Consider an underground cooling loop that serves a building

Consider an underground cooling loop that serves a building with a cooling load of 4kW. Determine the volume of earth that must participate in the cooling for a cooling period of 50 days and an allowable ground temperature rise of 10o C. The properties of the ground are estimated to be cp = 0.8 kJ /kgK, = 1520 kg/m^3. Recall that Q=m*cp *T

Solution

>> As, Q = mCp*dT

and, it is given that,

Q = 4 kW

m = ?

Cp = 0.8 KJ/Kg-K

dT = 10 C

>> Putting all values,

=> 4 = m*0.8*10

=> m = 0.5 Kg

Now, Density = 1520 Kg/m³

>> As, mass = Volume*Density

=> 0.5 = Volume*1520

=> Required Volume = 3.289*10^-4 m³