The efficiencies of air conditioners and heat pumps sold in the United States are often stated in terms of an energy efficiency ratio (EER): This peculiar ratio can be compared to the more straightforward coefficient of performance by converting BTU/hr to watts: Therefore CP = EER x 0.292. Therefore, the colder the surroundings, the lower the COP of any heat pump or refrigerator. Unfortunately, heat pumps have problems that do limit their usefullness. There is a theoretical maximum CP, that of the Carnot cycle : For a refrigerator, however, the useful quantity is the heat extracted, QC , not the heat exhausted. This is a range of 1.6 to 3.1 in CP. Reversed Carnot cycle is completely reversible and It is a highly efficient cycle. The Carnot thermal COP of a HACD is derived in Herold et al (1996) by coupling a Carnot power production cycle to a Carnot heat pump cooling cycle. The Carnot COP relation in Equation 6.27 is the upper limit for any heat-driven cooling system that operates in a closed cycle (e.g., an absorption chiller). Heat Electricity Storage” (PHES), a Carnot Battery transforms electricity into heat, stores the heat in inexpensive storage media such as water or molten salt and transforms the heat back to electricity when required. That is higher efficiency than a typical forced-air natural gas furnace which brings the primary fuel to the house. In a Carnot cycle, the system executing the cycle undergoes a series of four internally reversible processes: two isentropic processes (reversible adiabatic) alternated with two isothermal processes:. Reversing the Carnot cycle does reverse the directions of heat and work interactions. The cycle moves counter-clockwise along the process path on a PV Diagram. They are quite expensive to purchase compared to resistive heating elements, and, as the performance coefficient for a Carnot heat pump shows, they become less effective as the outside temperature decreases. If we attach a Carnot heat engine (in the center of the figure) to this heat pump, the resulting engine would absorb heat from a single thermal reservoir (the cold reservoir), and would deliver an equivalent amount of work. The reversible Carnot cycle is compared to a range of engine cycles. A Carnot heat pump is to be used to heat a house and maintain it at 25 {eq}^o{/eq}C in winter. Carnot Cycle – Processes. For an ideal gas, these heat energies are: After substituting the values of Q1 and Q2 in the coefficient of performance expression we have: We can simplify this expression by using the equation of an adiabatic process for processes 1-2 and 3-4: And after dividing both expressions, we obtain the following relation between the volumes: Therefore, after simplifying, the coefficient of performance of the Carnot heat pump is: Where both temperatures are given in kelvin (K). COP Of A Heat Pump. The coefficient of performance (COP) of reversible or irreversible refrigerator or heat pump is given by COP R = 1/ ((Q H /Q L)-1) COP HP = 1/ (1- (Q L /Q H)) This pair of engines receives no outside energy, and operates solely on the energy released when heat is transferred from the hot and into the cold reservoir. Air conditioners and heat pumps are heat engines like the refrigerator. Solution. 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