I2 Thermodynamics

Classical thermodynamics represents our understanding of the relationships of energy transport to properties and characteristics of various types of systems. This science allows us to describe the global behavior of energy-sensitive devices. The relationships that can be developed will find application in both fluid-flow and heat-transfer systems.

A thermodynamic system is a region in space that we select for analysis. The boundary of the system must be defined. Usually, the system boundary will coincide with the physical shell of a piece of hardware. A closed system is one where no mass may cross the boundary, whereas an open system, sometimes called a control volume, will generally have mass flowing through it.

We generally divide energy into two categories: stored and transient types of energy. The stored forms are potential, kinetic, internal, chemical, and nuclear. These terms are fairly self-descriptive in that they relate to ways in which the energy is stored. Chemical and nuclear energy represent the energy tied up in the structure of the molecular and atomic compounds themselves. These two types of stored energy presently form the prime energy sources for most industrial and utility applications and thus are of great importance to us.

Potential, kinetic, and internal energy forms generally are nonchemical and nonnuclear in nature. They relate to the position, velocity, and state of material in a thermodynamic system. More detailed representations of these energy forms will be shown later.

I.2.1 Properties and States

Thermodynamic systems are a practical necessity for the calculation of energy transformations. But to do this, certain characteristics of the system must be defined in a quantifiable way. These characteristics are usually called properties of the system. The properties form the basis of the state of the system. A state is the overall nature of the system defined by a unique relationship between properties.

Properties are described in terms of four fundamental quantities: length, mass, time, and temperature. Mass, length, and time are related to a force through Newton's second law.

In addition to the fundamental quantities of a system there are other properties of thermodynamic importance. They are pressure, volume, internal energy, enthalpy, and entropy—P, V, U, H, and S, respectively.

Equation of State. Returning to the concept of a state, we use an equation of state to relate the pertinent properties of a system. Generally, we use P = P(m, V, T) as the functional equation of state. The most familiar form is the ideal gas equation of state written as or

Equation I.1 is based on the mass in a system, whereas equation 1.2 is molal-based. R is called the gas constant and is unique to a particular gas. R, on the other hand, is called the universal gas constant and retains the same value regardless of the gas (i.e., R = 1545 ft lbf/lbm • mol • °R = 1.9865 Btu/lbm • mol • °R. It can be easily shown that R is simply R/M, where M is the molecular weight of the gas.

The ideal gas equation is useful for superheated but not for saturated vapors. A vexing question that often arises is what is the range of application of the ideal gas equation. Figure I.1 shows the limits of appli-

pressures. This uses the concept that the volume of a system is occupied by all the components. Using a two-component system as an example, we write

P1V1 = n1RT1

and P2V2 = niRT 2


Since V, R, and T are the same for all three equations above, we see that

Fig. I.1 Applicability of ideal gas equation of state.

cability. The shaded areas demonstrate where the ideal gas equation applies to within 10% accuracy.

If high pressures or vapors near saturation are involved, other means of representing the equation of state are available. The compressibility factor Z for example Z = PV/RT, is a means of accounting for nonideal gas conditions. Several other techniques are available; see Ref. 1 for example.

Changes of state for materials that do not behave in an ideal way can be calculated by use of generalized charts for property changes. For example, changes in enthalpy and entropy can be presented in terms of reduced pressure and temperature, Pr and Tr. The reduced properties are the ratio of the actual to the critical properties. These charts (see Appendix II) can be used to calculate the property changes for any change in state for those substances whose thermophysical properties are well documented.

Ideal Gas Mixtures. Where several gases are mixed, a way to conveniently represent the properties of the mixture is needed. The simplest way is to treat the system as an ideal gas mixture. In combustion systems where fuel vapor and air are mixed, and in the atmosphere where oxygen nitrogen and water vapor form the essential elements of air, the concept of the ideal gas mixture is very useful.

There are two ways to represent gas mixtures. One is to base properties on mass, called the gravimetric approach. The second is based on the number of moles in a system, called a molal analysis. This leads to the definition of a mass fraction, Xi = mjmt, where m.[ is the mass of the ¿th component in the mixture and mt is the total mass of the system, and the mole fraction, y = njnt, where n represents the number of moles.

Commonly, the equation of state for an ideal mixture involves the use of Dalton's law of additive and

for a mixture. Each gas in the mixture of ideal gases then behaves in all respects as though it exists alone at the volume and temperature of the total system.

1.2.2 Thermodynamic Processes

A transformation of a system from one state to another is called a process. A cycle is a set of processes by which a system is returned to its initial state. Thermo-dynamically, it is required that a process be quantifiable by relations between properties if an analysis is to be possible.

A process is said to be reversible if a system can be returned to its initial state along a reversed process line with no change in the surroundings of the system. In actual practice a reversible process is not possible. All processes contain effects that render them irreversible. For example, friction, nonelastic deformation, turbulence, mixing, and heat transfer are all effects that cause a process to be irreversible. The reversible process, although impossible, is valuable, because it serves as a reference value. That is, we know that the ideal process is a theoretical limit toward which we can strive by minimizing the irreversible effects listed above.

Many processes can be described by a phrase which indicates that one of its properties or characteristics remains constant during the process. Table I.1 shows the more common of these processes together with expressions for work, heat transfer, and entropy change for ideal gases.

1.2.3 Thermodynamic Laws

Thermodynamic laws are relationships between mass and energy quantities for both open and closed systems. In classical form they are based on the conservation of mass for a system with no relativistic effects. Table 1.2 shows the conservation-of-mass relations for

Table I.1 Ideal Gas Processes0


Describing Equations

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