Question

The Bodø NATO base in northern Norway uses a heat pump to extract heat from ocean water. 7.0∘C ocean water is continuously drawn into the system, heat is extracted, and the water is returned to the ocean at 3.0∘C. When the system is working at full capacity, 2000 kW of heat is delivered to the building at the cost of 600 kW of electric energy.

a)How much energy is removed from the water (the cold reservoir) each second?

b)What is the mass of water that moves through the system each second?

Answer 1

Inlet water temperature = T₁ = 7 ^oC

Outlet water temperature = T₂ = 3 ^oC

Heat delivered to the building = Q_H = 2000 kW

Electric energy consumed = W = 600 kW

Energy removed from the water = Q_C

Q_C = Q_H - W

Q_C = 2000 - 600

Q_C = 1400 kW

Therefore 1400 kJ of energy is removed from the water in one second.

Specific heat of water = C = 4186 J/(kg.^oC)

Mass flow rate of water = m

Q_C = mC(T₁ - T₂)

1400 x 10³ = m(4186)(7 - 3)

m = 83.61 kg/s

Therefore 83.61 kg of water moves through the system each second.

a) Energy removed from water each second = 1400 kJ

b) Mass of water that moves through the system each second = 83.61 kg