Volume Change after Temperature Jump

ISOTHERMAL VOLUME CHANGE AFTER TEMPERATURE JUMP 

The time-dependent volume contraction which follows a sudden quench to a temperature near Tg has been illustrated in Fig. 11-7, and the prolongation of shear relaxation times which occurs during the course of such a contraction has been described in Section D3 of Chapter 11. The reverse experiment of a sudden positive change in temperature is characterized by an autoaccelerating volume change which is accompanied by corresponding shortening of shear relaxation 

The approach to voluminal equilibrium after a sudden temperature change ( temperature jump ) is closely analogous to that described in the preceding section after sudden pressure change ( pressure jump ), though it has been pointed out by Meixner that the relaxation times describing the approach to equilibrium may 

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B. ISOTHERMAL VOLUME CHANGE AFTER TEMPERATURE JUMP... 

A very important aspect of kinetic theories now surfaces. Equation (5-23) is concerned with the time dependence of volume recovery after a temperature jump. For the volume to change, the molecules must move. However, as discussed in Chapters 3 and 4, the rate at which the molecules can move is a sensitive function of the free volume, and the free volume is varying with time in Figure 5-9. Thus, it is clear that the retardation time in equation (5-23) must itself depend upon 8 and vary with time. This situation can be treated in quite a straightforward way by modifying equation (4-16) as... 

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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