2 CHAPTER Properties of Pure Substances

Constant-Pressure Phase-Change Process 2-1 Constant-Pressure Phase-Change Process (fig. 2-16)

T-v Diagram of a Pure Substance 2-2 T-v Diagram of a Pure Substance Energy, not mass, crosses closed-system boundaries (Fig. 2-18)

P-v Diagram of a Pure Substance 2-3 P-v Diagram of a Pure Substance (Fig. 2-19) SUPERHEATED

P-v Diagram of Substance that Contracts on Freezing 2-4 P-v Diagram of Substance that Contracts on Freezing (Fig. 2-21)

P-v Diagram of Substance that Expands on Freezing 2-5 P-v Diagram of Substance that Expands on Freezing (Fig. 2-22)

P-T Diagram of Pure Substances 2-6 P-T Diagram of Pure Substances (Fig. 2-25)

P-v-T Surface of a Substance that Contracts on Freezing 2-7 P-v-T Surface of a Substance that Contracts on Freezing (Fig. 2-26)

P-v-T Surface of a Substance that Expands on Freezing 2-8 P-v-T Surface of a Substance that Expands on Freezing (Fig. 2-27)

Partial List of Table A-4 2-9 Partial List of Table A-4 (Fig. 2-35)

Quality Shown in P-v and T-v Diagrams 2-10 Quality Shown in P-v and T-v Diagrams Quality is related to the horizontal differences of P-V and T-v diagrams (Fig. 2-41)

Partial List of Table A-6 2-11 Partial List of Table A-6 (Fig. 2-45)

Pure Substances can Exist as Compressed Liquids 2-12 Pure Substances can Exist as Compressed Liquids At a given P and T, a pure substance will exist as a compressed liquid if T<T sat @ P (Fig. 2-49)

The Region Where Steam can be Treated as an Ideal Gas 2-13 The Region Where Steam can be Treated as an Ideal Gas (Fig. 2-54)

Comparison of Z Factors for Various Gases 2-14 Comparison of Z Factors for Various Gases (Fig. 2-57)

Percent of Error in Equations for the State of Nitrogen 2-15 Percent of Error in Equations for the State of Nitrogen (Fig. 2-66)

2-16 Chapter Summary A substance that has a fixed chemical composition throughout is called a pure substance.

2-17 Chapter Summary A pure substance exists in different phases depending on its energy level. In the liquid phase, a substance that is not about to vaporize is called a compressed or subcooled liquid.

2-18 Chapter Summary In the gas phase, a substance that is not about to condense is called a superheated vapor.

2-19 Chapter Summary During a phase-change process, the temperature and pressure of a pure substance are dependent properties. At a given pressure, a substance changes phase at a fixed temperature, called the saturation temperature. At a given temperature, the pressure at which a substance changes phase is called the saturation pressure. During a boiling process, both the liquid and the vapor phases coexist in equilibrium, and under this condition the liquid is called saturated liquid and the vapor saturated vapor.

2-20 Chapter Summary In a saturated liquid-vapor mixture, the mass fraction of the vapor phase is called the quality and is defined as The quality may have values between 0 (saturated liquid) and 1 (saturated vapor). It has no meaning in the compressed liquid or superheated vapor regions.

2-21 Chapter Summary In the saturated mixture region, the average value of any intensive property y is determined from where f stands for saturated liquid and g for saturated vapor.

2-22 Chapter Summary In the absence of compressed liquid data, a general approximation is to treat a compressed liquid as a saturated liquid at the given temperature, that is, where y stands for v, u, or h.

2-23 Chapter Summary The state beyond which there is no distinct vaporization process is called the critical point. At supercritical pressures, a substance gradually and uniformly expands from the liquid to vapor phase.

2-24 Chapter Summary All three phases of a substance coexist in equilibrium at states along the triple line characterized by triple-line temperature and pressure.

2-25 Chapter Summary Various properties of some pure sub-stances are listed in the appendix. As can be noticed from these tables, the compressed liquid has lower v, u, and h values than the saturated liquid at the same T or P. Likewise, superheated vapor has higher v, u, and h values than the saturated vapor at the same T or P. is a major application area of thermodynamics.

2-26 Chapter Summary Any relation among the pressure, temperature, and specific volume of a substance is called an equation of state. The simplest and best-known equation of state is the ideal-gas equation of state, given as where R is the gas constant. Caution should be exercised in using this relation since an ideal gas is a fictitious substance. Real gases exhibit ideal-gas behav-ior at relatively low pressures and high temperatures.

2-27 Chapter Summary The deviation from ideal-gas behavior can be properly accounted for by using the compressibility factor Z, defined as

(Continued on next slide) 2-28 Chapter Summary The Z factor is approximately the same for all gases at the same reduced temperature and reduced pressure, which are defined as where Pcr and Tcr are the critical pressure and temperature, respectively. This is known as the principle of corresponding states. (Continued on next slide)

These charts show the conditions for which Z = 1 and the gas behaves as an ideal gas: 1. PR < 10 and TR > 2 or P < 10Pcr and T > 2Tcr 2. PR << 1 or P << Pcr Note: When PR is small, we must make sure that the state is not in the compressed liquid region for the given temperature. A compressed liquid state is certainly not an ideal gas state.

Example 2-6 Calculate the specific volume of nitrogen at 300 K and 8.0 Mpa and compare the result with the value given in a nitrogen table as v = 0.011133 m3/kg. From Table A.1 for nitrogen Tcr = 126.2 K, P cr = 3.39 MPa R = 0.2968 kJ/kg-K Since T > 2T cr and P < 10P cr, we use the ideal gas equation of state Nitrogen is clearly an ideal gas at this state

(Continued from previous slide) 2-29 Chapter Summary (Continued from previous slide) When either P or T is unknown, Z can be determined from the compressibility chart with the help of the pseudo-reduced specific volume, defined as

2-30 Chapter Summary The P-v-T behavior of substances can be represented more accurately by the more complex equations of state. Three of the best known are van der Waals: where

2-31 Chapter Summary Beattie-Bridgeman: where

Chapter Summary Benedict-Webb-Rubin: 2-32 The constants appearing in the Beattie-Bridgeman and Benedict-Webb-Rubin equations are given in Table A-29 for various substances.