On a day when the average outdoor temperature remains at about 2°C, the house is estimated to lose heat at a rate of 82,000 kJ/h. Carnot Heat Pump: Carnot heat pump is defined as the heat pump, which follows the reversed Carnot cycle. 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. The reversible Carnot cycle is compared to a range of engine cycles. During the charging process, electricity is converted into heat and kept in heat storage. Unfortunately, heat pumps have problems that do limit their usefullness. Unfortunately, heat pumps have problems that do limit their usefullness. In a Carnot battery, energy is converted into heat at a temperature between 90°C and 500°C by using a high-temperature heat pump. It is valid only for reversible processes and depends only on temperature difference between reservoirs. The coefficient of performance (COP) of a heat pump is the ratio of heat absorbed from the cold thermal reservoir (Q2) to the absolute value of the work done on the system: In addition, the absolute value of the work done on the system is given by: Where Q1 is the heat the working fluid discharges to the hot thermal reservoir and Q2 is the heat removed from the cold thermal reservoir. Practical engine cycles are irreversible and therefore have inherently much lower efficiency than the Carnot efficiency when working at similar temperatures. We combine a Kelvin–Planck engine with a Carnot heat pump, and make the work performed on the Carnot heat pump in one cycle equal to the work performed by the Kelvin–Planck engine in one cycle, as shown in Fig. Heat Engines. Even in the air that seems too cold, heat energy is present. 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)) The COP for a Carnot heat pump cycle is a bit different from a Carnot refrigeration cycle because the objectives of the cycles are different. A heat pump is subject to the same limitations from the second law of thermodynamicsas any other heat engine and therefore a maximum efficiency can be calculated from the Carnot cycle. Heat pump hot water works on the principle of reverse Carnot cycle. As we will show below, it is the most efficient heat pump operating between two given temperatures. 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. 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. We will use a proof technique known as “reductio ad absurdum” to demonstrate that no heat pump can be more efficient than a Carnot heat pump working between the same heat reservoirs. The reverse Carnot cycle consists of four reversible processes: The reverse Carnot cycle is shown on a PV diagram in the following figure: As you can see in this figure, the cycle goes anticlockwise, because a heat pump requires work to operate (W<0). Heat pumps, air conditioners, and refrigerators utilize heat transfer from cold to hot. The theoretic maximum efficiency of a transcritical heat pump is described by the Lorentz efficiency. The Carnot cycle has been used for power, but we can also run it in reverse. The ratio of the energy transferred to the electric energy used in the process is called its coefficient of performance (CP). 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