Thermal expansion of a copper pipe

In summary, the conversation discusses the calculation of the minimum volume of a reservoir tank needed for a hot-water heating system, taking into account the expansion of water and copper pipe when heated. The calculated change in volume of the pipe and water should be subtracted to determine the overflow volume that the tank needs to accommodate. Units should always be included in calculations and it is important to consider the volumetric expansion coefficient provided by the teacher.
  • #1
slaw155
41
0

Homework Statement


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?

Homework Equations


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

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?
 
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  • #2
You should always include units in your calculations. How else can you tell what these numbers mean?
 
  • #3
The units are in the question.
 
  • #4
The expansion vessel only has to accommodate the extra volume.

Domestic models are typically specified in Litres rather than cubic meter. Google them.
 
  • #5
I think you should calculate change in water volume too, use volumetric coefficient as 0.000214/deg C. initial volume of water is same as copper pipe.
From the values we can understand change in volume of water will be much greater compared to copper , also liquid expands more than solid.
If you subtract the volume change of water - volume change of copper, you will get the overflowing water volume i.e the answer.
 
  • #6
slaw155 said:
Now would I add this change in volume
You have calculated a change in interior volume of pipe, correct? Is it an increase or a decrease? How does that relate to overflow?
 
  • #7
You guys realize that this thread is 4 years old, right?
 
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Likes haruspex
  • #8
Chestermiller said:
You guys realize that this thread is 4 years old, right?
Ah.
 
  • #9
If you as the initial volume to the change in volume, it won't change the results. Because initial volume will get added to both water and copper, so they will cancel each other

V initial +chage in V of water =V initial + change in V of copper

Thus, the initial volume will get canceled on each side
 

What is thermal expansion?

Thermal expansion is the tendency of a material to expand in volume as its temperature increases. This is due to the increase in molecular motion and the resulting increase in distance between molecules.

Why does a copper pipe expand when heated?

Copper has a high coefficient of thermal expansion, meaning that it expands significantly when heated. This is due to the fact that copper is a good conductor of heat, and as the temperature increases, the molecules in the copper pipe vibrate more and take up more space, causing the pipe to expand.

How does thermal expansion affect the size of a copper pipe?

When a copper pipe is heated, it will increase in length, diameter, and volume. The amount of expansion depends on the material's coefficient of thermal expansion and the change in temperature.

What are the practical implications of thermal expansion in copper pipes?

Thermal expansion can cause copper pipes to warp, bend, or even burst if they are not properly installed or supported. It is important to consider thermal expansion when designing and installing piping systems to ensure they can withstand changes in temperature.

How can thermal expansion be managed in copper pipes?

To minimize the effects of thermal expansion, expansion joints or loops can be installed in the piping system to allow for movement without causing damage. Additionally, using materials with lower coefficients of thermal expansion, such as plastic, can help reduce the overall expansion of the system.

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