Thermodynamics: An Engineering Approach 9th Edition Yunus A. Cengel, Michael A. Boles, Mehmet Kanoglu McGraw-Hill Education, 2019 Chapter 3 PROPERTIES OF PURE SUBSTANCES Copyright McGraw-Hill Education. Permission

required for reproduction or display. Objectives Introduce the concept of a pure substance. Discuss the physics of phase-change processes. Illustrate the P-v, T-v, and P-T property diagrams and P-v-T surfaces of pure substances. Demonstrate the procedures for determining thermodynamic properties of pure substances from tables of property data. Describe the hypothetical substance ideal gas and the ideal-gas equation of state. Apply the ideal-gas equation of state in the solution of typical

problems. Introduce the compressibility factor, which accounts for the deviation of real gases from ideal-gas behavior. Present some of the best-known equations of state. 2 PURE SUBSTANCE Pure substance: A substance that has a fixed chemical composition throughout. Air is a mixture of several gases, but it is considered to be a pure substance.

FIGURE 31 Nitrogen and gaseous air are pure substances. FIGURE 32 A mixture of liquid and gaseous water is a pure substance, but a mixture of liquid and gaseous air is not. 3 PHASES OF A PURE

SUBSTANCE FIGURE 33 The molecules in a solid are kept at their positions by the large springlike inter-molecular forces. FIGURE 34

The arrangement of atoms in different phases: (a) molecules are at relatively fixed positions in a solid, (b) groups of molecules move about each other in the liquid phase, and (c) molecules move about at random in the gas phase.. 4 PHASE-CHANGE PROCESSES OF PURE SUBSTANCES Compressed liquid (subcooled liquid): A substance that it is not

about to vaporize FIGURE 35 At 1 atm and 20C, water exists in the liquid phase (compressed liquid). 5 Saturated liquid: A liquid that is about to vaporize FIGURE 36 At 1 atm pressure and 100C, water

exists as a liquid that is ready to vaporize (saturated liquid). 6 Saturated liquidvapor mixture: The state at which the liquid and vapor phases coexist in equilibrium. FIGURE 37 As more heat is transferred, part of the saturated liquid vaporizes (saturated

liquidvapor mixture). 7 Saturated vapor: A vapor that is about to condense. FIGURE 38 At 1 atm pressure, the temperature remains constant at 100C until the last drop of liquid is vaporized (saturated vapor).

8 Superheated vapor: A vapor that is not about to condense (i.e., not a saturated vapor). FIGURE 39 As more heat is transferred, the temperature of the vapor starts to rise (superheated vapor). 9

If the entire process between state 1 and 5 is reversed by cooling the water while maintaining the pressure at the same value, the water will go back to state 1, retracing the same path, and in so doing, the amount of heat released will exactly match the amount of heat added during the heating process. FIGURE 310 T-v diagram for the heating process of water at constant pressure. 10

Saturation Temperature and Saturation Pressure The temperature at which water starts boiling depends on the pressure; therefore, if the pressure is fixed, so is the boiling temperature. Water boils at 100C at 1 atm pressure. Saturation temperature Tsat: The temperature at which a pure substance changes

phase at a given pressure. Saturation pressure Psat: The pressure at which a pure substance changes phase at a given temperature. FIGURE 311 The liquidvapor saturation curve of a pure substance (numerical values are for water). 11

12 Latent heat: The amount of energy absorbed or released during a phasechange process. Latent heat of fusion: The amount of energy absorbed during melting. It is equivalent to the amount of energy released during freezing. Latent heat of vaporization: The amount of energy absorbed during vaporization and it is equivalent to the energy released during condensation.

The magnitudes of the latent heats depend on the temperature or pressure at which the phase change occurs. At 1 atm pressure, the latent heat of fusion of water is 334 kJ/kg and the latent heat of vaporization is 2257 kJ/kg. The atmospheric pressure, and thus the boiling temperature of water, decreases with elevation. 13 Some

Consequences of Tsat and Psat Dependence FIGURE 312 The temperature of liquid nitrogen exposed to the atmosphere remains constant at 196C, and thus it maintains the test chamber at 196C. 14 FIGURE 313

The variation of the temperature of fruits and vegetables with pressure during vacuum cooling from 25C to 0C. 15 FIGURE 314 In 1775, ice was made by evacuating the airspace in a water tank. 16

PROPERTY DIAGRAMS FOR PHASE-CHANGE PROCESSES The variations of properties during phase-change processes are best studied and understood with the help of property diagrams such as the T-v, P-v, and P-T

diagrams for pure substances. FIGURE 315 T-v diagram of constant-pressure phase-change processes of a pure substance at various pressures (numerical values are for water). 17

Critical point: The point at which the saturated liquid and saturated vapor states are identical. FIGURE 316 At supercritical pressures (P > Pcr), there is no distinct phase-change (boiling) process.

18 Saturated liquid line Saturated vapor line Compressed liquid region Saturated liquid vapor mixture region (wet region) Superheated vapor region

FIGURE 317 Property diagrams of a pure substance. 19 FIGURE 318 The pressure in a pistoncylinder device can be reduced by reducing the weight of the piston. FIGURE 317 Property diagrams of a pure substance.

20 Extending the Diagrams to Include the Solid Phase FIGURE 319 P-v diagrams of different substances. 21 For water,

Ttp = 0.01C Ptp = 0.6117 kPa FIGURE 320 At triple-point pressure and temperature, a substance exists in three phases in equilibrium. 22 Sublimation: Passing from the solid phase directly into the vapor phase.

FIGURE 321 At low pressures (below the triplepoint value), solids evaporate without melting first (sublimation). 23 Phase Diagram FIGURE 322 P-T diagram of pure substances. 24

The P-v-T surfaces present a great deal of information at once, but in a thermodynamic analysis it is more convenient to work with two-dimensional diagrams, such as the P-v and T-v diagrams. FIGURE 323 P-v-T surface of a substance that contracts on freezing. FIGURE 324 P-v-T surface of a substance that expands on freezing (like water). 25

PROPERTY TABLES For most substances, the relationships among thermodynamic properties are too complex to be expressed by simple equations. Therefore, properties are frequently presented in the form of tables. Some thermodynamic properties can be measured easily, but others cannot and are calculated by using the relations between them and measurable properties. The results of these measurements and calculations are presented in tables in a convenient format.

26 EnthalpyA Combination Property FIGURE 325 The combination u + Pv is often encountered in the analysis of control volumes. FIGURE 326 The product pressure X volume

has energy units. 27 Saturated Liquid and Saturated Vapor States FIGURE 327 A partial list of Table A4. Table A4: Saturation properties of water under temperature. Table A5: Saturation properties of water under pressure.

28 Enthalpy of vaporization, (Latent heat of vaporization) hfg The amount of energy needed to vaporize a unit mass of saturated liquid at a given temperature or pressure. It represents the amount of energy needed to vaporize a unit mass of saturated liquid at a given temperature or pressure. It decreases as the temperature or pressure

increases and becomes zero at the critical point. 29 FIGURE 328 Schematic and T-v diagram for Example 31. FIGURE 330 Schematic and P-v diagram for Example 33. Examples: Saturated

FIGURE 329 Schematic and P-v diagram for Example 32. liquid and saturated vapor states of water on T-v and P-v diagrams. 30 Saturated LiquidVapor Mixture Quality, x : The ratio of the mass of vapor to the total mass of the mixture. Quality is between 0 and 1

0: sat. liquid, 1: sat. vapor. The properties of the saturated liquid are the same whether it exists alone or in a mixture with saturated vapor. Temperature and pressure are dependent properties for a mixture. FIGURE 331 The relative amounts of liquid and vapor phases in a saturated mixture

are specified by the quality x. 31 FIGURE 332 A two-phase system can be treated as a homogeneous mixture for convenience. 32 y

v, u, or h FIGURE 333 Quality is related to the horizontal distances on P-v and T-v diagrams. 33 FIGURE 334 The v value of a saturated liquid vapor mixture lies between the vf and vg values at the specified T or P.

34 Examples: Saturated liquid-vapor mixture states on T-v and P-v diagrams. FIGURE 335 Schematic and T-v diagram for Example 34. FIGURE 336 Schematic and P-v diagram for Example 35.

35 Superheated Vapor Compared to saturated vapor, superheated vapor is characterized by In the region to the right of the saturated vapor line and at temperatures above the critical point temperature, a substance exists as superheated vapor. In this region, temperature and pressure are independent properties.

FIGURE 339 At a specified P, superheated vapor exists at a higher h than the saturated vapor (Example 37). 36 FIGURE 337 A partial listing of Table A6. 37

Compressed Liquid Compressed liquid is characterized by The compressed liquid properties depend on temperature much more strongly than they do on pressure. y v, u, or h

A more accurate relation for h FIGURE 341 Schematic and T-u diagram for Example 38. 38 FIGURE 340 A compressed liquid may be approximated as a saturated liquid at the given temperature.

39 FIGURE 342 At a given P and T, a pure substance will exist as a compressed liquid if T < Tsat @ P. 40 Reference State and Reference Values The values of u, h, and s cannot be measured directly, and they are calculated from measurable properties using the relations between properties.

However, those relations give the changes in properties, not the values of properties at specified states. Therefore, we need to choose a convenient reference state and assign a value of zero for a convenient property or properties at that state. The reference state for water is 0.01C and for R-134a is -40C in tables. Some properties may have negative values as a result of the reference state chosen. Sometimes different tables list different values for some properties at the same state as a result of using a different reference state. However, In thermodynamics we are concerned with the changes in properties, and the reference state chosen is of no consequence in calculations.

41 42 THE IDEAL-GAS EQUATION OF STATE Equation of state: Any equation that relates the pressure, temperature, and specific volume of a substance. The simplest and best-known equation of state for substances in the gas phase is the ideal-gas equation of state. This equation predicts the P-v-T behavior of a gas quite accurately within some properly selected region. Ideal gas equation of state

R gas constant M molar mass (kg/kmol) Ru universal gas constant 43 FIGURE 343 Different substances have different gas constants. 44

Mass = Molar mass Mole number Various expressions of ideal gas equation Ideal gas equation at two states for a fixed mass Real gases behave as an ideal gas at low densities (i.e., low pressure, high temperature).

FIGURE 344 Properties per unit mole are denoted with a bar on the top. 45 Is Water Vapor an Ideal Gas? At pressures below 10 kPa, water vapor can be treated as an ideal gas, regardless of its temperature, with negligible error (less than 0.1 percent). At higher pressures, the ideal gas assumption yields unacceptable errors, particularly in the vicinity of the critical point and the saturated vapor line.

In air-conditioning applications, the water vapor in the air can be treated as an ideal gas. Why? In steam power plant applications, however, the pressures involved are usually very high; therefore, ideal-gas relations should not be used. 46 FIGURE 346 Percentage of error ([vtable videal/vtable] 100) involved in assuming steam to be an

ideal gas, and the region where steam can be treated as an ideal gas with less than 1 percent error. 47 COMPRESSIBILITY FACTORA MEASURE OF DEVIATION FROM IDEAL-GAS BEHAVIOR Compressibility factor Z A factor that accounts for the deviation of real gases from ideal-gas behavior at a given temperature and pressure. FIGURE 347

The compressibility factor is unity for ideal gases. 48 The farther away Z is from unity, the more the gas deviates from idealgas behavior. Gases behave as an ideal gas at low densities (i.e., low pressure, high temperature). Question: What is the criteria for low pressure and high temperature? Answer: The pressure or temperature of a gas is high or low relative to its critical temperature or pressure.

FIGURE 349 At very low pressures, all gases approach ideal-gas behavior (regardless of their temperature). 49 Reduced pressure Reduced temperature

FIGURE 348 Comparison of Z factors for various gases. Pseudoreduced specific volume 50 FIGURE 350 Gases deviate from the ideal-gas behavior the most in the neighborhood

of the critical point. FIGURE 351 The compressibility factor can also be determined from a knowledge of PR and vR. 51 OTHER EQUATIONS OF STATE The ideal-gas equation of state is very simple, but its range of

applicability is limited. It is desirable to have equations of state that represent the P-v-T behavior of substances accurately over a larger region with no limitations. Such equations are naturally more complicated. Several equations have been proposed.

FIGURE 354 Several equations of state have been proposed throughout history. 52 van der Waals Equation of State This model includes two effects not considered in the ideal-gas model: - the intermolecular attraction forces - the volume occupied by the molecules themselves.

The accuracy of the van der Waals equation of state is often inadequate. FIGURE 355 Critical isotherm of a pure substance has an inflection point at the critical state. 53 Beattie-Bridgeman Equation of State The constants are given in Table 34

for various substances. It is known to be reasonably accurate for densities up to about 0.8cr. 54 Benedict-Webb-Rubin Equation of State The constants are given in Table 34. This equation can handle substances at densities up to about 2.5 cr. Virial Equation of State

The coefficients a(T), b(T), c(T), and so on, that are functions of temperature alone are called virial coefficients. 55 56 FIGURE 356 Complex equations of state represent the P-v-T behavior of gases more accurately over a wider range.

57 FIGURE 357 Percentage of error involved in various equations of state for nitrogen (% error = [(vtable vequation)/vtable] 100). 58 Summary Pure substance Phases of a pure substance Phase-change processes of pure

substances Property diagrams for phase change processes Property tables The ideal gas equation of state Compressibility factor Other equations of state 59

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