ENGSC 2333 – Thermodynamics Chapter 3

1. ENGSC 2333 – ThermodynamicsChapter 3

2. Objectives • 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 objective of Chapter 3 is to introduce property relations relevant to engineering thermodynamics. We will focus on the use of the closed system energy balance introduce in Chapter 2, together with the property relations considered in this chapter.

3. State principal Simple compressible system p-υ-T surface 2-phase region Triple line Triple point Saturation state Vapor dome Critical point p-υ diagram T-υ diagram Subcooled (compressed) liquid Superheated vapor 2-phase liquid-vapor mixture Quality Some Concepts and Definitions

4. 3.1 Fixing the State For simple, compressible systems, the state principle indicates that the number of independent intensive properties is two. Intensive properties such as velocity and elevation that are assigned values relative to datum outside the system are excluded from present considerations.

5. 3.2 p-υ-T Relation Figure 3.1

6. Examples Virtual pvT diagram

7. 3.2 Phase Diagram Figure 3.1

8. 3.2 T-υ Diagram

9. 3.2 p-υ Diagram Figure 3.1

10. 3.2.3 Quality For a two-phase liquid-vapor mixture, the ratio of the mass of vapor to the total mass of the mixture is call quality, represented as x.

11. ENGSC 2333 – ThermodynamicsChapter 3

12. 3.3.1 Specific Volume The specific volume of a two-phase liquid-vapor mixture can be determined by using the saturation tables and the definition of quality.

13. 3.3.1 Specific Volume The specific volume of a two-phase liquid-vapor mixture can be determined by using the saturation tables and the definition of quality.

14. 3.3.2 Specific Internal Energy The specific internal energy of a two-phase liquid-vapor mixture can be determined by using the saturation tables and the definition of quality.

15. 3.3.2 Specific Enthalpy In many thermodynamic analyses the sum of the internal energy U and the product of pressure p and volume V appears. Because the sum U + pV appears so frequently, we give this combination a name, enthalpy, and a distinct symbol, H.

16. 3.3.2 Specific Enthalpy The specific internal energy of a two-phase liquid-vapor mixture can be determined by using the saturation tables and the definition of quality.

17. Examples For water at the following conditions, determine the phase or phases present: • T = 40ºC, P = 0.09593 bar • T = 250ºC, P = 39.73 bar, υ = 0.04 m3/kg • T = 250ºC, P = 39.73 bar, υ = 0.0012512 m3/kg • T = 90ºF, υ = 500 ft3/lbm • P = 50 psi, υ = 0.01727 ft3/lbm • P = 50 psi, m = 10 kg

18. 3.3.5 Evaluating specific heats The intensive properties cv and cp are defined for pure, simple compressible substances as partial derivatives of the functions u(T,v) and h(T,p) respectively. We also use the specific heat ratio, k.

19. 3.3.5 Evaluating specific heats Figure 3.9 cp of water vapor

20. 3.3.6 Incompressible substance model Approximations for liquids using saturated liquid data:

21. 3.3.6 Incompressible substance model For a substance modeled as incompressible, the specific heats cv and cp are equal.

22. 3.3.6 Incompressible substance model Assuming the specific heats are constant (not a function of temperature)…

23. 3.4 Generalized compressibility chart The ideal gas law: Where:

24. 3.4 Generalized compressibility chart For ideal gases: Where: Always use absolute pressures and temperatures!!!

25. 3.4 Generalized compressibility chart Universal gas constant: Compressibility factor: Figure 3.10

26. 3.4 Generalized compressibility chart For compressible gases: Where: Always use absolute pressures and temperatures!!!

27. 3.4 Generalized compressibility chart For compressible gases: Where: Always use absolute pressures and temperatures!!!

28. 3.4 Generalized compressibility chart Z values from Figures A-1, A-2, and A-3 in appendices. Figure 3.11

29. 3.4 Generalized compressibility chart The principle of corresponding states: Reduced pressure: Reduced temperature: Figure 3.2

30. 3.4 Generalized compressibility chart The principle of corresponding states: Figure 3.12

31. 3.5 Ideal gas model properties

32. Examples For water at 374.15 ºC and 219.9 bar (gage), determine: • PR • TR • Z Assume Patm=1 bar

33. ENGSC 2333 – ThermodynamicsChapter 3

34. 3.4 Generalized compressibility chart Compressibility factor: Reduced pressured: Reduced temperature:

35. 3.4 Generalized compressibility chart The principle of corresponding states: Figure 3.12

36. 3.4 Generalized compressibility chart Figure 3.3

37. 3.5 Ideal gas model properties

38. 3.5 Ideal gas model properties

39. 3.5 Ideal gas model properties cp in Table A-19 Note: cv not given For monatomic gases, cp=(5/2)R

40. 3.6 U and H of ideal gases

41. 3.6 Specific heat functions Values of the constants are listed in Table A-21.

42. 3.7 Specific heats… simplified Using ideal gas tables (A-22 and A-23)… Evaluate the change in specific enthalpy for air from a state where T1=400 K to a state where T2=900 K.

43. 3.7 Specific heats… simplified Assuming constant specific heats (A-20)… Evaluate the change in specific enthalpy for air from a state where T1=400 K to a state where T2=900 K.

44. 3.8 Polytropic processes of an Ideal Gas For a polytropic process of a closed system…

45. 3.8 Polytropic processes of an Ideal Gas For a polytropic process of a closed system… Isobaric Isothermal Also, when specific heats are constant, the value of the exponent n corresponding to an adiabatic polytropic process of an ideal gas is the specific heat ratio, k.

46. 3.8 Polytropic processes of an Ideal Gas Remember from Chapter 2… Valid for any gas.

47. 3.8 Polytropic processes of an Ideal Gas Using pV=mRT… Valid for ideal gases.