Introduction to Thermal Systems...echanics, and Heat Transfer.rar - c04

Introduction to Thermal Systems...echanics, and Heat Transfer.rar - c04

(Parte 1 de 7)



To apply the energy balance to a system of interest requires knowledge of the properties of the system and how the properties are related. The objectiveof this chapter is to introduce property relations relevant to engineering thermodynamics. As part of the presentation,several examples are provided that illustrate the use of the closed system energy balance introduced in Chap. 3 together with the property relations considered in this chapter.

Fixing the State

The state of a closed system at equilibrium is its condition as described by the values of its thermodynamic properties. From observation of many systems,it is known that not all of these properties are independent of one another,and the state can be uniquely determined by giving the values of the independentproperties. Values for all other thermodynamic properties can be determined once this independent subset is specified. A general rule known as the state principlehas been developed as a guide in determining the number of independent properties required to fix the state of a system.

For most applications,we are interested in what the state principle says about the intensive states of systems. Of particular interest are systems of commonly encountered substances,such as water or a uniform mixture of nonreacting gases. These systems are classed as simple compressible systems.Experience shows that the simple compressible systems model is useful for a wide range of engineering applications. For such systems,the state principle indicates that the number of independent intensive properties is two.

For Example…in the case of a gas,temperature and another intensive property such as specific volume might be selected as the two independent properties. The state principle then affirms that pressure,specific internal energy,and all other pertinent intensiveproperties could be determined as functions of Tand v:p p(T,v),u u(T,v),and so on. The functional relations would be developed using experimental data and would depend explicitly on the particular chemical identity of the substances making up the system.

Intensive properties such as velocity and elevation that are assigned values relative to datums outsidethe system are excluded from present considerations.Also,as suggested by the name,changes in volume can have a significant influence on the energy of simple compressible systems.The only mode of energy transfer by work that can occur as a simple compressible system undergoes quasiequilibriumprocesses,is associated with volume change and is given by p dV.

4.1 chapter objective state principle simple compressible systems

Evaluating Properties: General Considerations

This part of the chapter is concerned generally with the thermodynamic properties of simple compressible systems consisting of puresubstances. A pure substance is one of uniform and invariable chemical composition. Property relations for systems in which composition changes by chemical reaction are not considered in this book. In the second part of this chapter,we consider property evaluation using the ideal gas model.

p–v–T Relation

We begin our study of the properties of pure,simple compressible substances and the relations among these properties with pressure,specific volume,and temperature. From experiment it is known that temperature and specific volume can be regarded as independent and pressure determined as a function of these two:p p(T,v). The graph of such a function is a surface,the p–v–Tsurface.

4.2.1 p–v–T Surface

Figure 4.1 is the p–v–Tsurface of water. Since similarities exist in the p–v–Tbehavior of most pure substances,Fig. 4.1 can be regarded as representative. The coordinates of a point on the p–v–Tsurface represents the values that pressure,specific volume,and temperature would assume when the substance is at equilibrium.

There are regions on the p–v–Tsurface of Fig. 4.1labeled solid,liquid,and vapor. In these single-phaseregions,the state is fixed by anytwo of the properties:pressure,specific volume,and temperature,since all of these are independent when there is a single phase present. Located between the single-phase regions are two-phase regionswhere two phases exist in equilibrium:liquid–vapor,solid–liquid,and solid–vapor. Two phases can coexist during changes in phase such as vaporization,melting,and sublimation. Within the two-phase regions,pressure and temperature are not independent; one cannot be changed without changing the other. In these regions the state cannot be fixed by temperature and pressure alone; however,the state can be fixed by specific volume and either pressure or temperature. Three phases can exist in equilibrium along the line labeled triple line.

A state at which a phase change begins or ends is called a saturation state.The domeshaped region composed of the two-phase liquid–vapor states is called the vapor dome.The lines bordering the vapor dome are called saturated liquid and saturated vapor lines. At the top of the dome,where the saturated liquid and saturated vapor lines meet,is the critical point.The critical temperatureTcof a pure substance is the maximum temperature at which liquid and vapor phases can coexist in equilibrium. The pressure at the critical point is called the critical pressure,pc. The specific volume at this state is the critical specific volume. Values of the critical point properties for a number of substances are given in Tables T-1 and

T-1E located in the Appendix.

The three-dimensional p–v–Tsurface is useful for bringing out the general relationships among the three phases of matter normally under consideration. However,it is often more convenient to work with two-dimensional projections of the surface. These projections are considered next.

4.2.2Projections of the p–v–TSurface

The Phase Diagram

If the p–v–Tsurface is projected onto the pressure–temperature plane,a property diagram known as a phase diagramresults. As illustrated by Fig. 4.1b,when the surface is projected two-phase regions triple line saturation state vapor dome critical point phase diagram in this way,the two-phase regionsreduce to lines. A point on any of these lines represents all two-phase mixtures at that particular temperature and pressure.

The term saturation temperaturedesignates the temperature at which a phase change takes place at a given pressure,and this pressure is called the saturation pressurefor the given temperature. It is apparent from the phase diagrams that for each saturation pressure there is a unique saturation temperature,and conversely.

The triple lineof the three-dimensional p–v–Tsurface projects onto a pointon the phase diagram. This is called the triple point.Recall that the triple point of water is used as a reference in defining temperature scales (Sec. 2.5.4). By agreement, the temperature assigned to the triple point of water is 273.16 K (491.69 R). The measuredpressure at the triple point of water is 0.6113 kPa (0.00602 atm).

The line representing the two-phase solid–liquid region on the phase diagram,Fig. 4.1b, slopes to the left for substances such as water that expand on freezing and to the right for those that contract. Although a single solid phase region is shown on the phase diagram,


Specif ic v olume Temperature


Liquid apor

Solid-v apor

Triple line Vapor Tc

Critical point

Pressure Pressure

Temperature Specific volume (b)( c)

Critical point


LiquidSolid Critical point

VaporL V

V STriple pointTriple line


VaporSolid T > Tc

Tc T < Tc

Figure 4.1p–v–Tsurface and projections for water (not to scale). (a) Three-dimensional view. (b) Phase diagram. (c) p–vdiagram.

saturation temperature saturation pressure triple point

solids can exist in different solid phases. For example,seven different crystalline forms have been identified for water as a solid (ice).

p–v Diagram

Projecting the p–v–Tsurface onto the pressure–specific volume plane results in a p–v diagram,as shown by Fig. 4.1c. The figure is labeled with terms that have already been introduced.

When solving problems,a sketch of the p–vdiagram is frequently convenient. To facilitate the use of such a sketch,note the appearance of constant-temperature lines (isotherms). By inspection of Fig. 4.1c,it can be seen that for any specified temperature less thanthe critical temperature,pressure remains constant as the two-phase liquid–vapor region is traversed,but in the single-phase liquid and vapor regions the pressure decreases at fixed temperature as specific volume increases. For temperatures greater than or equal to the critical temperature,pressure decreases continuously at fixed temperature as specific volume increases. There is no passage across the two-phase liquid–vapor region. The critical isotherm passes through a point of inflection at the critical point and the slope is zero there.

T–v Diagram

Projecting the liquid,two-phase liquid–vapor,and vapor regions of the p–v–Tsurface onto the temperature–specific volume plane results in a T–vdiagram as in Fig. 4.2.

As for the p–vdiagram,a sketch of the T–vdiagram is often convenient for problem solving. To facilitate the use of such a sketch,note the appearance of constant-pressure lines (isobars). For pressures less thanthe critical pressure,such as the 10 MPa isobar on Fig.4.2,the pressure remains constant with temperature as the two-phase region is traversed. In the singlephase liquid and vapor regions,the temperature increases at fixed pressure as the specific volume increases. For pressures greater than or equal to the critical pressure,such as the one marked 30 MPa on Fig. 4.2,temperature increases continuously at fixed pressure as the specific volume increases. There is no passage across the two-phase liquid–vaporregion.

The projections of the p–v–Tsurface used in this book to illustrate processes are not generally drawn to scale. A similar comment applies to other property diagrams introduced later.

4.2.3Studying Phase Change

It is instructive to study the events that occur as a pure substance undergoes a phase change. To begin,consider a closed system consisting of a unit mass (1 kg or 1 lb) of liquid water

(68°F) Specific volume

T emperature Liquid Vapor

10 MPa pc = 2.09 MPa (3204 lbf/in.2) 30 MPa l f g


Critical point

100°C (212°F)Figure 4.2Sketch of a temperature–specific volume diagram for water showing the liquid, two-phase liquid–vapor, and vapor regions (not to scale).

at 20 C (68 F) contained within a piston–cylinder assembly,as illustrated in Fig. 4.3a. This state is represented by point l on Fig. 4.2. Suppose the water is slowly heated while its pressure is kept constant and uniform throughout at 1.014 bar (14.7 lbf/in.2).

Liquid States

As the system is heated at constant pressure,the temperature increases considerably while the specific volume increases slightly. Eventually,the system is brought to the state represented by f on Fig. 4.2. This is the saturated liquid state corresponding to the specified pressure. For water at 1.014 bar (14.7 lbf/in.2) the saturation temperature is 100 C (212 F). The liquid states along the line segment l–f of Fig. 4.2are sometimes referred to as subcooled liquidstates because the temperature at these states is less than the saturation temperature at the given pressure. These states are also referred to as compressed liquidstates because the pressure at each state is higher than the saturation pressure corresponding to the temperature at the state. The names liquid,subcooled liquid,and compressed liquid are used interchangeably.

Two-Phase, Liquid–Vapor Mixture

When the system is at the saturated liquid state (state f of Fig. 4.2), additional heat transfer at fixed pressure results in the formation of vapor without any change in temperature but with a considerable increase in specific volume. As shown in Fig. 4.3b,the system would now consist of a two-phase liquid–vapor mixture. When a mixture of liquid and vapor exists in equilibrium,the liquid phase is a saturated liquid and the vapor phase is a saturated vapor. If the system is heated further until the last bit of liquid has vaporized, it is brought to pointg on Fig. 4.2,the saturated vapor state. The intervening two-phase liquid–vapor mixturescan be distinguished from one another by the quality,an intensive property.

For a two-phase liquid–vapor mixture,the ratio of the mass of vapor present to the total mass of the mixture is its quality,x. In symbols,

The value of the quality ranges from zero to unity:at saturated liquid states,x 0,and at saturated vapor states,x 1.0. Although defined as a ratio,the quality is frequently given as a percentage. Examples illustrating the use of quality are provided in Sec. 4.3. Similar parameters can be defined for two-phase solid–vapor and two-phase solid–liquid mixtures.

mliquid mvapor

Figure 4.3Illustration of constant-pressure change from liquid to vapor for water.

subcooled liquid compressed liquid two-phase liquid–vapor mixture quality

Liquid water Water vaporWater vapor

Vapor States

Let us return to a consideration of Figs. 4.2 and 4.3. When the system is at the saturated vapor state (state g on Fig. 4.2), further heating at fixed pressure results in increases in both temperature and specific volume. The condition of the system would now be as shown in Fig. 4.3c. The state labeled s on Fig. 4.2is representative of the states that would be attained by further heating while keeping the pressure constant. A state such as s is often referred to as a superheated vaporstate because the system would be at a temperature greater than the saturation temperature corresponding to the given pressure.

Consider next the same thought experiment at the other constant pressures labeled on

Fig.4.2,10 MPa (1450 lbf/in.2),2.09 MPa (3204 lbf/in.2),and 30 MPa (4351 lbf/in.2). The first of these pressures is less than the critical pressure of water,the second is the critical pressure,and the third is greater than the critical pressure. As before,let the system initially contain a liquid at 20 C (68 F). First,let us study the system if it were heated slowly at 10MPa (1450 lbf/in.2). At this pressure,vapor would form at a higher temperature than in the previous example, because the saturation pressure is higher (refer to Fig. 4.2). In addition,there would be somewhat less of an increase in specific volume from saturated liquid to vapor,as evidenced by the narrowing of the vapor dome. Apart from this,the general behavior would be the same as before. Next,consider the behavior of the system were it heated at the critical pressure,or higher. As seen by following the critical isobar on Fig. 4.2,there would be no change in phase from liquid to vapor. At all states there would be only one phase. Vaporization (and the inverse process of condensation) can occur only when the pressure is less than the critical pressure. Thus,at states where pressure is greater than the critical pressure,the terms liquid and vapor tend to lose their significance. Still,for ease of reference to states where the pressure is greater than the critical pressure,we use the term liquid when the temperature is less than the critical temperature and vapor when the temperature is greater than the critical temperature.

(Parte 1 de 7)