I've attempted several solutions to the following problem and I always arrive at roughly -49C, but when I submitted that answer it was marked wrong. They said the right answer is 10.8.


The density of glycerin at 25∘C is 1.26201x10³ kg/m3. It's thermal volume expansion coefficient is 4.85×10^-4 1/C. Imagine that I have a 1 cm diameter ball of some material with a density of 1.27000×10³ kg/m3 and a linear thermal expansion coefficient of 3.59 ×10^-4 1/C sitting in 25∘C glycerin. How much do I have to change the temperature of the glycerin and the ball to make the ball float (assuming that the glycerin and the ball are always in thermal equilibrium, that both the ball and the glycerin don't go through a phase change, and that the expansion coefficients don't change significantly over this temperature range)? Give a positive number if you need to increase the temperature, or a negative one if you need to decrease it.


My solution is to plug thermal expansion equations into the equation for the buoyant force after expansion, set that force equal to the weight of the object, which I can substitute with the density*volume*g, and solve for T. I get -49 degrees Celsius.

Are they wrong or am I wrong?

They tricked you by giving the volume expansion coefficient for glycerin but a linear expansion coefficient for the ball. You will need to determine the volume expansion coefficient for the ball - do you know how to do that?