化工热力学导论英文课件5热力学第二定律the second law of thermodynamics .ppt

1、化工热力学英文版化工热力学英文版chemical and engineering thermodynamicsChapter 5 the second law of thermodynamicsContents5.1 statements of the second law5.2 heat engines5.3 thermodynamic temperature scales5.4 entropy5.5 entropy changes of an ideal gas5.6 mathematical statement of the second law5.7 entropy balance f

2、or open systems5.8 calculation of ideal work5.9 lost work5.10 the third law of thermodynamics5.11 entropy from the microscopic viewpointEmphasis5.2 heat engines5.3 thermodynamic temperature scales5.4 entropy5.5 entropy changes of an ideal gas5.6 mathematical statement of the second lawDifficultiesEn

3、tropy,mathematical statement of the second lawThermodynamics is concerned with transformations of energy,and the laws of thermodynamics describe the bounds within which these transformations are observed to occur.The first law reflects the observation that energy is conserved,but it imposes no restr

4、iction on the process direction.Yet,all experience indicates the existence of such a restriction,the concise statement of whichconstitutes the second law.The difference between the two forms of energy,heat and work,provide some insight into the second law.In an energy balance,both work and heat are

5、included as additive terms,implying that one unit of heat,a joule,is equivalent to the same unit of work.Although this is true with respect to an energy balance,experience teaches that there is a difference of kind between heat and work.This experience is summarized by the following facts.Work is re

6、adily transformed into other forms of energy:for example,into potential energy by elevation of a weight,into kinetic energy by acceleration of a mass,into electrical energy by operation of a generator.These processes can be made to approach a conversion efficiency of 100%by elimination of friction,a

7、 dissipative process that transforms work into heat.Indeed,work is readily transformed completely into heat,as demonstrated by joules experiments.On the other hand,all efforts to devise a process for the continuous conversion of heat completely into work or into mechanical or electrical energy have

8、failed.Regardless of improvements to the devices employed,conversion efficiencies do not exceed 40%.Evidently,heat is a form of energy intrinsically less useful and hence less valuable than an equal quantity of work or mechanical or electrical energy.Drawing further on our experience,we know that th

9、e flow of heat between two bodies always takes place from the hotter to the cooler body,and never in the reverse direction.This fact is of such significance that its restatement serves as an acceptable expression of the second law.5.1statements of the second lawThe observations just described sugges

10、t a general restriction on processes beyond that imposed by the first law.The second law is equally well expressed in two statements that described this restriction:Statement 1:no apparatus can operate in such a way that its only effect(in system and surroundings)is to convert heat absorbed by a sys

11、tem completely Into work done by the system.Statement 2:no process is possible which consists solely in the transfer of heat from one temperature level to a higher one.Statement 1 does not say that heat cannot be converted into work;only that the process cannot leave both the system and its surround

12、ings unchanged.Consider a system consisting of an ideal gas in a piston/cylinder assembly expanding reversibly at constant temperature.According to Eq(2.3),Ut=Q+W.for an ideal gas,Ut=0,and therefore,Q=-W.the heat absorbed by the gas from the surroundings is equal to the work transferred to the surro

13、undings by the reversible expansion of the gas.At first this might seem a contradiction of statement 1,since in the surroundings the result is the complete conversion of heat into work.However,this statement requires in addition that no change occur in the system(expanding),a requirement that is not

14、met.This process is limited in another way,because the pressure of the gas soon reaches that of the surroundings,and expansion ceases.Therefore,the continuous production of work from heat by this method is impossible.If the original state of the system is restored in order to comply with the require

15、ments of statement 1,energy from the surroundings in the form of heat is transferred to the system to maintain constant temperature.This reverse process requires at least the amount of work gained from the expansion;hence no network is produced.Evidently,statement 1 may be expressed in an alternativ

16、e way:Statement 1a:it is impossible by a cyclic process to convert the heat absorbed by a system completely into work done by the system.The word cyclic requires that the system be restored periodically to its original state.In the case of a gas in a piston/cylinder assembly,its initial expansion an

17、d recompression to the original state constitute a complete cycle.If the process is repeated,it becomes a cyclic process.The restriction to a cyclic process in statement 1a amounts to the same limitation as that introduced by the words only effect in statement 1.The second law does not prohibit the

18、production of work from heat,but it does place a limit on how much of the heat directed into a cyclic process can be converted into work done by the process.With the exception of water and wind power,the partial conversion of heat into work is the basis for nearly all commercial production of power.

19、The development of a quantitative expression for the efficiencyof this conversion is the next step in the treatment of the second law.5.2 heat enginesThe classical approach to the second law is based on a macroscopic viewpoint of properties,independent of any knowledge of the structure or behavior o

20、f molecules.It arose from the study of heat engines,devices or machines that produce work from heat in a cyclic process.An example is a steam power plant in which the working fluid(steam)periodically returns to its original state.In such a power plant the cycle(in its simplest form)consists of the f

21、ollowing steps:Liquid water at ambient temperature is pumped into a boiler at high pressure.Heat from fuel(heat of combustion of a fossil fuel or heat from a nuclear reaction)is transferred in the boiler to the water,converting it to high-temperature steam at the boiler pressure.Energy is transferre

22、d as shaft work from the steam to the surroundings by a device such as a turbine,in which the steam expands to reduced pressure andtemperature.Exhaust steam from the turbine is condensed by transfer of heat to the surroundings,producing liquid water for return to the boiler,thus completing by cycle.

23、Essential to all heat-engine cycles are absorption of heat into the system at a high temperature,rejection of heat to the surroundings at a lower temperature,and production of work.In the theoretical treatment of heat engines,the two temperature level which characterize their operation are maintaine

24、d by heat reservoirs,bodies imagined capable of absorbing or rejecting an infinite quantity of heat without temperature change.In operation,the working fluidWith eq(5.1)this becomes:Or on the degree of reversibility of its operation.Indeed,a heat engine operating in a completely reversible manner is

25、 very special,and is called a carnot engine.The characteristic of such an ideal engine were first described by N.L.S.Carnot in 1824.the four steps that make up a carnot cycle are performed in the following order:Step1:a system at the temperature of a cold reservoir TC undergoes a reversible adiabati

26、c process that caused its temperature to rise to that of a hot reservoir at THStep2:the system maintains contact with the hot reservoir at TH,and undergoes a reversible isothermal process during which heat|QH|is absorbed from the hot reservoir.Step3:the system undergoes a reversible adiabatic proces

27、s in the opposite direction of step1 that brings its temperature back to that of the cold reservoir at TCStep4:the system maintains contact with the reservoir at TC,and undergoes a reversible isothermal process in the opposite direction of step2 that returns it to its initial state with rejection of

28、 heat|QC|to the cold reservoir.A carnot engine operates between two heat reservoirs in such a way that all heat absorbed is absorbed at the constant temperature of the hot reservoir and all heat rejected is rejected at the constant temperature of the cold reservoir.Any reversible engine operating be

29、tween two heat reservoirs is a carnot engine;an engine operating on a different cycle must necessarily transfer heat across finite temperature differences and therefore cannot be reversible.Carnots theoremStatement 2 of the second law is the basis for carnots theorem:For two given heat reservoirs no

30、 engine can have a thermal efficiency higher than that of a carnot engine.To prove carnots theorem assume the existence of an engine E with a thermal efficiency greater than that of a carnot engine which absorbs heat|QH|from the hot reservoir,produces work|W|,and discards heat|QH|-|W|to the cold res

31、ervoir.Engine E absorbs heat|QH|from the same hot reservoir,produces the same work|W|,and discards heat|QH|-|W|to the same cold reservoir.If engine E has the greater efficiency,Since a carnot engine is reversible,it may be operated in reverse;the carnot cycle is then traversed in the opposite direct

32、ion,andit becomes a reversible refrigeration cycle for which the quantities|QH|,|QC|and|W|are the same as for the engine cycle but are reversed in direction.Let engine E drive the carnot engine backward as a carnot refrigerator,as shown schematically in fig5.1.for the engine/refrigerator combination

33、,the net heat extracted from the cold reservoir is:The net heat delivered to the hot reservoir is also|QH|-|QH|.Thus,the sole result of the engine/refrigerator combination is the transfer of heat from temperature TC to the higher temperature TH.Since this is in violation of statement 2 of the second

34、 law,the original premise that engine E has a greater thermal efficiency than the carnot engine is false,and carnots theorem is proved.In similar fashion,one can prove that all carnot engines operating between heat reservoirs at the same two temperatures have the same thermal efficiency.Thus a corol

35、lary to carnots theorem states:The thermal efficiency of a carnot engine depends only on the temperature levels and not upon the working substances of the engine.5.3 ideal-gas temperature scales;carnots equationsThe cycle traversed by an ideal gas serving as the working fluid in a carnot engine is s

36、hown by a PV diagram in fig5.3.it consists of four reversible steps:ab adiabatic compression until the temperature rises from TC to THbc isothermal expansion to arbitrary point c with absorption of heat|QH|.cd adiabatic expansion until the temperature decreases to TCda isothermal compression to the

37、initial state with rejection of heat|QC|.ThereforeSince the left side of these two equations are the same,Equations(5.7)and(5.8)are known as carnots equations.In eq(5.7)the smallest possible value of|QC|is zero;the corresponding value of TC is the absolute zero of temperature on the kelvin scale.As

38、mentioned in Sec1.5,this occurs at-273.15.equation(5.8)shows that the thermal efficiency of a carnot engine can approach unity only when TH approaches infinity or TC approaches zero.Neither of these conditions is attainable;all heat engines therefore operate with thermal efficiency less than unity.T

39、he cold reservoirs naturally available on earth are the atmosphere,lakes and rivers,and the oceans,for which TC300K.Hot reservoirs are objects such as furnaces where the temperature is maintained by combustion of fossil fuel and nuclear reactors where the temperature is maintained by fission of radi

40、oactive elements.For these practical heat sources,TH 600K.With these values,This is a rough practical limit for the thermal efficiency of a carnot engine;actual heat engines are irreversible,and their thermal efficiencies rarely exceed 0.35 5.4 ENTROPYEquation(5.7)for a carnot engine may be written:

41、If the heat quantities refer to the engine(rather than to the heat reservoirs),the numerical value of QH is positive and that QC is negative.The equivalent equation written without absolute-value signs is thereforeorThus for a complete cycle of a carnot engine,the two quantities Q/T associated with

42、the absorption and rejection of heat by the working fluid of the engine sum to zero.The working fluid of cyclic engine periodically returns to its initial state,and its properties,e.g.,temperature,pressure,and internal energy,return to their initial values.Indeed,a primary characteristic of a proper

43、ty is that the sum of its changes is zero for any complete cycle.Thus for a carnot cycle,eq(5.9)suggests the existence of a property whose changes are given by the quantities Q/T.Our purpose now is to show that eq(5.9),applicable to the reversible carnot cycle,also applies to other reversible cycles

44、.The closed curve on the PV diagram of fig5.4 represents an arbitrary reversible cycle traversed by an arbitrary fluid.Divide the enclosed area by a series of reversible adiabatic curves.Since such curves cannot intersect,they may be drawn arbitrarily close to one another.Several such curves are sho

45、wn on the figures as long dashed lines.Connect adjacent adiabatic curves by two short reversible isotherms which approximate the curve ofthe arbitrary cycle as closely as possible.The approximation clearly improves as the adiabatic curves are more closely spaced.When the separation becomes arbitrari

46、ly small,the original cycle is faithfully represented.Each pair of adjacent adiabatic curves and their isothermal connecting curves represent a carnot cycle for which eq(5.9)applies.Each carnot cycle has its own pair of isotherms TH and TC and associated heat quantities QH and QC.These are indicated

47、 on fig5.4 for a representative cycle.When the adiabatic curves are so closely spaced that the isothermal steps are infinitesimal,the heat quantities become dQH and dQC,and eq(5.9)for each carnot cycle is written:In this equation TH and TC,absolute temperatures of the working fluid of the carnot eng

48、ines,are also the temperatures traversed by the working fluid of the arbitrary cycle.Summation of all quantities dQ/T for the carnot engines leads to integral:Where the circle in the integral sign signifies integration over the arbitrary cycle,and the subscript“rev”indicates that the cycle is revers

49、ible.Thus the quantities dQrev/T sum to zero for the arbitrary cycle,exhibiting the characteristic of a property.We therefore infer the existence of a property whose differential changes for the arbitrary cycle are given by these quantities.The property is called entropy,and its differential changes

50、 are:Points A and B on the PV diagram of fig5.5 represent two equilibrium states of a particular fluid,and paths ACB and ADB show two arbitrary reversible processes connecting these points.Integration of eq(5.11)for each path gives:Where in view of eq(5.10)the two integrals must be equal.We therefor