Thermal Energy Storage Systems and Applications. Ibrahim Dincer

independent of the pressure. For example, ice begins to melt at 0°C. The amount of heat required to melt one kilogram of ice at 0°C to one kilogram of water at 0°C is called the latent heat of fusion of water, and equals 334.92 kJ/kg. The removal of the same amount of heat from one kilogram of water at 0°C changes it back to ice.

      1.4.7 Vapor

      A vapor is a gas at or near equilibrium with the liquid phase – a gas under the saturation curve or only slightly beyond the saturated vapor line. Vapor quality is theoretically assumed; that is, when vapor leaves the surface of a liquid, it is pure and saturated at the particular temperature and pressure. In actuality, tiny liquid droplets escape with the vapor. When a mixture of liquid and vapor exists, the ratio of the mass of the liquid to the total mass of the liquid and vapor mixture is called the quality, and is expressed as a percentage or decimal fraction. Superheated vapor is the saturated vapor to which additional heat has been added, raising the temperature above the boiling point. Let us consider a mass m with a quality x. The volume is the sum of the volumes of both the liquid and the vapor, as defined below:

(1.10)

Equation (1.10) can also be written in terms of specific volumes as

      (1.11)

      Dividing all terms by the total mass yields

(1.12)

      where v_liq,vap = v_vap − v_liq.

      1.4.8 Thermodynamic Tables

The thermodynamic tables were first published in 1936 as steam tables by Keenan and Keyes, and later in 1969 and 1978, these were revised and republished. The use of thermodynamic tables of many substances ranging from water to refrigerants is very common in process design calculations. In the literature, they are also called either steam tables or vapor tables. In this book, we will refer to them as thermodynamic tables. These tables are normally given as different distinct phases (parts), for example, four different parts for water, such as saturated water, superheated vapor water, compressed liquid water, saturated solid–saturated vapor water; and two distinct parts for R‐134a, such as saturated and superheated. Each table is listed according to the values of temperature and pressure, with the remainder containing values of various other thermodynamic parameters such as specific volume, internal energy, enthalpy, and entropy. Normally, when we have values for two independent variables, we may obtain other data from the respective table. In learning how to use these tables, an important point is to specify the state using any two independent parameters. In some design calculations if we do not have the exact values of the parameters, we use interpolation to find the necessary values.

      Beyond thermodynamic tables, recently, much attention has been paid to computerized tables for such design calculations. Although computerized tables can eliminate several reading problems for data, they may provide students neither an understanding of the concepts nor a good comprehension of the subject. That is why in thermodynamics courses, it is important for the students to know how to obtain thermodynamic data from the appropriate thermodynamic tables. The Handbook of Thermodynamic Tables by Raznjevic [1] is one of the most valuable sources for several solids, liquids, and gaseous substances.

      1.4.9 State and Change of State

The state of a system or substance is defined as the condition of the system or substance characterized by certain observable macroscopic values of its properties, such as temperature and pressure. The term state is often used interchangeably with the term phase, for example, solid phase or gaseous phase of a substance. Each of the properties of a substance in a given state has only one definite value, regardless of how the substance reaches the state. For example, when sufficient heat is added or removed at a certain condition, most substances undergo a state change. The temperature remains constant until the state change is complete. This can be from solid to liquid, liquid to vapor, or vice versa. Figure 1.2 depicts typical examples of ice melting and water boiling.

A clearer presentation of solid, liquid, and vapor phases of water is provided on a temperature–volume (T–v) diagram in Figure 1.3. The constant pressure line ABCD represents the states that water passes through as follows:

       A–B: Represents the process where water is heated from the initial temperature to the saturation temperature (liquid) at constant pressure. At point B, the water is a fully saturated liquid with a quality x = 0, but no water vapor has formed.

       B–C: Represents a constant‐temperature vaporization process in which there is only phase change from a saturated liquid to a saturated vapor. As this process proceeds, the vapor quality varies from 0 to 100%. Within this zone, the water is a mixture of liquid and vapor. At point C, we have a completely saturated vapor and the quality is 100%.

       C–D: Represents the constant‐pressure process in which the saturated water vapor is superheated with increasing temperature.

       E–F–G: Represents a nonconstant‐temperature vaporization process. In this constant‐pressure heating process, point F is called the critical point where the saturated liquid and saturated vapor states are identical. The thermodynamic properties at this point are called critical thermodynamic properties, for example, critical temperature, critical pressure, and critical specific volume.Figure 1.2 The state‐change diagram of water.Figure 1.3 Temperature–volume diagram for the phase change of water.

       H–I: Represents a constant‐pressure heating process in which there is no change from one phase to another (only one is present). However, there is a continuous change in density during this process.

      The other process which may occur during melting of water is sublimation, in which the ice directly passes from the solid phase to the vapor phase. Another important point is that the solid, liquid, and vapor phases of water may be present together in equilibrium, leading to the triple point.

      1.4.10 Specific Internal Energy

Internal energy represents a molecular state type of energy. Specific internal energy is a measure per unit mass of the energy of a simple system in equilibrium as a function of c_vdT. For many thermodynamic processes in closed systems, the only significant energy changes are internal energy changes, and the significant work done by the system in the absence of friction is the work of pressure–volume expansion, such as in a piston–cylinder mechanism. The specific internal energy of a mixture of liquid and vapor can be written in a form similar to Eq. (1.12):

      (1.13)

      where, u_liq,vap = u_vap − u_liq.

      1.4.11 Specific Enthalpy

      Enthalpy is another measure of the energy