only 7% of the block is above the surface of the alcohol. This means that 93% of the block is submerged, so we can calculate the initial volume by dividing the submerged volume by 0.93.

Next, we can use the volume change equation to calculate the final volume of the block at the new temperature. We can then use this final volume to calculate the buoyant force at the new temperature. The buoyant force will increase as the volume of the block increases, and at some point, it will become greater than the weight of the block, causing it to sink. We can use this information to find the temperature at which the block will sink to the bottom.

Additionally, we can use the coefficient of thermal expansion for methyl alcohol to calculate the change in volume for a given change in temperature. This can help us to determine how much the volume of the block will increase as the temperature increases.

In summary, to solve this problem, we need to use the volume change equation, the buoyant force equation, and the coefficient of thermal expansion for methyl alcohol. By using these equations and identifying the key variables, we can determine the temperature at which the glass block will sink to the bottom of the container.