5.1 Introduction to the Second Law of Thermodynamics 5.2 Thermal ...

5.1 Introduction to the Second Law of ThermodynamicsIn the preceding chapters, we applied the conservation of energy principle or first law ofthermodynamics to open and closed systems. By now, it seems reasonable clear that in order for aprocess to occur, it must obey the first law (Energy can neither be created nor destroyed!). But commonexperience tells us that some processes proceed in certain directions. For instance, a hot cup of coffeein a cooler room eventually cools off. The process satisfies the first law since the amount of energy lostby the coffee is gained by the surrounding air. Now take the reverse process--a hot cup of coffee gettinghotter in a cooler room. We all know this could never happen, but doing so would not violate the first lawas long as the heat gained by the hot coffee is equal to the heat lost by the cool surroundings.This is where the second law of thermodynamics comes into the picture! The second lawaddresses the feasibility of processes and the directions they may or may not occur. The second lawalso asserts that energy has quality as well as quantity. Preserving the quality of energy is a majorconcern to engineers, and the second law provides the necessary means to determine the quality as wellas the degree of energy degradation during a process. The second law is also used to assess thetheoretical limits for the performance of commonly used engineering systems (e.g. refrigerators,air-conditioning units, heaters etc ...)5.2 Thermal Energy ReservoirsIn the development of the second law of thermodynamics, it is very useful to define a hypotheticalbody with a relatively large thermal capacity that can supply or absorb finite amounts of heat withoutundergoing any change in temperature (e.g. oceans, lakes, atmosphere and rivers). Such a body iscalled a thermal energy reservoir, or simply reservoir. A two-phase system can be considered areservoir because it can absorb or release heat at constant temperature.A reservoir that supplies energy in the form of heat is called a source, and one that absorbsenergy in the form of heat is called a sink.5.3 Heat EnginesConsider the system illustrated below ...WorkWaterHeatThe mechanical work done by the shaft is completely converted to internal energy and stored bythe water. This internal energy then leaves the water via heat transfer to the surroundings. We know,from experience, that reverse process is impossible (i.e. supplying heat to the water form thesurroundings will make the shaft rotate). Thus, we may conclude that work may be converted to heatENGS205--Introductory Thermodynamics page 47

directly and completely, but converting heat to work requires the use of a special device called a heatengine. Heat engines may vary considerably from one another, but share the following characteristics:‚ They receive heat from a high temperature source.‚ They convert part of this heat to work.‚ They reject the remaining waste heat to a low-temperature sink.‚ They operate on a cycle.The work-producing device that best fits the definition of a heat engine is the steam power plant.High Temp. SourceBoilerQ inWinPumpTurbineW outCondenserQ outLow Temp. Sourcewhere: ‚ Q in = amount of heat supplied to steam in boiler from a high temperature source (furnace)‚ Q out = amount of heat rejected from steam in condenser to a low temperature sink (river, etc...)‚ W out = amount of work delivered by steam as it expands in turbine‚ W in = amount of work required to compress water to boiler pressureUsually, a portion of the work output of a heat engine is consumed internally to maintaincontinuous operation (e.g. work input to pump). The net work output of this power plant is simply thedifference between the total work output of the plant and the total work input, or ...W net,out = W out − W in(5.3.1)The net work output of the power plant can also be obtained by treating the entire plant as aclosed system (no net mass flow of water into or out of the entire plant), and using the First law relationfor cycles to give ...(5.3.2)W net,out = Q in − Q outThe fraction of the heat input that is converted to net work output is a measure of theperformance of a heat engine and is called the thermal efficiency, η th . Performance or efficiency, ingeneral, can be expressed in terms of the desired output and the required input as:ENGS205--Introductory Thermodynamics page 47

(5.3.3)For heat engines, the desired output is the net work output, and the required input is the amountof heat supplied to the working fluid. Therefore, for heat engines ...(5.3.4)Typically, when dealing with heat engines, refrigerators, and heat pumps, we operate between ahigh temperature medium at temperature T H and a low temperature reservoir at temperature T L. As aresult, we usually define heat transfer items as:‚ Q H = magnitude of heat transfer between cyclic device and high temperature medium attemperature T H.‚ Q L = magnitude of heat transfer between cyclic device and low temperature medium attemperature T L.Therefore, for a heat engine, Eq. (5.3.4) is alternately expressed as:(5.3.5)The thermal efficiency of a heat engine is a measure of how efficiently a heat engine converts theheat that it receives to work. Amazingly, most heat engine devices possess very poor thermalefficiencies, with more than one-half of the thermal energy supplied to the working fluid ending up inrivers, lakes, and/or the atmosphere.Can we save Q out ?Unfortunately, heat rejection to a low temperature reservoir is a necessary part of thethermodynamic cycle. Without it, the thermodynamic cycle cannot be completed and cyclic devices,like steam power plants, cannot run continuously.The Second Law of Thermodynamics: Kelvin-Planck Statement :The Kelvin-Planck Statement asserts the requirement of Q out for thermodynamic cyclic devices.Simply stated, the Kelvin-Planck statement reads:It is impossible for any device that operates on a cycle to receive heat from a single reservoirand produce a net amount of work.That is, a heat engine must exchange heat with a low temperature sink as well as a hightemperature source to keep operating.ENGS205--Introductory Thermodynamics page 47

5.4 Refrigerators and Heat PumpsWe all know from experience that, in nature, heat flows in the direction of decreasingtemperature, i.e., from high temperature media to low temperature ones. The reverse process, however,cannot occur by itself and requires the use of special devices called refrigerators. Refrigerators, likeheat engines are cyclic devices. The working fluid used in the refrigeration cycle is called a refrigerant.The most frequently used refrigeration cycle is called the vapor-compression refrigeration cycle, shownschematically below ...High Temp. ReservoirCondenserQ HWExpansionCompressornet,inValveEvaporatorQ LRefrigerated SpaceThe refrigerant enters the compressor as a vapor and is compressed to the condenser pressure.It leaves the compressor at a relatively high temperature and cools down and condenses as it flowsthrough the coils of the condenser by rejecting heat to the surrounding medium. It then enters a capillarytube where its temperature and pressure drop drastically due to the throttling effect. The low temperatureENGS205--Introductory Thermodynamics page 47

efrigerant then enters the evaporator, where it evaporates by absorbing heat from the refrigerated space.The cycle is completed as the refrigerant leaves the evaporator and returns to the compressor.The efficiency of a refrigerator is expressed in terms of the coefficient of performance (COP),denoted by COP R. The COP of a refrigerator can be expressed as:(5.4.1)Note that the value of COP R can be greater than unity (and usually is for most refrigeratordevices)! That is, the amount of heat removed from the refrigerated space can be greater than theamount of work input.Another device that transfers heat from a low temperature medium to a high temperature one isthe heat pump. Refrigerators and heat pumps operate on the same thermodynamic cycle, but havedifferent objectives. The objective of a refrigerator is maintain the refrigerated space at a lowtemperature. The objective of a heat pump is to maintain a heated space at a high temperature. Thecoefficient of performance of a heat pump, COP HP, is defined as:Note!(5.4.2)We all know that air-conditioning units are basically refrigerators whose refrigerated space is aroom or building. Did you know the same air-conditioning unit can operate as a heat pump in the winterby installing it backwards!! In this mode, the air-conditioner absorbs heat from the refrigerated space(outdoors) and rejects it to the heated space (your house!!). The performance of refrigerators andair-conditioning units are often expressed in the U.S. in terms of the Energy Efficiency Rating (EER),which is the amount of heat removed (in BTU's) for 1 watt-hour of electricity consumed. The relationbetween EER and COP is:EER = 3.412COP R(5.4.3)The Second Law of Thermodynamics: Clausius Statement:Another classical statement of the Second Law of Thermodynamics, which is related torefrigerators and heat pumps, is known as the Clausius Statement. Simply stated, it reads:It is impossible to construct a device that operates in a cycle and produces no effect other thanthe transfer of heat from a lower temperature body to a higher temperature body.The Clausius Statement asserts that heat flows naturally in the direction of decreasingtemperature, but does not necessarily restrict the reverse from happening!! In fact, the statement isopen-ended and allows the possibility of work input to the refrigerator/heat pump device (into thecompressor !!) to accomplish heat flow from cold to hot temperature environments.5.5 Perpetual-Motion MachinesAny device that violates the First/Second Laws of Thermodynamics is called aperpetual-motion machine. Despite numerous attempts, no perpetual-motion machine is known tohave worked.of‚ Perpetual-motion machine of the first kind (PMM1): any device that violates the first lawthermodynamicsENGS205--Introductory Thermodynamics page 47

second‚ Perpetual-motion machine of the second kind (PMM2): any device that violates thelaw of thermodynamics5.6 Reversible and Irreversible ProcessesA reversible process is defined as a process which can be reversed without leaving any traceon its surroundings. That is, both the system and surroundings are returned to their initial states at theend of the reverse process. Processes that are not reversible are called irreversible processes.Reversible processes actually do not occur in nature. They are merely idealized processes, however,some processes can come pretty close to satisfying the reversibility criterion!! Thus, analyses of real lifequasi-reversible processes can be facilitated by assuming they are in fact reversible. Engineers areinterested in reversible processes because work-producing devices (such as car engines and steamturbines) deliver the most work and work consuming devices (such as compressors and pumps) requirethe least work when reversible processes are used instead of irreversible processes.Well, you might ask yourself, "What makes a process irreversible?" The answer is simple:irreversibilities!!, and here are a list of some common irreversibilities ...‚ electric resistances,‚ inelastic deformation of solids,‚ chemical reactions,‚ friction (this is a big one),‚ non quasi-equilibrium process (compression & expansions):‚ heat transfer across a finite temperature difference (another big one)Internally and Externally Reversible Processes:A process is called internally reversible if no irreversibilities occur within the boundaries of thesystem during the process. A process is called externally irreversible if no irreversibilities occuroutside the system boundaries during the process. A process is called totally reversible, or simplyreversible, if it involves no irreversibilities within the system or its surroundings.5.7 Carnot CycleThe efficiency of a heat engine cycle greatly depends on how the individual processes that makeup the cycle are executed. The net work, thus the cycle efficiency, can be maximized by using processesthat require the least amount of work and deliver the most, that is, by using reversible processes.Perhaps the best known reversible cycle is the Carnot cycle. The theoretical heat engine that operateson the Carnot cycle is called the Carnot heat engine. The Carnot cycle is composed of four reversibleprocesses:‚ Reversible isothermal expansion (process 1-2)‚ Reversible adiabatic expansion (process 2-3)‚ Reversible isothermal compression (process 3-4)ENGS205--Introductory Thermodynamics page 47

‚ Reversible adiabatic compression (process 4-1)P1Q HW net,out2T H =const.43T L =const.Q LvThe Reversed Carnot Cycle:The Carnot heat-engine cycle described above is a totally reversible cycle. Therefore, all theprocesses that comprise it can be reversed, in which case it becomes the Carnot refrigeration cycle.This time, the cycle remains exactly the same, except that the directions of any heat or work interactionsare reversed.5.8 The Carnot PrinciplesThe following conclusions can be drawn from the Second Law and reversibilities concepts:‚ The efficiency of an irreversible heat engine is always less than the efficiency of a reversibleone operating between the same two reservoirs.‚ The efficiencies of all reversible heat engines operating between the same two reservoirs arethe same.5.10 The Carnot Heat EngineThe thermal efficiency of any heat engine, reversible or irreversible, is given as:The thermal efficiency of a Carnot engine, or any reversible heat engine, is:(5.10.1)(5.10.2)where T L and T H are absolute temperatures. The thermal efficiencies of actual and reversible heatengines operating between the same temperature limits compare as follows:ENGS205--Introductory Thermodynamics page 47

if: η th < η th,rev (irreversible heat engine)η th = η th,rev (reversible heat engine)η th > η th,rev (impossible heat engine)ENGS205--Introductory Thermodynamics page 47

5.11 The Carnot Refrigerator or Heat Pumpby:The coefficient of performance of any refrigerator or heat pump, reversible or irreversible, is given(5.11.1)(5.11.2)The COP relation for reversible refrigerators and heat pumps is:(5.11.3)(5.11.4)These are the highest coefficients of performance that a refrigerator or a heat pump operatingbetween the temperature limits of T L and T H can have!! The coefficients of performance of actual andreversible (such as Carnot) refrigerators operating between the same temperature limits can becompared as follows:... and, the same goes for heat pumps!!if: COP R < COP R,rev (irreversible refrigerator)COP R = COP R,rev (reversible refrigerator)COP R > COP R,rev (impossible refrigerator)ENGS205--Introductory Thermodynamics page 47