it in relation to some reference state. The usual practice is to determine the reference values that are called the standard enthalpy of formation (or the heat of formation), particularly in combustion thermodynamics. The specific enthalpy of a mixture of liquid and vapor components can be written as Eq. (1.12):
(1.14)
where, hliq,vap = hvap − hliq.
1.4.12 Specific Entropy
Entropy is the ratio of the heat added to a substance to the absolute temperature at which it was added, and is a measure of the molecular disorder of a substance at a given state. The specific enthalpy of a mixture of liquid and vapor components can be written as Eq. (1.12):
(1.15)
where, sliq,vap = svap − sliq.
1.4.13 Pure Substance
A pure substance is defined as the one that has a homogeneous and invariable chemical composition. Despite having the same chemical composition throughout, it may be in more than one phase, namely, liquid, a mixture of liquid and vapor (e.g. steam), and a mixture of solid and liquid. Each phase has the same chemical composition. However, a mixture of liquid air and gaseous air cannot be considered a pure substance because the composition of each phase differs from that of the other. A thorough understanding of the pure substance is of significance, particularly for TES applications. Thermodynamic properties of water and steam can be obtained from tables and charts that are present in most thermodynamics books, based on experimental data or real‐gas equations of state, or obtained through computer calculations. It is important to note that the properties of low‐pressure water are of great significance in TES systems for cooling applications, since water vapor existing in the atmosphere typically exerts a pressure less than 1 psi (6.9 kPa). At such low pressures, it is known that water vapor exhibits ideal‐gas behavior.
1.4.14 Ideal Gases
In many practical thermodynamic calculations, gases such as air and hydrogen can often be treated as ideal gases, particularly for temperatures much higher than their critical temperatures and for pressures much lower than their saturation pressures at given temperatures. An ideal gas can be described in terms of three parameters: the volume it occupies, the pressure it exerts, and its temperature. In fact, all gases or vapors, including water vapor, at very low pressures exhibit ideal‐gas behavior. The practical advantage of treating real gases as ideal is that a simple equation of state with only one constant can be applied in the following form:
and
The ideal‐gas equation of state was originally established from experimental observations, and is also called a P–v–T relationship for gases. It is generally considered as a concept rather than a reality. It requires only a few data values to define a particular gas over a wide range of its possible thermodynamic equilibrium states.
The gas constant R is different for each gas depending on its molecular weight M:
where,
Equations (1.17) and (1.18) may be written on a mole‐basis as follows:
(1.19)
and
(1.20)
The other simplifying feature of ideal‐gas behavior is that, if assumed that the constant‐pressure and constant‐volume specific heats are constant, changes in specific internal energy and specific enthalpy can be calculated simply without referring to thermodynamic tables and graphs from the following expressions:
(1.21)
and
(1.22)
The following is another useful relation for ideal gases obtained from the expression, h = u + Pv = u + RT:
(1.23)
For the entire range of states, the ideal‐gas model may be found unsatisfactory. Therefore, the compressibility factor (Z) is introduced to measure the deviation of a real substance from the ideal‐gas equation of state. The compressibility factor is defined by the relation:
Figure 1.4 shows a generalized compressibility chart for simple substances. In the chart, we have two important parameters: the reduced temperature (Tr = T/Tc) and the reduced pressure (Pr = P/Pc). To calculate the compressibility factor, the values of Tr and Pr should be calculated using the critical temperature and pressure values of the respective substance, which can easily be obtained from thermodynamics books. As can be seen in Figure 1.4, at all temperatures, Z → 1 as Pr → 0. This means that the behavior of the actual gas closely approaches ideal‐gas behavior, as the pressure approaches zero. For real gases, Z takes on values between 0 and 1. If Z = 1, Eq. (1.24) becomes Eq. (1.16). In the literature, there are also several equations of state for accurately representing the P–v–T behavior of a gas over the entire superheated vapor region, for example, the Benedict–Webb–Rubin equation, the van der Waals equation, and the Redlich and Kwong equation. However, some of these equations of state are complicated due to the number
