Erratum: The thermodynamic efficiency of heat engines with friction (American Journal of Physics (2012) 80 (298-305) DOI: 10.1119/1.3680168);The thermodynamic efficiency of heat engines with friction

American Journal of Physics

Volumn 80, Issue 4, 2012, Pages 298-305

  Bizarro, João P S ^a  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

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[No Author keywords available]

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EID: 84858802707     PISSN: 00029505     EISSN: 19432909     Source Type: Journal    
DOI: 10.1119/1.5049354     Document Type: Erratum

References (39)

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19. The symmetry of Fig. 1 might lead to the incorrect conclusion that the two reservoirs are connected by an arrow representing energy flow between them. The directions of the arrows indicate that there is no possibility of a direct transfer of energy from one to the other, and the two are effectively isolated from each other.
20. A device is a part of an engine, which consists of two reservoirs and the mechanical device M where the processes undergone by the working fluid take place, as in Ref. 13.
21. As an example, we may think of the valve-exhaust process after the power stroke in an internal combustion engine described by a Diesel or a Otto cycle, during which an isochoric, non-isothermal cooling takes place while energy is removed from the fluid to the cold reservoir, as discussed in Refs. 13-15.
22. Although the processes undergone by the working fluid are assumed to be the same in this comparison, the engines with and without friction are different because the net amount of energy coming out from the hot reservoir is not identical in the two cases, as well as the net amount of energy transferred to the cold reservoir.
23. c are the net energies transferred into and out of the fluid. In the absence of friction these three sets of quantities reduce to a single one, as shown by Eqs. (2), (6), (11), and (12).
24. Equation (17) is the same as Eq. (24) in Ref. 10.
25. fric are both less than unity.
26. c stems from the second law, as explained in Ref. 9 in connection with Eqs. (20) and (21).
27. Deviations from Eq. (20) in the region where η approaches one are not a problem because engine operation with efficiencies close to unity is hindered by the second law.
28. Esposito M. Kawai R. Lindenberg K. Van den Broeck C. Efficiency at maximum power of low-dissipation Carnot engines. Phys. Rev. Lett. 2010, 105:150603. 10.1103/PhysRevLett.105.150603.
29. exch,h for η require work from the fluid equal to or greater than the work the fluid delivers in the engine with friction; but the alternatives allow only for an amount of energy into the fluid less than in the engine with friction. These two facts make it almost impossible for the fluid in the frictionless engine to go through a thermodynamic cycle of the same type as in the engine with friction.
30. (1-γ)/γ, as follows from Eqs. (31) and (36) in Ref. 9.
31. c, which are the temperature changes for its hot and cold isobarics, respectively.
32. Recall that the working fluid and the components in these heat engines operate cyclically so, when ΔS is calculated, the focus is on the entropy change of the reservoirs.
33. Compare, for instance, Eqs. (35)-(37) with Eq. (16) in Ref. 10.
34. exch is an exception to the sign convention adopted earlier in the paper, because it may be either positive or negative.
35. h is sometimes interpreted as a switching time.
36. exch, consistent with a friction force being linear in the engine speed, as in a well-lubricated system according to Ref. 4.
37. For instance, the quantity optimized in Ref. 5 is output power, more precisely, average power or output work per cycle, which amounts to maximizing the numerator in Eq. (A3), an increasing function of α.
38. In Refs. 3 and 6, additional energy loss terms were considered which are not discussed in the present work, which focuses only on friction. With this distinction in mind, Eq. (A5) is equivalent to Eq. (19) in Ref. 6.
39. 2.