# Thermal expansion of copper pipe

1. Aug 19, 2014

### slaw155

1. The problem statement, all variables and given/known data
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 63.1 m of copper pipe whose inside radius is 7.69 x 10^-3 m. When the water and pipe are heated from 20.3 to 60.2 °C, what must be the minimum volume of the reservoir tank to hold the overflow of water?

2. Relevant equations
change in volume = initial volume x change in temp x volumetric expansion coefficient
coefficient as provided by teacher = 51 x 10^-6 /degC

3. The attempt at a solution
change in vol = 63.1m^3 x ∏ x (7.69x10^-3)^2 x (60.2-20.3) x 51 x 10^-6 = 2.3854 x 10^-5 m^3
Now would I add this change in volume to the volume of the pipe initially or is this in itself the correct answer?

Last edited: Aug 19, 2014
2. Aug 19, 2014

### SteamKing

Staff Emeritus
You should always include units in your calculations. How else can you tell what these numbers mean?

3. Aug 19, 2014

### slaw155

The units are in the question.

4. Aug 19, 2014

### CWatters

The expansion vessel only has to accommodate the extra volume.

Domestic models are typically specified in Litres rather than cubic meter. Google them.