A hollow glass block floats in a container of ethanol. Initially, everything is at a temperature of 20 degrees C, and 6% of the block is above the surface of the ethanol. If you everything gradually and evenly, at what temperature will the block sink to the bottom?

Question

Beta value for glass is 27*10^-6
Beta value for ethanol is 1100*10^-6

I don't know if the beta value for air is relevant (since the hollow block is filled with air?), but it is 3400*10^-6

My physics prof says that we don't need to know the densities of ethanol or glass. I'm not even sure how to start this problem.

Answer 1

Liquids have greater expansion than glass, that is the point. Forget the air, air in a steamship will never sink the ship.

bouyancy= wt of liquid displaced
volume glass=Vo
volume alcohol=.94Vo
final volumes=Vo*(1+Beta*deltaT)

in the end,
final glass volume=finalalcoholvolume
Vo(1+27E-6*deltaT)=.94Vo(1+1100E-6deltaT)

check my thinking.