Thermodynamic Equilibrium of Phases

Abstract

In this chapter, we define a phase as a homogeneous stable state of matter and establish conditions of equilibrium between the phases. Then, we consider various classifications of phase transitions and conclude with the description of Gibbsian ideas about the interface separating phases at equilibrium.

Exercises

• 1. From the following list of thermodynamic systems, select the ones which are examples of a phase: (a) ice water that is, ice cubes in a glass of water; (b) a bar magnet that is, ferromagnetic alloy broken into magnetic domains; (c) solution of a magnetic salt in strong magnetic field.

• 2. Assuming that the latent heat and transformation volume between the liquid and solid phases of a pure substance are not functions of temperature or pressure, derive the melting point versus pressure relationship. Hint: use the results of Example 2.1. Give examples of metals, which obey and disobey this relationship.

• 3. During the equilibrium solidification of liquid bismuth at 1 atm, the extraction of heat is stopped when 50% of the metal is solidified. What will happen if now you will try to increase the pressure holding the temperature constant?

• 4. At the atmospheric pressure, the latent heat of water is 79.7 cal/g, the specific volume of ice is 1090 cm³/g, and that of water is 1000 cm³/g (by definition). (a) How much pressure do you need to apply to decrease the melting temperature of water by 1 °C? (b) What is the melting temperature on top of the Mount Everest?

• 5. Verify that the specific heat at constant pressure and isothermal compressibility of the phases in Example 2.1 are equal and independent of temperature and pressure.

• 6. Verify the Clapeyron-Clausius relation (2.8) for the system in Example 2.1.

• 7. Determine the domain of applicability of (2E.3) in Example 2.2 of a system with significant temperature dependence of the latent heat.