In commercial greenhouse cultivation, root-zone heating systems are used to maintain optimal soil temperatures. Direct resistive soil-heating cables heat the ground directly using electrical resistance. Alternatively, a water-source heat pump system uses a compression cycle to transfer thermal energy from a surrounding environmental reservoir to the root-zone water loop.
Direct resistive heating cables require about 15.0 kWh15.0\text{ kWh}15.0 kWh of electrical energy to complete a heating cycle for a specific greenhouse zone. A heat pump system requires only about 3.5 kWh3.5\text{ kWh}3.5 kWh of electrical energy to deliver the same quantity of thermal energy to the same zone.
Explain, with reference to the first law of thermodynamics, why the heat pump system requires less electrical energy than the direct resistive heating system.
The root-zone water loop is maintained at a temperature of 28 ∘C28\text{ }^\circ\text{C}28 ∘C. The heat pump can extract thermal energy from either an underground geothermal loop at 12 ∘C12\text{ }^\circ\text{C}12 ∘C or from an outdoor irrigation pond at 4 ∘C4\text{ }^\circ\text{C}4 ∘C.
Deduce which of these two reservoirs results in lower running costs for the greenhouse heating system. Support your answer with calculations of the maximum thermodynamic coefficient of performance.
