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7. Melting and Vaporization: Entropy and Phase Change


Laws of balance

When a substance is melted or vaporized, entropy is needed for the phase change (Fig. 1). This means that entropy and energy are added to the substance, and the stored quantities of entropy and energy (of the system composed of both phases) increases. Some energy may be emitted (or absorbed) as the consequence of a volume change of the systems (this is important in vaporization, but much less so in melting). The laws of balance of entropy and energy for the systems are
   3.27
   3.28
At the same time, a chemical process takes place (Fig. 2): One of the phases of the substance disappears, whereas the other is produced. The laws of balance of amount of substance are
   3.29


Figure 1







Figure 2

Constitutive laws

The constitutive law of a phase change expresses the relation between the rate at which entropy is needed and the rate at which one of the phases is produced. The two are proportional and simply depend on the substance and its conditions:
   3.30
lambda_m is called the molar latent entropy of fusion or of vaporization of the substance undergoing phase change. The specific latent entropy is calculated as follows: lambda = lambda_m/Mo, where Mo is the molar mass of the substance.
Since the temperature during phase change is constant, the energy flow accompanying the entropy flow in the heating during phase change is calculated by
   3.32
Phase change temperatures and latent entropies depend upon the circumstances of the phase change. The most important factor is the pressure. This is particularly important in the case of vaporization. The temperature of vaporization is sensitive to the pressure of the fluid. There is a unique pressure-temperature relation for the phase change which is called the vapor pressure of the substance. The vapor pressure of water at 100°C is 1 bar. The Ts-diagram therefore depends upon the pressure of the fluid as well (see Chapter 4).