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18     CHAPTER 2 THE SECOND LAW AND EQUILIBRIUM





                The coefficient of performance of a heat pump can be related to that of a refrigerator by the simple
             equation

                                                     Q 2
                                              0                                           (2.15)
                                             b ¼ 1 þ    ¼ 1 þ b
                                                     W S

             2.7.2 ENGINE WITH THERMAL EFFICIENCY OF 100%
             The efficiency of a heat engine is defined in Eqn (2.12) as

                                          W S  Q 1   Q 2     Q 2     T 2
                                     h ¼     ¼         ¼ 1     ¼ 1
                                      th
                                          Q 1     Q 1        Q 1     T 1
                The efficiency of a heat engine can be 100% if Q 2 ¼ 0. This would be a PMM2 and violate the
             Kelvin–Planck statement of the Second Law.


             2.7.3 REVERSIBLE HEAT ENGINE
             The concept of reversible processes is a very important one and is discussed in the web version (http://
             booksite.elsevier.com/9780444633736) of Chapter 2.
                It is possible to define a cycle made up of such processes, and because each of the processes in the
             cycle is reversible then the cycle will be reversible. A heat engine could execute such a cycle, and this
             heat engine would be called a reversible heat engine. Since all the processes are reversible, then an
             engine operating on this cycle can work with equal ‘efficiency’ in either direction, i.e. it could operate
             either as an engine or a heat pump or refrigerator.


             2.8 REVERSIBILITY AND IRREVERSIBILITY (FIRST COROLLARY OF
                  SECOND LAW)

             As stated previously, the Second Law defines the direction of energy transfer during a process. All real
             processes are irreversible, due to friction, turbulence, mixing, electrical resistance, etc. However, it is
             useful to postulate what would happen in reversible processes, because these will give a yardstick at
             which to aim when designing engines. This is similar to neglecting friction at bearings when assessing
             the operation of a mechanism.


             2.8.1 REVERSIBLE PROCESSES
             A reversible process is one which can be taken from its initial state to another state, and then back to
             the initial state without any change to either the system or the surroundings. Examples of these are the
             following:
                •  frictionless motion of solids (no friction between mating surfaces)
                •  extension of springs (no hysteresis losses in the materials)
                •  slow adiabatic compression or expansion of gases (so that nopressurewaves are set upin thegas)
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