The Carnot cycle is a reversible heat engine, and a reversed Carnot Cycle is a refrigerator or a heat pump. Lets first examine the stages of Carnot cycle: 3.1. Carnot cycle. Carnot cycle is an example of a reversible cycle. It was named after French engineer Nicolas Sadi Carnot (1769-1832). Carnot cycle is composed of four reversible processes: 2 adiabatic and 2 reversible isothermal heat transfers: Process 1-2: Reversible isothermal heat addition at high temperature, TH > TL to the working fluid in a piston-cylinder device which does some boundary work. Process 2-3: Reversible adiabatic expansion during which the system does work as the working fluid temperature decreases from TH to TL. Process 3-4: The system is brought in contact with a heat reservoir at TL < TH and a reversible isothermal heat exchange takes place while work of compression is done on the system. Process 4-1: A reversible adiabatic compression process increases the working fluid temperature from TL to TH The area inside the figure represents the work 3.2. Reversed Carnot Cycle. As it was mentioned earlier reversed Carnot Cycle is a refrigerator or a heat pump. The scheme of reversed Carnot Cycle is shown on figure: 1. The refrigerant absorbs heat isothermally from a low-temperature source at TL in the amount of QL in process (2-3). 2. The refrigerant is compressed adiabatically to state 4, and its temperature rises to TH. 3. Then the heat is rejected isothermally to a high-temperature sink at TH in the amount of QH in process (4-1). 4. Finally the refrigerant expands adiabatically to state 2, where the temperature drops to TL. A refrigerator takes heat from a cold body and delivers the heat to body at higher temperature. This process clearly can never happen spontaneously since this would imply that heat can spontaneously flow from a cold body to a hot body, something that has never been observed, and which would violate the Second Law. An object which is cooler than its environment is in a state of low entropy compared to the environment. Hence to keep a body cooler than its ambient environment's temperature we have to constantly do work. We all know this is the case from daily experience: if one switches off the air conditioner, the room soon warms up. Note a refrigerator is in essence similar to a living cell. The reason being that the cell maintains itself in a low entropy state compared to its environment by constantly doing work, and hence the need of a living organism to regularly consume food. The most efficient refrigerator is, as one can guess, a reversible one in which all the processes taking place are reversible, and which leads to no increase in the entropy of the whole system. Suppose the cold reservoir C is at temperature TC, from which the refrigerator extracts heat of amount QC (and by doing work W), and discharges heat QE to the environment E at temperature TE. A reversible refrigerator is one for which the total change of entropy in one complete cycle is zero. From ΔS =0, we have Entropy lost by cold body = Entropy gained by environment => Slost by C = Sgained by E => QC/TC = QH/TH => QE = (TE/TC)QC > QC Since the heat delivered to the environment QE is greater than QC, we necessarily have to do work on the system to generate the extra heat required by the Second Law. Let the work done on the system be W>0; hence we have from energy conservation that QE = QC +W > QC In other words, to keep cooling the refrigerator, we take heat QC from the refrigerator, add to it heat equal to the amount of work W to it, and then discharge heat of amount QE to the environment - which is the minimum heat that is required by the Second Law. Since the refrigerator is reversible, the work W that we do is the minimum amount of work required for achieving ΔS =0. Similar to a heat engine, the efficiency of a refrigerator, called K, the coefficient of performance (K is also denoted as COP), is given by the amount of heat extracted per unit amount of work. That is K = QC/W Since W = QE – QC (from the first law (conservation of energy)), we have the following: K = QC/( QE – QC) Hence for a reversible refrigerator, its efficiency is given by K = TC/( TE – TC) Unlike the efficiency of a heat engine where it is less than 1, we have that the coefficient of performance of a refrigerator K > 1. In a household refrigerator, the value of K ≈ 5, and for air conditioners it is about 2 - 3. The reason that K cannot be made infinitely large is a consequence of the second law, since this case would imply that heat would then flow from a cold body to a hot body without any work being done.