The Backward Equation T p h

The backward equation T ( p, h ) for region 1 has the following dimensionless form:

where 6 = T/T*, fi = p/p*, and V = h/h* with T* = 1 K, p* = 1 MPa, and h* = 2500 kJ kg"1. The coefficients ni and exponents and Ji of Eq. (11) are listed in Table 6.

Table 6. Numerical values of the coefficients and exponents of the backward equation T( p, h) for region 1, Eq. (11)

i

Ii

Ji

ni

i

Ii

Ji

ni

1

0

0

- 0.238 724 899 245 21 x 103

11

1

4

- 0.659 647 494 236 38 x 101

2

0

1

0.404 211 886 379 45 x 103

12

1

10

0.939 654 008 783 63 x 10"2

3

0

2

0.113 497 468 817 18 x 103

13

1

32

0.115 736 475 053 40 x 1r6

4

0

6

- 0.584 576 160 480 39 x 101

14

2

10

- 0.258 586 412 820 73 x 1r4

5

0

22

- 0.152 854 824 131 40 x 1r3

15

2

32

- 0.406 443 630 847 99 x 1r8

6

0

32

- 0.108 667 076 953 77 x 10"5

16

3

10

0.664 561 861 916 35 x 1r7

7

1

0

- 0.133 917 448 726 02 x 102

17

3

32

0.806 707 341 030 27 x 10"10

8

1

1

0.432 110 391 835 59 x 102

18

4

32

- 0.934 777 712 139 47 x 10"12

9

1

2

- 0.540 100 671 705 06 x 102

19

5

32

0.582 654 420 206 01 x 10"14

10

1

3

0.305 358 922 039 16 x 102

20

6

32

- 0.150 201 859 535 03 x 10"16

Range of validity

Equation (11) covers the same range of validity as the basic equation, Eq. (7), except for the metastable region (superheated liquid), where Eq. (11) is not valid.

Numerical consistency with the basic equation

For ten million random pairs of p and h covering the entire region 1, the differences A T between temperatures from Eq. (11) and from Eq. (7) were calculated and the absolute maximum difference |A T | max and the root-mean-square difference A TRMS were determined. These actual inconsistency values and the tolerated value |A T | tol (see the beginning of Section 5.2) amount to:

|A T | t0l = 25 mK ; A Trms = 13.4 mK ; |A T | max = 23.6 mK . (12)

Computer-program verification

To assist the user in computer-program verification of Eq. (11), Table 7 contains the corresponding test values.

Table 7. Temperature values calculated from Eq. (11) for selected values of p and ha

p /MPa

h/(kJ kg1)

T/K

3

500

0.391 798 509 x

103

80

500

0.378 108 626 x

103

80

1500

0.611 041 229 x

103

a It is recommended to verify the programmed equation (8 byte real values) for all three combinations of p and h given in this table.

a It is recommended to verify the programmed equation (8 byte real values) for all three combinations of p and h given in this table.

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