minimum volume?

Question

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 the house has 76 m of copper wire whose inside radius is 9.5 X 10^-3 m. when the water and the 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?

Answer 1

Density of water at 24 oC = 0.999953 g/cm^3 = 1000.0 kg/m^3
Density of water at 80 oC (closest I could get) = 0.97487 g/cm^3 = 975 kg/m^3

The difference in density tells you how much expansion is required.

I gather, given the way question has been phrased, that you can ignore the expansion of the copper pipe? - it will get very complicated if not!

Volume = pi x r^2 x length
= pi x (9.5 x 10^-3)^2 x 76 = 0.0215 m^3
mass water (24oC) = density * volume = 1000 * 0.0215 = 21.5 kg

Volume of water (80) oC = mass / density (80)
= 21.5 / 975 = 0.0221 m^3

Expansion volume = 0.0221 - 0.0215 = 0.0006 m^3
(you could recalculate to another decimal place if you want a slightly more accurate answer)

1000 L = 1 m^3
therefore 0.0006 m^3 = 1000 * 0.0006 L = 0.6 Litres or 600 mL (its small, but your pipe is only 9.5 mm radius!)

Answer 2

Volume expansion coeff. of Water ????????