Melting Point of Ice as a Function

The melting and boiling points for a substance are determined by the vapor pressures of the solid and liquid states. Figure 16.51 shows the vapor pressures of solid and liquid water as functions of temperature near 0°C. Note that below 0°C the vapor pressure of ice is less than the vapor pressure of liquid water. Also note that the vapor pressure of ice has a larger temperature dependence than that of the liquid. That is, the vapor pressure of ice increases more rapidly for a given rise in temperature than does the vapor pressure of water. Thus, as the temperature of the solid is increased, a point is eventually reached where the liquid and solid have identical vapor pressures. This is the melting point. 

FIGURE 8.11 State diagram for food materials, showing the Tg curve and isoviscous states above Tg. Maximally freeze-concentrated solids with a solute concentration of C g have Tg at T g. Ice melting within maximally freeze-concentrated materials occurs at T m. The equilibrium melting curve shows the equilibrium melting point Tm as a function of concentration. (From Roos, Y.H. and Karel, M., Food Technol., 45, 66, 1991b.)... 

There are a number of characteristics of the type of phase transitions we have considered so far. In practice, these characteristics are often used to determine data points for phase equilibrium lines. One of the obvious characteristics is a discontinuity in enthalpy as a function of temperature. Consider a sample of ice at -100°C and a pressure of 1 bar. The enthalpy changes smoothly as the temperature is increased until the system reaches 0°C, the melting temperature. At this point, there is a jump in the enthalpy corresponding to the enthalpy of melting. After all the ice has melted, the temperature can be increased and the enthalpy will be a new but different function of the temperature. Since the heat capacity, Cp, is the derivative of the enthalpy with respect to temperature, Cp as a function of temperature is also discontinuous at the phase transition. Vaporization of liquid water at 100°C and 1 bar leads to a sharp increase in volume. Thus, volume is a discontinuous function at a phase transition. The same holds for entropy. 

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