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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 59.7 m of copper pipe whose inside radius is 9.20 x 10- 3 m. When the water and pipe are heated from 20.5 to 64.5 °C, what must be the minimum volume of the reservoir tank to hold the overflow of water

Answer :

Answer:

[tex]108.306\times 10^{-6}m^3[/tex]

Explanation:

According to volume thermal expansion the expansion in volume due to temperature is given by [tex]\Delta V=V_0\beta \Delta T[/tex] here [tex]\beta[/tex] is coefficient of volume expansion

The volume of copper pipe before expansion is [tex]V_0=\pi r^2L=3.14\times (9.20\times 10^{-3})^2\times 59.7=0.0158m^3[/tex]

Now the increase of copper pipe due to increase in temperature = [tex]\Delta V_c=V_0\beta _c\Delta T=0.0158\times 51\times 10^{-6}\times (64.5-20.5)=35.6\times 10^{-6}m^3[/tex]  

As [tex]\beta[/tex] for copper is [tex]51\times 10^{-6}[/tex]

Now the increase of water due to increase in temperature = [tex]\Delta V_w=V_0\beta _c\Delta T=0.0158\times 207\times 10^{-6}\times (64.5-20.5)=143.906\times 10^{-6}m^3[/tex]

As [tex]\beta[/tex] for water is [tex]207\times 10^{-6}[/tex]

So the minimum volume of reservoir tank to hold the overflow of water = [tex]\Delta V=\Delta V_w-\Delta V_c=143.906\times 10^{-6}-35.6\times 106{-6}=108.306\times 10^{-6}m^3[/tex]

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