Physics... yah fun!?!?

Question

I need help working these problems out... BUT I have answers so showing me the work would be great!

Many hot water heating systems have a reservoir tank connected directly to the pipeline, so as to allow for expansion when the water becomes hot. The heating system of a house has 76 m of copper wire whose inside radius is 9.5 x 10^-3 m. When the water and pipe are heated from 24 to 78 degrees C, what must be the minimum volume of the reservoir tank to hold the overflow of water? (Chapter 13)

Answer 1

When water is heated from 24 to 78 degrees C it expands. So do the pipes that are carrying it.

If all the pipes are full at 24 degrees and if water expands more than the copper, then there will end up being more water than the pipes can hold.

So:

- First you have to determine by what percentage the volume of water will increase.

- Next you have to determine by what percentage the volume of the pipes will increase.

- If the percentage increase of the water were less than that of the pipes, you would be done. But it isn't, so the next step is to determine the initial volume of pipes and water.

- Then you have to compute the expanded volume of both and the difference between the two.

For information on the volume thermal expansion, check out:
http://physics.bu.edu/~duffy/py105/Temperature.html
http://en.wikipedia.org/wiki/Coefficient_of_thermal_expansion

For the coefficient values themselves, check out:
http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Thermal/ThermExpan.html