Consider a house in a northern location that needs a total of 100 GJ of thermal energy over a winter season from November through March. Assume that the house has a ground source heat pump that operates with a CoP of 3. The ground around the house has reasonable moisture content, a heat capacity of 3 MJ/m³ K, and a thermal conductivity of 1.5 W/mK. Ground temperatures average 10 ^◦C at 6 m. Compute

a) the volume of round whose temperature must be reduced by 8K in order to provide thermal energy to supply the season’s heating energy needs for the house, 

b) the area of a horizontal piping field needed for the rate of thermal energy replacement through ground conduction to match the average rate of power needed over the winter, assuming a gradient near the pipes of 8 K/m.