In industrial biotechnology, maintaining a bioreactor at a stable warm temperature is critical for fermentation. This can be achieved either by using direct electrical resistance heating ribbons or by utilizing a reversed-cycle heat pump system to transfer heat from nearby utility outputs into the bioreactor vessel.
A direct electrical resistance ribbon heater requires about 8.0 kWh8.0\text{ kWh}8.0 kWh of electrical energy to raise a batch of culture to the operating temperature. In contrast, a heat pump system requires only about 1.6 kWh1.6\text{ kWh}1.6 kWh of electrical energy to deliver the exact same amount of thermal energy to the bioreactor.
Explain why the heat pump system requires significantly less electrical energy than the direct resistance heater to achieve the same temperature rise.
The fermentation mixture in the bioreactor must be continuously maintained at a temperature of 38 ∘C38\text{ }^\circ\text{C}38 ∘C. To run the heat pump, the plant engineers can draw thermal energy from one of two available reservoirs:
Deduce which of these two reservoirs results in lower operating costs for the heat pump system. Support your answer with calculations of the maximum theoretical coefficient of performance (COPHP\text{COP}_{\text{HP}}COPHP) for each option.
