Is There a Relationship Between the Ideal Carnot Cycle and the Actual Ideal Carnot Cycle and the Acutual Vapor Compression Cycle?

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1 Purdue University Purdue e-pubs International Refrigeration and Air Conditioning Conference School of Mechanical Engineering 1994 Is There a Relationshi Between the Ideal Carnot Cycle and the Actual Ideal Carnot Cycle and the Acutual Vaor Comression Cycle? D. R. Riffe Americold Follow this and additional works at: htt://docs.lib.urdue.edu/iracc Riffe, D. R., "Is There a Relationshi Between the Ideal Carnot Cycle and the Actual Ideal Carnot Cycle and the Acutual Vaor Comression Cycle?" (1994). International Refrigeration and Air Conditioning Conference. Paer 49. htt://docs.lib.urdue.edu/iracc/49 This document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact eubs@urdue.edu for additional information. Comlete roceedings may be acquired in rint and on CD-ROM directly from the Ray W. Herrick Laboratories at htts://engineering.urdue.edu/ Herrick/Events/orderlit.html

2 Is There a Relationshi Between The Ideal Carnot Cycle and The Actual Vaor Comression Cycle? Delmar Ray Riffe Americold ABSTRACT Historically the Carnot cycle has been acceted as a reference oint for comarison in the design and evaluation of engines and similarly the "reversed" Carnot cycle has been acceted as a reference oint for comarison in the design and evaluation of refrigeration systems. It is normally assumed that the Carnot cycle reresents the best engine and that the reversed Camot cycle reresents the best refrigeration system of any conceivable engine or refrigeration system oerating between an uer and a lower temerature limit. It will be shown herein that in the case of the refrigeration system this assumtion may not be accurate; it may be theoretically ossible that there could be refrigeration systems that are better than this ideal reversed Carnot Cycle as this reversed Camot cycle is normally defined. This conclusion is reached as a result of an examination of the Carnot cycle itself and an examinatibn of PH diagrams of hyothetical but theoretically ossible refrigerants suorts this conclusion. Before attemting to draw similar conclusions in regard to engines it should be borne in mind that in the case of refrigeration it is desirable for the work to be a minimum but in the case of engines it is desirable for the work to be a maximum. The ideal Camot cycle may reresent the best conceivable engine but the ideal "reversed" Carnot cycle, as normally defined, does not always reresent the best conceivable refrigeration system. INTRODUCTION The term coefficient of erformance, COP, is by definition the ratio of the refrigeration received to the work required to obtain this refrigeration. Thus the reversed Camot cycle COP is the ratio ofthe reversed Camot cycle refrigeration received to the reversed Camot cycle work required to obtain this refrigeration. THE REVERSED CARNOT CYCLE Figure 1 illustrates the classical reversed Camot Cycle for refrigeration. The cycle consist of two isentroic and two isothermal rocesses as illustrated by oints 1,,3 and 4. In this ideal reversed Camot cycle gas is comressed isentroically from oint 1 to oint. It is imortant to note that in the case ofthe ideal reversed Carnot cycle Tt is below some available sink temerature, T 0, and that T is above this available sink temerature. The gas rejects heat isothermally along ath to 3. It exands isentroically along ath 3 to 4 and finally absorbs heat (refrigeration) isothermally along ath 4 to 1. 05

3 The refrigeration received from this ideal reversed Camot cycle, as shown in any basic thermodynamics text, is determined by the relationshi The work of this ideal reversed Camot cycle is determined by the relationshi which is reresented by the enclosed area defined by 1,,3,4,1. The COP is determined by the relationshi 3 COP= Ref/W = T1/(T- T1) T a..-T T T T - 4 Figure 1: Ideal Camot Cycle T>To>Tt COP= T 1/ (T - T J)..,....- T I 4., s Figure 3: Possible Cycle COP > Ideal Camot Cycle COP ~T8 T 4 Figure : Possible Cycle COP > Ideal Camot Cycle COP Tz To --' s...---t , -T, To -TB s Figure 4: I~ossible Cycle Violates n Law of Thermodynamics These relationshis are arrived at without any regard to the thermodynamic roerties of the refrigeration medium, but as it shall be seen later, all refrigerants are not the same; they do not all result in the same COP even though the comressor isentroic comression efficiency may be the same for all of them. The work of the isentroic comression rocess is determined by the relationshi 06

4 The work of a olytroic comression rocess would be reresented by the exression l (N-1) W= ~~~~~ (~:)"-I J which is similar to the exression for the work of the isentroic comression rocess excet that k is relaced by n. The value ofn is always less than the value ofk and greater than 1. Thus the olytroic comression work is always.less than the isentroic comression work. As n aroaches 1, the exression becomes an indeterminate (infinity x zero) but it can be shown that as n aroaches 1 the exression for work (isothermal or constant temerature) reduces to the exression W=P,V,Ln(~) Figure and 3 illustrated cycles that do not violate any of the laws of thermodynamics but that have COP's greater than the ideal reversed Carnot cycle COP. Figure 4 illustrates a cycle that is not ossible, it violates the second law oftherrnodynamics. The comression rocess as illustrated in Figure is an isentroic (no heat absorbed or rejected) comression rocess from oint 1 to oint b which is at a temerature above ambient temerature, To. From oint b to oint the comression rocess is olytroic (some heat is rejected to the ambient sink). The net effect is that the cycle work is less in this cycle illustrated in Figure than it is in the ideal reversed Carnot cycle as illustrated in Figure 1 but the refrigeration, T 1 (S 1-84), is the same in both cases. Thus the COP of the cycle illustrated in Figure is greater than that of the ideal reversed Carnot cycle COP and there is no violation of any ofthe laws of thermodynamics. Figure 3 illustrates another aroach to obtaining a COP greater than the ideal Carnot cycle COP and again this cycle does not violate any of the laws of thermodynamics. It is imortant to observe that the temerature at oint 3 is lower than that of oint but it is above the available sink temerature, To. Figure 4 illustrates a cycle that would aear to result in a COP greater than the ideal reversed Carnot cycle COP but there is a fallacy. This cycle illustrates a olytroic comression rocess from oint b to oint but this is not ossible because the temerature at b is less than the available sink temerature, To. For this cycle to exist it would require that heat flow from a lower temerature to a higher temerature which is contrary to the second law of thermodynamics. 07

5 ACTUAL REFRIGERATION CYCLES Figure 5 illustrates a cycle on the TS diagram that is more nearly reresentative of the actual refrigerant cycle and Figure 6 illustrates this cycle on the PH diagram which is more commonly used to illustrate the vaor comression refrigeration rocess. T TB -T - - s H Figure 5: Actual Refrigeration Cycle Figure 6: Actual Refrigeration Cycle The Carnot cycl~ COP is defmed as Tt/(T-Tt) and in the case ofthe ideal reversed Camot cycle there is no question as to which temerature is Tt and which temerature is T but this is not the case, in the actual cycle. In the actual cycle is T to be taken as Ta or Tb or Tc or T or even To. Is T1 to be taken as T 1 or Ta? In defining a COP of an actual cycle it is conventional to assume that T 1 is the evaorator saturation temerature and T is the condenser saturation temerature but this definitely is not the temerature limits that the cycle oerates between as is secified in describing the ideal reversed Camot cycle. The temerature of the refrigerant entering the condenser is normally much higher than the condenser saturation temerature and the highest temerature of the gas in the comressor is even higher. There does not aear to be any relationshi between the COP of the ideal reversed Camot cycle and the COP of the actual vaor comression refrigeration cycle. The ideal reversed Camot cycle does not aear to set any boundary or limit as to theoretically how high the actual COP could be. An examination of some PH diagrams of the vaor comression cycle using hyothetical refrigerants leads to similar conclusions. 08

6 Figure 7 illustrates the conventional vaor comression cycle on a PH diagram excet that three alternate comression rocesses are shown. H H Figure 7: Conventional Vaor Comression Cycle Figure 8: Conventional Vaor Comression Cycle An isentroic comression rocess (as used in the ideal reversed Camot cycle) is illustrated by line 1- B and W reresents the comression work in this case. In the case of any isentroic comression rocess W = AH. A olytroic comression rocess is illustrated by line 1-C and the olytroic comression work is always less than the isentroic comression work. Based on actual measurements in a comressor line 1-A illustrates aroximately the actual comression rocess and the work of this actual rocess is normally greater than the isentroic comression work. Isentroic comression efficiency is defined as the ratio of the isentroic comression work to the actual work. If the actual comression rocess was olytroic or if the first art of the comression stroke was isentroic and the later art of the comression stroke was olytroic which theoretically it could be, then the isentroic comression efficiency could theoretically be greater than 1 00%. In actual comressors it is not greater than I 00%; it is about 59% in good resent day refrigerator freezer comressors, but theoretically it could be greater than 100%. Sometimes the motor losses are searated out to arrive at what could be called a shaft work isentroic comression efficiency which would be about 69.4% (85% efficient motor). Further friction and windage losses could be searated out to arrive at a iston work isentroic comression efficiency which would be about 79.7% (13% friction and windage losses or 87% friction and windage efficiency). The fact that actual resent day isentroic comression efficiencies are less than 1 00% does not reclude the ossibility that theoretically they could be greater than 100%. Thus far ideal cycles have been considered without regard to the actual thermodynamic roerties of the gas. From Figure 7 it is obvious that the refrigeration obtained is indeendent ofthe comression rocess but it is determined by the thermodynamic roerties of the refrigerant. The work and hence the COP does deend on the comression rocess. 09

7 Figure 8 illustrates an extreme case that is not likely to occur in an actual refrigeration machine but under some conditions it ossibly could occur. In this figure an isothermal (constant temerature) comression ro-cess is illustrated. If the gas was excetionally hot when it entered the comressor, above the available ambient heat sink temerature, then in theory it could be comressed at a constant temerature. This in effect is saying that n could aroach 1 in the olytroic comression rocess. The COP deends on the comression rocess but it also deends very much on the thermodynamic roerties of the refrigerant. This is illustrated in Figure 9A, 9B, 9C and 9D. For urose of illustrating the effect that these thermodynamic roerties have on the COP an isentroic comression rocess is illustrated in these four figures (1 00% isentroic comression efficiency) but bear in mind that theoretically the comression rocess could be better than isentroic. The sloe of the isentroes (constant entroy lines) and the heat of vaorization have a great effect on determining the work, the refrigeration and the COP of a refrigeration system. The sensible heat of the liquid and esecially the sensible heat of the vaor also hel to determine the refrigeration and the COP. Figure 9A can be taken as a base or starting oint for comarison. / I 4~ Figure 9A: Hyothetical Refrigerant H / H Figure 9B: Hyothetical Refrigerant / 4 1<1'...--REF~W-, Figure 9C Hyothetical Refrigerant H 10 H Figure 90: Hyothetical Refrigerant

8 The length of line 4-1 reresents the refrigeration obtained. The length ofthe horizontal rojection of line 1- reresents the work (isentroic work). Figure 9B reresents a different hyothetical but theoretically ossible refrigerant. The refrigeration effect is the same as that illustrated in 9A but as a result of the steeer sloe of the isentroes which does not violate any ofthe laws oftherrnodynamics, the work is less. Figure 9C reresents another hyothetical but theoretically ossible refrigerant. In this case the work is the same as that of Figure 9A but as a result of the greater heat of vaorization which also does not violate any of the laws oftherrnodynamics, the refrigeration effect is greater. Figure 9D reresents still another hyothetical but theoretically ossible refrigerant. In this case the work is the same as that of Figure 9B but the refrigeration effect is the same as that of 9C. This results in a hyothetical suer refrigerant that does not violate any of the laws of thermodynamics. There are chemical considerations that have been roosed that suggest that there are limits as to how good a refrigerant may be but these limits are in regard to the chemical make u of the molecule itself and are in no way related to the reversed Carnot cycle or any other cycle. Table 1 lists some calculations of refrigeration, of work and of COP for several different refrigerants. Table 1 Theoretical Performance of Refrigerants Refrigerant Ref Isen. Cam Work COP (Btu/lb) (Btu/lb) R Rl34a R15a R R R R R14b R143a R R RC RC R600a The calculations assume that the evaorator temerature is -1 QOF, the condenser temerature is 13 oo, the return gas (suerheat) temerature is 900F and the liquid temerature (subcooled) is 9QOF. The calculations are based on available NIST data oftherrnodynamic roerties of the refrigerants. As can be seen there is about a 4 to 1 variation in the amount of refrigeration obtained er ound of refrigerant circulated ifrc70 is comared to RC318 but the ower required to obtain this refrigeration also varies by almost as much. The net effect is that although there is some variation in COP it is only about 1.5%. This table list actual refrigerants that were examined. It is theoretically ossible that there could be some better ones. 11

9 The likelihood of finding a really suer refrigerant may not be great. Some chemical observations have been reorted that suggest that there are limits as to how good the refrigerant may be, however, it is theoretically ossible that there could be a refrigeration system with a COP greater than the ideal reversed Camot cycle COP. Present day systems have COP's about 50% of the ideal reversed Camot cycle COP but in theory they could have COP's greater than 100% ofthe ideal reversed Carnot cycle COP. It is the chemistry ofthe refrigerant as well as the quality of the comressor not the ideal reversed Carnot cycle that determines how high or how low the actual COP will be. Present day isentroic comression efficiencies are about 59%. There is no theoretical reason that they could not be greater than 100% and there is no theoretical limit as to how good the refrigerant could be. In summary neither the isentroic comression rocess nor the ideal Camot Cycle COP reresent absolute limits as to how efficient a refrigeration system can be. 1