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16     CHAPTER 2 THE SECOND LAW AND EQUILIBRIUM




                                    R
             This can only be the case if  dQ R  is a property of the system: it is called the entropy and is denoted by
                                      T
             the symbol S, while specific entropy (i.e. entropy per unit mass) is s.
                                                                             Z 2
                                                                                dQ R
                         The change of entropy between states 1 and 2 is S 2   S 1 ¼       (2.6)
                                                                                 T
                                                                              1
             2.6.1 THE SIGNIFICANCE OF ENTROPY
                1. Entropy is evaluated from reversible processes.
                2. Entropy can be used with irreversible processes.
                3. The factor 1/T is the integrating factor that turns dQ R from an indefinite integral into a definite
                  one.
                4. Entropy is a measure of the order or disorder of a system.

             2.6.2 EVALUATION OF ENTROPY CHANGE FOR AN IRREVERSIBLE PROCESS
             The change of entropy for an irreversible process must be evaluated by considering the change of
             entropy for a reversible process (or processes) that achieves the same two end states. A good example
             of such a process occurs in a throttling process: this is discussed in the web version (http://booksite.
             elsevier.com/9780444633736) of Chapter 2.

             2.6.3 ENTROPY CHANGE AS ENVISAGED BY CLAUSIUS
             Clausius suggested that the change of entropy could be considered to be made up of two terms.

                                                    dðIEÞ
                                               dS ¼      þ dZ                              (2.7)
                                                     T
             where d(IE) is the change of ‘internal heat’ of the system ¼ dQ   dW S and dZ is the change in
             disgregation of the molecules of the system i.e. a measure of the molecular spacing.

             2.6.4 ENTROPY CHANGES FOR PURE SUBSTANCES
                                               TdS ¼ dU þ pdV                              (2.8)

                Also, H ¼ U þ pV, giving dH ¼ dU þ pdV þ Vdp, and

                                               TdS ¼ dH   Vdp                              (2.9)
                Specific entropy is the entropy per unit mass, hence s ¼ S/m and
                                                du þ pdv  dh   vdp
                                           ds ¼        ¼                                  (2.10)
                                                   T         T
                Since this is a relationship between the properties u, p, T and h it is possible to evaluate the entropy
             of a fluid at any state defined by two independent properties. Also, since entropy is a property it can be
             used as a co-ordinate in a state diagram.

             2.6.4.1 Temperature–entropy diagram for a pure substance
             In these diagrams, entropy is usually used as the abscissa (i.e. the x-axis) of the diagram.
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