The Vapor-Compression Refrigeration Cycle

The first law of thermodynamics states that energy is conserved. We may express it as follows: Increase in internal energy of a system is equal to heat put into the system with the deduction of work done by the system on its surroundings, or ΔU = ΔQ - ΔW, where U ?internal energy Q ?heat W - work A system can be anything. It is most convenient if it has well defined boundaries. DQ is positive if it is put into the system, and negative if it is taken out of the system. DW is positive if the system does work on its surroundings and is negative if work is done on the system. The internal energy is the sum of the kinetic and potential energies of atoms and molecules that make up the system. 2. The second law of thermodynamics Sadi Carnot (1796 -1832), Rudolf Clausius (1822-1888), Wiliam Thomson (Lord Kelvin 1824-1907) established the second law of thermodynamics. The second law is a statement that all processes go only in one direction to a state of higher and higher entropy (in other words, in the direction of greater and greater degradation of energy). An isolated system always goes from a less probable to a more probable configuration. We hence have the following statement for the second law. The first statement of the 2nd law: In any physical process, the entropy S for an isolated system never decreases; that is, we always have ΔS ≥ 0 Unlikely as it may sound, the second law is one of the few fundamental laws of physics that historically arose from very practical questions, in particular the need to understand the theory of heat engines. Carnot analyzed how much mechanical work could be extracted from heat, and what, in principle, is the most efficient heat engine that one could construct. His analysis was the beginning of the concept of entropy. It was only much later, in the work of Boltzmann, that there emerged a microscopic and more fundamental understanding of the principle of entropy. Based on the considerations of heat and work, we have a few other formulations of the second law. The second statement of the 2nd law: No mechanical work can be extracted from an isolated system at a single temperature. The third statement of the 2nd law: Heat cannot spontaneously flow from a cold body to a hot body. Although these formulations may seem to be a far cry from Statement I of the second law, it will be shown to be identical to it. Since only changes in entropy are defined, it was thought that there was an additive constant which would always be arbitrary. However, it was realized that this was not so. 3. The Third Law of Thermodynamics. The Third Law of Thermodynamics states that as temperature tends to absolute zero, so does entropy. In other words S(T) → 0 as T → 0

Clausius Statement of the Second Law of thermodynamics is the following: It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body.

In order to accomplish heat transfer from cold to hot ?you need a device, like a heat pump or refrigerator, which consumes work:

Energy from the surroundings in the form of work or heat has to be expended to force heat to flow from a low-temperature media to a high-temperature media. Thus, the coefficient of performance of a refrigerator or heat pump must be less than infinity. For a refrigerator it is equal to:

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.

4.1. The Vapor-Compression Refrigeration Cycle The vapor-compression refrigeration cycle has four components: evaporator, compressor, condenser, and expansion (or throttle) valve. The most widely used refrigeration cycle is the vapor-compression refrigeration cycle. In an ideal vapor-compression refrigeration cycle, the refrigerant enters the compressor as a slightly superheated vapor at a low pressure. It then leaves the compressor and enters the condenser as a vapor at some elevated pressure, where the refrigerant is condensed as heat is transferred to cooling water or to the surroundings. The refrigerant then leaves the condenser as a high-pressure liquid. The pressure of the liquid is decreased as it flows through the expansion valve, and as a result, some of the liquid flashes into cold vapor. The remaining liquid, now at a low pressure and temperature, is vaporized in the evaporator as heat is transferred from the refrigerated space. This vapor then reenters the compressor. The refrigerant enters the compressor Vapor-compression refrigeration cycles specifically have two additional advantages. First, they exploit the large thermal energy required to change a liquid to a vapor so we can remove lots of heat out of our air-conditioned space. Second, the isothermal nature of the vaporization allows extraction of heat without raising the temperature of the working fluid to the temperature of whatever is being cooled. This is a benefit because the closer the working fluid temperature approaches that of the surroundings, the lower the rate of heat transfer. The isothermal process allows the fastest rate of heat transfer. The cycle operates at two pressures, Phigh and Plow, and the statepoints are determined by the cooling requirements and the properties of the working fluid. Most coolants are designed so that they have relatively high vapor pressures at typical application temperatures to avoid the need to maintain a significant vacuum in the refrigeration cycle.

The ideal vapor-compression cycle consists of four processes. Ideal Vapor-Compression Refrigeration Cycle Process Description 1-2 Isentropic compression 2-3 Constant pressure heat rejection in the condenser 3-4 Throttling in an expansion valve 4-1 Constant pressure heat addition in the evaporator

The P-h diagram is another convenient diagram often used to illustrate the refrigeration cycle.

The ordinary household refrigerator is a good example of the application of this cycle

Actual Vapor-Compression Refrigeration Cycle

4.2. Cascade refrigeration systems Very low temperatures can be achieved by operating two or more vapor-compression systems in series, called cascading. The COP of a refrigeration system also increases as a result of cascading.

4.3. Multistage compression refrigeration systems

4.4. Multipurpose refrigeration systems A refrigerator with a single compressor can provide refrigeration at several temperatures by throttling the refrigerant in stages

4.5. Liquefaction of gases Another way of improving the performance of a vapor-compression refrigeration system is by using multistage compression with regenerative cooling. The vapor-compression refrigeration cycle can also be used to liquefy gases after some modifications.

4.6. Gas Refrigeration Systems The power cycles can be used as refrigeration cycles by simply reversing them. Of these, the reversed Brayton cycle, which is also known as the gas refrigeration cycle, is used to cool aircraft and to obtain very low (cryogenic) temperatures after it is modified with regeneration. The work output of the turbine can be used to reduce the work input requirements to the compressor. Thus, the COP of a gas refrigeration cycle is

4.7. Absorption Refrigeration Systems Another form of refrigeration that becomes economically attractive when there is a source of inexpensive heat energy at a temperature of 100 to 200癈 is absorption refrigeration, where the refrigerant is absorbed by a transport medium and compressed in liquid form. The most widely used absorption refrigeration system is the ammonia-water system, where ammonia serves as the refrigerant and water as the transport medium. The work input to the pump is usually very small, and the COP of absorption refrigeration systems is defined as

4.8. Thermoelectric Refrigeration Systems A refrigeration effect can also be achieved without using any moving parts by simply passing a small current through a closed circuit made up of two dissimilar materials. This effect is called the Peltier effect, and a refrigerator that works on this principle is called a thermoelectric refrigerator. The thermoelectric device, like the conventional thermocouple, uses two dissimilar materials. There are two junctions between these two materials in a thermoelectric refrigerator. One is located in the refrigerated space and the other in ambient surroundings. When a potential difference is applied, as indicated, the temperature of the junction located in the refrigerated space will decrease and the temperature of the other junction will increase. Under steady-state operating conditions, heat will be transferred from the refrigerated space to the cold junction. The other junction will be at a temperature above the ambient, and heat will be transferred from the junction to the surroundings. A thermoelectric device can also be used to generate power by replacing the refrigerated space with a body that is at a temperature above the ambient.

4.9. Air conditioners An air conditioner uses a material called a "working fluid" to transfer heat from inside of a room to the great outdoors. The working fluid is a material which transforms easily from a gas to a liquid and vice versa over a wide range of temperatures and pressures. This working fluid moves through the air conditioner's three main components, the compressor, the condenser, and the evaporator in a continuous cycle.

The working fluid enters the evaporator inside the room as a low-pressure liquid at approximately outside air temperature. (1) The evaporator is typically a snake-like pipe. The fluid immediately begins to evaporate and expands into a gas. In doing so, it uses its thermal energy to separate its molecules from one another and it becomes very cold. Heat flows from the room to this cold gas. The working fluid leaves the evaporator as a low-pressure gas a little below room temperature and heads off toward the compressor. (2) It enters the compressor as a low-pressure gas roughly at room temperature. The compressor squeezes the molecules of that gas closer together, increasing the gas's density and pressure. Since squeezing a gas involves physical work, the compressor transfers energy to the working fluid and that fluid becomes hotter. The working fluid leaves the compressor as a high-pressure gas well above outside air temperature. (3) The working fluid then enters the condenser on the outside, which is typically a snake-like pipe. Since the fluid is hotter than the surrounding air, heat flows out of the fluid and

into the air. The fluid then begins to condense into a liquid and it gives up additional thermal energy as it condenses. This additional thermal energy also flows as heat into the outside air. The working fluid leaves the condenser as a high-pressure liquid at roughly outside air temperature. (4) It then flows through a narrowing in the pipe into the evaporator. When the fluid goes through the narrowing in the pipe, it's pressure drops and it enters the evaporator as a low-pressure liquid. The cycle repeats. Overall, heat is been extracted from the room and delivered to the outside air. The compressor consumes electric energy during this process and that energy also becomes thermal energy in the outside air. The maximum coefficient of such an air conditioner is Emax = Troom / (Toutside ?Troom).