Question

Interactive LearningWare 12.1 provides some useful background for this problem. 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 53.4 m of copper pipe whose inside radius is 7.70 x 10^{- 3} m. When the water and pipe are heated from 25.9 to 83.4 °C, what must be the minimum volume of the reservoir tank to hold the overflow of water?

Answer 1

When the water and pipe are heated then

expansion of volume of water will be given by

dV_w = *V0*dT

Expansion of Volume of copper pipe will be given by:

dV_c = *V0*dT

Here, V0 = Initial Volume of water and pipe = Volume of cylinder =  *R^2*L

R = radius of pipe = 7.70*10^-3 m

L = Length of pipe = 53.4 m

dT = Change in temperature = 83.4 - 25.9 = 57.5 C

= Volumetric Expansion coefficient of water = 207*10^-6 /C

= Volumetric Expansion coefficient of Copper pipe = 51*10^-6 /C

Now minimum volume of reservoir tank will be:

dV = dV_w - dV_c

dV = *V0*dT - *V0*dT

dV = ( - )V0*dT

Using known values:

dV = (207*10^-6 - 51*10^-6)*pi*(7.70*10^-3)^2*53.4*57.5

dV = 8.92*10^-5 m^3 = required Volume of reservoir tank

Let me know if you've any query.