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L  = T (S  – S ) – (J  – J )                    (3.4.1)
                                                                L
                                                                        G
                                                                              L
                                             min
                                                         G
                                                      0
            where  T   is  the  temperature  of  the  surroundings,  S   and  S   are,
                        0
                                                                                                     L
                                                                                        G
            respectively, the entropies of the gas and liquid, and J  and J  are the heat
                                                                                            L
                                                                                  G
                                                            content  (enthalpies)  of  the  gas  and
                                                            liquid.
                                                                  The  industrial  liquefaction  of
                                                            gases  having  critical  temperatures  T
                                                                                                            c
                                                            above  the  temperature  of  the
                                                            surroundings,  for  example,  ammonia
                                                            and chlorine, is accomplished through
                                                            compression  of  the  gas  in  a
                                                            compressor         and      a      subsequent

                                                            condensation  of  the  gas  in  a  heat
                                                            exchanger cooled with water or brine.
                       Figure 3.4.1                         The  liquefaction  of  a  gas  having  T
                                                                                                            c
                                                            significantly          below          ambient
                                                            temperature  is  accomplished  by
            copious-cooling  methods. More  often,  for  the  liquefaction  of  gases  with

            low  T ,  refrigeration  cycles  based  on  the  throttling  of  a  compressed  gas
                    c
                                                                         (use of the Joule-Thomson
                                                                         effect),  the  expansion  of

                                                                         the  compressed  gas  with
                                                                         the  production  of  external
                                                                         work  in  an  expander,  and
                                                                         the  expansion  of  a  gas

                                                                         from  a  constant  volume
                                                                         without              performing
                                                                         external  work  (heat-pump

                                                                         method)  are  used.  In
                                                                         laboratory               practice,
                                                                         multistage          refrigeration
                                                                         (liquefaction) is sometimes

                   Figure 3.4.2                                          used.
                                                                              Design  scheme  and  a

                                                                         diagram  of  the  throttling
            cycle of gas liquefaction are given in Figure3.4.2 Scheme and temperature-
            entropy diagram for a gas-liquefaction cycle based on the Joule-Thomson
            effect:  (C)  compressor,  (H1),  (H2),  and  (H3)  heat  exchangers,  and  (Th)




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