## 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.

 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.

 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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