(Pr. 8) The crystal phase of a certain compound melts at T_(m)=220K, with a latent heat of fusion equal to 25 kJ
mol^(-1). The same compound can be vitrified from the liquid phase, with a glass transition at T_(g)=150K. It is
found that from 0 K to T_(g) the heat capacity of the glass is the same as that of the crystal, and that between 150
and 152 K , the heat capacity of the glass reaches that of the liquid, so that, the excess specific heat at 152 K is
\Delta C_(p)=C_(p) (liquid) -C_(p) (crystal) =200JK^(-1)mol^(-1). For temperatures between 152 K and T_(m), it is observed that
\Delta C_(p)=(\beta )/(T), where \beta is a constant.
(a) Find the melting enthalpy, and graph in the same sketch the temperature dependence of the enthalpy of the
crystal, glass, and liquid phases. In a different sketch, graph together C_(p) for the liquid and crystal phases near
T_(g) and near T_(m), and explain the relation between the two sketches you made.
(b) What is the relationship between the excess specific heat and the excess entropy \Delta S=S (liquid) -S (crystal)?
What is the relationship between the excess entropy and the configurational entropy of the glass? Explain.
(c) Find the numerical value of \beta T_(K) T_(K) assuming that \Delta C_(p) of the supercooled liquid obeys a (1)/(T) law all the way between T_(K) and the melting point.
How many degrees below T_(g) is T_(K) ? Explain the relationship between T_(K) and the Vogel-Fulcher temperature T_(VF)
appearin
