Basic Equation

The basic equation for this region is a fundamental equation for the specific Gibbs free energy g. This equation is expressed in dimensionless form, y = g/( RT), and is separated into two parts, an ideal-gas part yo and a residual part yr, so that g P, T)

The equation for the ideal-gas part yo of the dimensionless Gibbs free energy reads

where k = p/p* and t = T*/ T with p* = 1 MPa and T* = 540 K. The coefficients nO and n2 were adjusted in such a way that the values for the specific internal energy and specific entropy in the ideal-gas state relate to Eq. (8). Table 10 contains the coefficients nO and exponents J° of Eq. (16).

Table 10. Numerical values of the coefficients and exponents of the ideal-gas part yo of the dimensionless Gibbs free energy for region 2, Eq. (16)a jo jo

Table 10. Numerical values of the coefficients and exponents of the ideal-gas part yo of the dimensionless Gibbs free energy for region 2, Eq. (16)a

1a

0

- 0.969 276 865 002 17 x 101

6 - 2 0.142 408 191 714 44 x 101

2a

1

0.100 866 559 680 18 x 102

7 - 1 - 0.438 395 113 194 50 x 101

3

- 5

- 0.560 879 112 830 20 x 10"2

8 2 - 0.284 086 324 607 72

4

- 4

0.714 527 380 814 55 x 10"1

9 3 0.212 684 637 533 07 x 10"1

5

- 3

- 0.407 104 982 239 28

If Eq. (16) is incorporated into Eq. (18), instead of the values for n1 and n 0 given above, the following values for these two coefficients must be used: n ° = - 0.969 372 683 930 49 x 101 , n 2 = 0.100 872 759 700 06 x 102.

If Eq. (16) is incorporated into Eq. (18), instead of the values for n1 and n 0 given above, the following values for these two coefficients must be used: n ° = - 0.969 372 683 930 49 x 101 , n 2 = 0.100 872 759 700 06 x 102.

The form of the residual part yr of the dimensionless Gibbs free energy is as follows:

where k = p/p and r = T*/ T with p* = 1 MPa and T* = 540 K. The coefficients ni and exponents Ij and Jt of Eq. (17) are listed in Table 11.

Table 11. Numerical values of the coefficients and exponents of the residual part yr of the dimensionless Gibbs free energy for region 2, Eq. (17)

i

Ii

Ji

ni

1

1

0

- 0.177 317 424 732 13 x 10^2

2

1

1

- 0.178 348 622 923 58 x 10"1

3

1

2

- 0.459 960 136 963 65 x 10"1

4

1

3

- 0.575 812 590 834 32 x 10"1

5

1

6

- 0.503 252 787 279 30 x 10"1

6

2

1

- 0.330 326 416 702 03 x 10"4

7

2

2

- 0.189 489 875 163 15 x 10^3

8

2

4

- 0.393 927 772 433 55 x 10"2

9

2

7

- 0.437 972 956 505 73 x 10"1

10

2

36

- 0.266 745 479 140 87 x 10"4

11

3

0

0.204 817 376 923 09 x 10"7

12

3

1

0.438 706 672 844 35 x 10"6

13

3

3

- 0.322 776 772 385 70 x 10"4

14

3

6

- 0.150 339 245 421 48 x 10^2

15

3

35

- 0.406 682 535 626 49 x 10"1

16

4

1

- 0.788 473 095 593 67 x 10"9

17

4

2

0.127 907 178 522 85 x 10"7

18

4

3

0.482 253 727 185 07 x 10"6

19

5

7

0.229 220 763 376 61 x 10"5

20

6

3

- 0.167 147 664 510 61 x 10"10

21

6

16

- 0.211 714 723 213 55 x 10^2

22

6

35

- 0.238 957 419 341 04 x 102

23

7

0

- 0.590 595 643 242 70 x 10"17

24

7

11

- 0.126 218 088 991 01 x 10"5

25

7

25

- 0.389 468 424 357 39 x 10"1

26

8

8

0.112 562 113 604 59 x 10"10

27

8

36

- 0.823 113 408 979 98 x 10 1

28

9

13

0.198 097 128 020 88 x 10^7

29

10

4

0.104 069 652 101 74 x 10"18

30

10

10

- 0.102 347 470 959 29 x 10"12

31

10

14

- 0.100 181 793 795 11 x 10^8

32

16

29

- 0.808 829 086 469 85 x 10"10

33

16

50

0.106 930 318 794 09

34

18

57

- 0.336 622 505 741 71

35

20

20

0.891 858 453 554 21 x 10^24

36

20

35

0.306 293 168 762 32 x 10"12

37

20

48

- 0.420 024 676 982 08 x 10"5

38

21

21

- 0.590 560 296 856 39 x 10"25

39

22

53

0.378 269 476 134 57 x 10"5

40

23

39

- 0.127 686 089 346 81 x 10"14

41

24

26

0.730 876 105 950 61 x 10^28

42

24

40

0.554 147 153 507 78 x 10"16

43

24

58

- 0.943 697 072 412 10 x 10^6

All thermodynamic properties can be derived from Eq. (15) by using the appropriate combinations of the ideal-gas part yo, Eq. (16), and the residual part yr, Eq. (17), of the dimensionless Gibbs free energy and their derivatives. Relations between the relevant thermodynamic properties and y0 and yr and their derivatives are summarized in Table 12. All required derivatives of the ideal-gas part and of the residual part of the dimensionless Gibbs free energy are explicitly given in Table 13 and Table 14, respectively.

Table 12. Relations of thermodynamic properties to the ideal-gas part yo and the residual part y r of the dimensionless Gibbs free energy and their derivatives a when using Eq. (15) or Eq. (18)

Property

Relation

Specific volume v = (dgld p)T

Specific internal energy u = g- T(dgld T) - p(dgldp) t

0 0

Post a comment