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 74 m of copper pipe whose inside radius is 9.10 10-3 m. When the water and pipe are heated from 20 to 75°C, what must be the minimum volume of the reservoir tank to hold the overflow of water?

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 a house has 74 m of copper pipe whose inside radius is 9.10  10-3 m. When the water and pipe are heated from 20 to 75°C, what must be the minimum volume of the reservoir tank to hold the overflow of water?
 m3

drwls · Answer

The volume of the pipe is
pi R^2 L = 1.93*10^-2 m^2 = 19.3 liters

Calculate how much that volume of water increases when being heated from 20 to 75 C. You will need the bulk thermal expansion coefficient of water. It varies a lot from 20 to 75 C, but a suitable mean value is 4*10^-4 K^-1. See
http://hypertextbook.com/physics/thermal/expansion/

delta V = V*4*10^-4*(75 - 20)
= 0.43 liters

That volume expansion will be the minimum reservoir volume needed.