Procedure

1. Tables of Thermodynamic PropertiesbyDr. M. A. HabibProfessor,Mechanical Engineering Department, KFUPM

2. Procedure The procedure of calculating the thermodynamic property is as follows: • Define the state by two independent properties. • Choose SI units tables. • Choose the table of the concerned substance. • Define the region being compressed liquid, saturation or superheated. • Determine the required property from the table.

3. Defining the state • The state is defined by two independent properties. It should be noted that, in the saturation region, P and T are two dependent properties.

4. 3. Calculation of the thermodynamic properties3.1 Saturation region • Given T and x • Example: • Saturation water at T=100 oC and x=0.4. Find P and v. • Solution: • From saturation table at T=100oC, read P= 101.3 kPa, vf = 0.001044 m3/kg and vfg= 1.67185 m3/kg, then: • v= vf + x (vfg) = 0.6698 m3/kg

5. 3.1 Saturation region

6. 3.1 Saturation region_ Given P,x • Given P,x • Example • Saturated water at P= 100 kPa and x=0.6. Find T and v. • Solution • From saturation table at P=100 kParead T= 99.62 oC, vf =0.001043 m3/kgand and vfg= 1.67185 m3/kg . Then

7. 3.1 Saturation region_ Given P,x • v= vf + x (vfg) • = 1.01682 m3/kg

8. 3.1 Saturation region_ Given T,v • Given T,vExample • Saturated R134a at T=10 oC and v=0.02 m3/kg. Find x and P • Solution • From saturation table at T=10oC read P= Psat = 415.8 kPa, vf = 0.000794 m3/kg and vfg= 0.04866 m3/kg, then

9. 3.1 Saturation region_ Given T,v = 0.3947

10. 3.1 Saturation region_ Given P,v • Given P,v Example. • Saturated water at P=100 kPa and v=0.1m3/kg. Determine T and x. • Solution • From saturation table at P=100 kPa read vf = 0.001043 m3/kg and vfg= 1.69296 m3/kg and T= Tsat =99.62 oC. Then:

11. 3.1 Saturation region_ Given P,v

12. Given P, T and Given T,v and T > Tc • Given P, T Since the pressure and temperature are two dependent properties inside the saturation region, therefore, this state is not inside the saturation region • Given T,v and T > Tc The state is not inside the saturation region

13. Interpolation • Interpolation is required when the given property is not found, but instead it lies between two given values in the tables • Example • Given saturated water at T= 102 oC, x=0.4. Determine P and v. T, oC P, kPa vf, m3/kgvfg, m3/kg 100 101.3 0.001044 1.67185 105 120.8 0.001047 1.41831

14. Interpolation • Solution • The available table provides only T=100 oC and T= 105oC as shown. Therefore, the student has to create another table having T = 102 oC as shown in the table below. The values P, vf and vfg at 102 oC can be obtained by interpolation. As an example, P102 can be obtained from the following equation:

15. Interpolation Thus, P102 =109.1 kPa

16. Superheated Region Superheated region • Given P, T Example • Water vapor at • P=1 MPa, • T=300 oC. • Calculate v.

17. Superheated Region • Solution v=0.25794 m3/kg

18. Superheated Region • Given T, v • Example • Water vapor at T=300 oC, v=0.3 m3/kg. Determine P. • Solution

19. Superheated Region Interpolation gives:

20. Superheated Region • Given P, v • Example: • R134a vapor at P=0.8 MPa, v=0.035 m3/kg. Determine T.

21. Superheated Region • Solution Thus T= 98.55oC

22. Double interpolation • Double interpolation • Example • Given water at P= 1.1 MPa, T= 220 oC. • Solution • First, interpolate between v1a and v1b to get v1 • Then, interpolate between v2a and v2b to get v2 • Then, interpolate between v1 and v2 to get v.

23. Double interpolation

24. Compressed-liquid region • Given P,T • Example: • Compressed-liquid water at P=10 MPa and T=100 oC. Find v. • Solution: • From compressed-liquid table, at P = 10 MPa and T= 100 oC read: • v= 0.001039 m3/kg

25. Other Problems (Special cases) • Case of compressed liquid water at low pressure • Example: • Compressed liquid water at P=100 kPa, T=20 oC. Calculate the specific volume.

26. Solution: • The first available pressure in the compressed liquid table is 5000 kPa. Thus P<< 5000 kPa, therefore, the following approximation will be performed: • Using the saturation table, read: • v=vf at T= 20 oC, thus v= 0.001002 m3/kg.

27. Compressed liquid table is not available. • Case of state in the compressed liquid region and the compressed liquid table is not available. • Example: • Compressed liquid R134a at P=1.0 MPa and T=10 oC. Determine v. • Solution

28. Compressed liquid table is not available • The compressed-liquid table is not available, therefore, the following approximation will be performed: • Using the saturation table, read: • v= vf at T=10 oC, thus, v= 0.000794 m3/kg.

29. Close to saturated vapor • A state in the superheated region and close to saturated vapor. • Example • Water vapor at P= 800 kPa and T=180 oC. Determine v. • Solution: • Interpolation between Saturation temperature and T= 200 oC, thus:

31. Thus: Thus v= 0.247 m3/kg

32. Defining the region • Defining the region • The region in which the state lies is determined by its two independent properties. The following are examples. This section is only concerned with defining the region.

33. The properties can then be determined according to the procedures given in Section 3 based on the region being compressed liquid, saturation or superheated.

34. Given (T, x) OR (P, x) • Given (T, x) OR (P, x) • The state has to be inside saturation region because x (having a value between 0 and1) indicates a mixture of liquid and vapor.

35. Given T, v • Given T, v From saturation tables, determine vf and vg at T. The region is determined based on the following conditional table:

36. Given T,v

37. Given T,v • Example: • R134a at T= 0 oC, v= 0.3 m3/kg. Define the region. • Solution: • At T= 0 oC, vf = 0.000773 m3/kg and vg=0.06919 m3/kg, thus v > vg, then, the state is in superheated region.

38. Given P, v Given P, v • From saturation tables determine vf and vg at Psat = P then:

39. Given P, v • Example: • Water at P= 150 kPa, v= 1.0 m3/kg. Define the region. • Solution: • At P= 150 kPa, read vf=0.001053 m3/kg and vg= 1.15933 m3/kg , Thus vf < v < vg , then the state is in the saturation region.

40. Given P, T • Given P, T • One of two alternative methods can be used as follows: • a. Method 1: Starting with temperature: • From saturation tables determine Psat at T, then, according to the following table the region can be determined:

41. Given P, T Example: Water given at 100kPa and 40 oC

42. Given P, T • Solution: • Psat (at T= 40 oC) = 7.384 kPa. Thus, P > Psat, therefore, the state is in the compressed liquid region. • Property diagrams for case of P > Psat (The state is in the compressed-liquid region).

43. Given P, T

44. Given P, T • Example • R134a at 1.0 MPa and T=50 oC. Define the region. • Solution: • From saturation tables, determine Psat (at T= 50 oC). Thus Psat = 1318.1 kPa. Therefore, P< Psat. Then, the state is in the superheated region.

45. Property diagrams for case of P < Psat (The state is in the superheated region).

46. Method 2: Starting with temperature • b. Method 2: Starting with temperature: • From saturation tables determine Tsat at P, then, according to the following table, the region can be determined:

47. Method 2: Starting with temperature • Example: • Water at 300 oC and P=1 MPa. Define the region. • Solution: • From saturation table at P=1 MPa, read Tsat = 179.91oC, thus, T > Tsat . The state is in the superheated region.

48. Method 2: Starting with temperature • Property diagrams for case of T > Tsat (The state is in the superheated region).

49. Method 2: Starting with temperature • Example • Water at 200 oC and P=3 MPa. Define the region. • Solution • From saturation table at P= 3MPa get Tsat = 233.9. Thus, T< Tsat. Therefore, the state is in the compressed-liquid region.

50. Method 2: Starting with temperature • Property diagrams for case of T < Tsat (The state is in the compressed-liquid region.