Pure Substance
    m                                   The schematic temperature dependence of 
                     curvature          the chemical potential of the solid, liquid, 
    ,
    l
    a                                   and gas phases of a substance.
    i
    t   Solid         
    n                                   (In reality, the lines are curved).
    e
    t                 ×
    o
    p
     
    l              Liquid               The phase with the lowest chemical poten-
    a
    c
    i                                   tial at the specified T and P is the most sta-
    m
    e                           Gas     ble.
    h
    C
                                        The transition temperatures, the melting 
                                        and boiling temperatures, are the tempera-
         Solid       Liquid   Gas       tures at which the chemical potentials of 
         stable      stable   stable    two phases are equal. 
                  T          T
                   f          b
                Temperature, T
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                                                   Figure 4.4
                                        Critical   The general regions of pressure and 
           Solid                        point      temperature where solid, liquid, or gas 
     p
                                                   is stable (that has the lowest chemical 
     ,                   Liquid
     e
     r                                             potential).
     u
     s
     s
     e
     r                                             The solid phase is the most stable phase 
     P
             Triple                                at low temperatures and high pressures. 
             point
                           Vapor
                     T                  T
                       3                  c
                 Temperature, T
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   Uniform Chemical Potential 
                          In Equilibrium
                            Figure 4.5 
                            The vapor pressure of a liquid or 
                  Vapor     solid is the pressure exerted by the 
                            vapor in equilibrium with the con-
              V atom        densed (L or S) phase. 
              ↓ ↑
                    S atom   T < T
                                  sublimation
                  Solid     (T < T    )
                                  boiling
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                  T > Tc  or
   T < Tc or                        Figure 4.4
                  P > P  
   P < P                 c (a) A liquid in equilibrium with its vapor.
          c
                          (b) When a liquid is heated in a sealed con-
                             tainer, the density of the vapor phase in-
                             creases and that of the liquid decreases 
    V       V                slightly.
                   V = L  (c) There comes a stage at which the two 
                             densities are equal, and the interface be-
                             tween the fluids disappears.  This disap-
                             pearance occurs at the critical tempera-
    L       L                ture.
                               The container needs to be strong: the 
                             critical temperature of water is 374˚C 
      T + P  going up        and the vapor pressure is then 218 atm. 
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                       Figure  4.8 
                       Phase diagram for carbon dioxide. 
                       As the triple point lies at pressures well 
                       above atmospheric, liquid carbon dioxide 
                       does not exist under normal conditions
                       A pressure of at least 5.11 atm must be 
                       applied. 
                   
                          Dry ice
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