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discontinuously,  as  a  result  of  some  external  condition,  such  as
            temperature, pressure, and others. For example, a liquid may become gas
            upon heating to the boiling point, resulting in an abrupt change in volume.
            The measurement of the external conditions at which the transformation

            occurs  is  termed  the  phase  transition.  Phase  transitions  are  common  in
            nature and used today in many technologies.


            In the modern classification scheme, phase transitions are divided into two
            broad categories.

                      First-order  phase  transitions  are  those  that  involve  a  latent  heat.
                                                             During  such  a  transition,  a  system
                                                             either  absorbs  or  releases  a  fixed
                                                             (and  typically  large)  amount  of

                                                             energy.  During  this  process,  the
                                                             temperature  of  the  system  will  stay

                                                             constant as heat is added: the system
                                                             is  in  a  "mixed-phase  regime"  in
                                                             which some parts of the system have
                                                             completed  the  transition  and  others

                                                             have not. Familiar examples are the
                                                             melting of ice or the boiling of water
                                                             (water  does  not  instantly  turn  into

                                                             vapor, but forms a turbulent mixture
                                                             of  liquid  water  and  vapor  bubbles).
                                                             Fig.5.1  shows  the  nomenclature  for
                          Figure 5.1
                                                             the     different      first-order      phase

                                                             transitions
                      Second-order  phase  transitions  are  also  called  continuous  phase
            transitions. They are characterized by a divergent susceptibility, an infinite

            correlation length, and a power-law decay of correlations near criticality.
            Examples  of  second-order  phase  transitions  are  the  ferromagnetic
            transition, superconductor and the superfluid transition



                                         5.2. Aggregate Substance States


                Removing  energy  from  a  gas  lowers  its  temperature.  For  many  gases
            liquefaction  occurs,  and  if  still  more  energy  is  taken  away,  the  liquid
            solidifies. Such changes in phase are typically reversible, so that adding




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