Chapter 3 Properties of a Pure Substance

1. Chapter 3Properties of a Pure Substance • Three familiar properties of a substance in the previous chapter — • specific volume, • pressure, and • temperature.

2. 3.1 THE PURE SUBSTANCE • has a homogeneous and invariable chemical composition, • exist in more than one phase, and • exist with no change of phase. • Examples : • liquid water, • a mixture of ice and liquid water, • a mixture of gases, such as air • A mixture of liquid air and gaseous air – ( X ) • Because the chemical composition of the liquid phase is different from that of the vapor phase. )

3. Simple Compressible Substances (system) • Those whose surface effects, magnetic effects, and electrical effects are insignificant when dealing with the substances. • But changes in volume, such as those associated with the expansion of a gas in a cylinder, are very important.

4. 3.2 VAPOR–LIQUID–SOLID-PHASE EQUILIBRIUM IN A PURE SUBSTANCE 0.1MPa 20 0C,1kg Heat ,ν Heat, ν 99.6 0C Fig.3.1

5. Saturation Temperature • The temperature at which vaporization takes place at a given pressure. • And this given pressure is called the Saturation Pressure for the given temperature.

6. Fig. 3.2 A vapor-pressure curve for a pure substance Sub-cooled liquid Compressed liquid

7. Saturated liquid (state) • A substance exists as liquid (state) at the saturation temperature and pressure. • Subcooled liquid(Compressed liquid) • If the temperature of the liquid is lower than the saturation temperature for the existing pressure, it is called either a subcooled liquid (implying that the temperature is lower than the saturation temperature for the given pressure) or a compressed liquid (implying that the pressure is greater than the saturation pressure for the given temperature).

8. Quality of substance • When a substance exists as part liquid and part vapor at the saturation temperature,its quality is definedas the ratio of the mass of vapor to the total mass. • Quality has meaning only when the substance is in a saturated state.

9. Saturated vapor • A substance exists as vapor at the saturation temperature. • The quality of dry saturated vaporis 100%.

10. Superheated vaporis the vapor at a temperature greater than the saturation temperature. • Actually, the substances we call gases are highly superheated vapors.

11. oC 20 Fig. 3.3 Temperature–volume diagram for water showing liquid and vapor phases. Supercritical fluid

12. Table 3.1

13. FIGURE 3.4T –v diagram for the two-phase liquid–vapor region to show the quality specific volume relation.

14. To Derivative the Quality, x • V =Vliq+Vvap= mliq v f+mvapv gthen divide the above equation by total mass m,

16. Table 3.2

17. FIGURE 3.5 Pressure temperature diagram for a substance such as water.

18. FIGURE 3.6 Carbon dioxide phase diagram.

19. Fig. 3.7 Water phase diagram.

20. 3.3 INDEPENDENT PROPERTIES OF A PURE SUBSTANCE • The state of a simple compressible pure substance is defined by two independent properties. • For example, if the specific volume and temperature of superheated steam are specified, the state of the steam is determined.

21. A exception, in a saturation state, should be noted. • Consider the saturated-liquid and saturated-vapor states of a pure substance. These two states have the same pressure and the same temperature, but they are definitely not the same state. Therefore, in a saturation state, pressure and temperature are not independent properties. • Two independent properties such as pressure and specific volume or pressure and quality are required to specify a saturation state of a pure substance.

22. A mixture of gases, such as air, has the same characteristics as a pure substance as long as only one phase is present, concerns precisely this point. • The state of air, which is a mixture of gases of definite composition, is determined by specifying two properties as long as it remains in the gaseous phase.

23. oC Pg=1.554 Pg=5.0 Pg=1.0 200 FIGURE 3.8 Listing of the steam tables. 3.4 TABLES OF THERMODYNAMIC PROPERTIES

24. ExampleLet us calculate the specific volume of saturated steam at 200oC having a quality of 70%. • <Solution>Using Eq. 3.1, and looking up Table B.1.3 givesv = 0.3 (0.001 156) +0.7 (0.127 36) = 0.0895 m 3 /kg

25. Example. 3.1

26. Example 3.2

27. continued

28. Example 3.3

29. Example 3.4 (p.412)

30. 3.5 THERMODYNAMIC SURFACES

31. 3.6 THE P–V–T BEHAVIOR OF LOW- AND MODERATE-DENSITY GASES • At very low densities the average distances between molecules is so large that the intermolecular ( IM ) potential energy may effectively be neglected. • In such a case, the particles would be independent of one another, and the situation is referred to as an ideal gas. • Therefore, a very low density gas behaves according to theideal gas equation of state.

32. +

33. Ris a different constant for each particular gas. The value of R for a number of substances is given in Table A.5 of Appendix A.

34. Example 3.5

35. Example 3.6

36. Over what range of density will the idealgas equation of state hold with accuracy? • How much does an actual gas at a givenpressure and temperature deviate from ideal gas behavior?

37. As would be expected, at very low pressure or high temperaturethe error is small and the gas behaviorbecomes closer to the ideal gas model. • But this error becomes severe as the densityincreases (specific volume decreases).

38. FIGURE 3.14 Temperature-specific volume diagram for water that indicates the error in assuming ideal gas for saturated vapor and for superheated vapor.

39. Compressibility factor,Z • A more quantitative study of the question of the ideal-gas approximation • Z =1, for an ideal gas • The deviation of Z from unity is a measure of the deviation of the actual relation from the ideal-gas equation of state.

40. Fig.3.15 Compressibility of nitrogen

41. Is there a way in which we can put all of the substances on a commonbasis? To do so, we “reduce” the properties with respect to the values at the critical point.

43. Example 3.7

44. Example 3.8