Question

As we’ve seen, 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, 2,000 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. How much water moves through the system each second?

Answer 1

Answer:

Part a)

$Q_{rem} = 1400 kW$

Part b)

$\frac{dm}{dt} = 83.6 kg/s$

Explanation:

Part a)

Energy delivered to the building is given as

$E_{out} = 2000 kW$

Work done by the electricity is given as

$W = 600 kW$

so we have

$Q_{rem} + W = E_{out}$

$Q_{rem} = 2000 - 600$

$Q_{rem} = 1400 kW$

Part b)

As we know that water in and out temperature is given as

$T_1 = 7 degree$

$T_2 = 3 degree$

so we have

$Q = \frac{dm}{dt} s \Delta T$

$1400 \times 10^3 = \frac{dm}{dt} (4186) (7 - 3)$

$\frac{dm}{dt} = 83.6 kg/s$