Merkava120 Posts: 2, Reputation: 1 New Member #1 Jan 15, 2019, 01:23 PM
Physics problem with buoyancy and thermal expansion
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?
 ebaines Posts: 12,131, Reputation: 1307 Expert #2 Jan 16, 2019, 08:19 AM
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?

 Question Tools Search this Question Search this Question: Advanced Search

## Check out some similar questions!

Thermal expansion tank [ 26 Answers ]

I have city water with no check valves. Electric water heater. Problem I have is with the Thermal Expansion Tank. As pressure builds it releases water back out to main. When pressure is needed again it brings water back in. Problem is, it does this all day long and I am paying for same water over...

Thermal expansion tank [ 3 Answers ]

Is it necessary to install a pressure gauge and a pressure reducing valve with by-pass in a standard installation of a thermal expansion tank

Thermal expansion [ 5 Answers ]

On heating why aluminium rod expands more than steel rod?:

Physics Buoyancy need elp [ 4 Answers ]

currently I am doing coursework where I am dropping a buoyant ball from different heights above a water tank into the water tank. I am then measuring the depth. I lack results so I was wondering if I plotted a graph of height vs depth - would it be a straight line? I think it is because I can say...