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Subregione 2b
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Subregione 2b

In questa sezione sono presenti solo le equazioni inverse T(p,h) e T(p,s) relative alla sola subregione 2b. Per tutte le altre informazioni (eq. fondamentali, eq. di base, ecc.) consultare la regione 2


Equazione inversa T(p,h) subregione 2b

L’equazione inversa T(p,h) per la subregione 2a in forma adimensionale è la seguente:

 (23)

dove: θ=T/T*,   p=p/p*, e η=h/h* con T*=1 K, p*=1 MPa, e h*=2000 kJ·kg-1.

I coefficenti ni e gli esponenti Ii e Ji si trovano nella seguente tabella 20b:

TABELLA 20b
Valori dei coefficenti e degli esponenti dell’equazione inversa T(p,h) relativa alla subregione 2b come da eq. (23)

i
Ii
Ji
ni
1
0
0
0.148 950 410 795 16 x 104
2
0
1
0.743 077 983 140 34 x 103
3
0
2
-0.977 083 187 978 37 x 102
4
0
12
0.247 424 647 056 74 x 101
5
0
18
-0.632 813 200 160 26
6
0
24
0.113 859 521 296 58 x 101
7
0
28
-0.478 118 636 486 25
8
0
40
0.852 081 234 315 44 x 10-2
9
1
0
0.937 471 473 779 32
10
1
2
0.335 931 186 049 16 x 101
11
1
6
0.338 093 556 014 54 x 101
12
1
12
0.168 445 396 719 04
13
1
18
0.738 757 452 366 95
14
1
24
-0.471 287 374 361 86
15
1
28
0.150 202 731 397 07
16
1
40
-0.217 641 142 197 50 x 10-2
17
2
2
-0.218 107 553 247 61 x 10-1
18
2
8
-0.108 297 844 036 77
19
2
18
-0.463 333 246 358 12 x 10-1
20
2
40
0.712 803 519 595 51 x 10-4
21
3
1
0.110 328 317 899 99 x 10-3
22
3
2
0.189 552 483 879 02 x 10-3
23
3
12
0.308 915 411 605 37 x 10-2
24
3
24
0.135 555 045 549 49 x 10-2
25
4
2
0.286 402 374 774 56 x 10-6
26
4
12
-0.107 798 573 575 12 x 10-4
27
4
18
-0.764 627 124 548 14 x 10-4
28
4
24
0.140 523 928 183 16 x 10-4
29
4
28
-0.310 838 143 314 34 x 10-4
30
4
40
-0.103 027 382 121 03 x 10-5
31
5
18
0.282 172 816 350 40 x 10-6
32
5
24
0.127 049 022 719 45 x 10-5
33
5
40
0.738 033 534 682 92 x 10-7
34
6
28
-0.110 301 392 389 09 x 10-7
35
7
2
-0.814 563 652 078 33 x 10-13
36
7
28
-0.251805 456 829 62 x 10-10
37
9
1
-0.175 652 339 694 07 x 10-17
38
9
40
0.869 341 563 441 63 x 10-14

Intervallo di validità

L’equazione (23) è valida solo per la subregione 2b e quindi sono escluse le regioni in fase vapore metastabile. La pressione piu bassa per l’eq.(23) ammonta a 611.153 Pa a cui corrisponde una temperatura di sublimazione pari a 273.15 K.

Tolleranza numerica

Per almeno 106 valori random calcolati in p ed in h la differenza ΔT tra le temperature calcolate con l’eq. (23) e l’eq. (15) devono soddisfare i seguenti criteri:

|ΔT|tol = 10 mK   ;  |ΔT|max = 9.6 mK  ;  ΔTrms = 3.9 mK  

Test calcolo computer

La seguente tabella 22b contiene i valori di verifica relativi alla eq. (23).

TABELLA 22b
Valori delle temperature calcolati con l’eq. (23) in funzione di p e h

p (MPa)
h (kJ·kg-1)
T (K)
5
3500
0.801 299 102 x 103
5
4000
0.101 531 583 x 104
25
3500
0.875 279 054 x 103

Equazione inversa T(p,s) subregione 2b

L’equazione inversa T(p,s) per la subregione 2b in forma adimensionale è la seguente:

 (26)

dove: θ=T/T*,   p=p/p*, e σ=s/s* con T*=1 K, p*=1 MPa, e s*=0.7853 kJ·kg-1·K-1.

I coefficenti ni e gli esponenti Ii e Ji si trovano nella seguente tabella 21b:

TABELLA 21b
Valori dei coefficenti e degli esponenti dell’equazione inversa T(p,s) relativa alla regione 2b come da eq. (26)

i
Ii
Ji
ni
1
-6
0
0.316 876 650 834 97 x 106
2
-6
11
0.208 641 758 818 58 x 102
3
-5
0
-0.398 593 998 035 99 x 106
4
-5
11
-0.218 160 585 188 77 x 102
5
-4
0
0.223 697 851 942 42 x 106
6
-4
1
-0.278 417 034 458 17 x 104
7
-4
11
0.992 074 360 714 80 x 101
8
-3
0
-0.751 975 122 991 57 x 105
9
-3
1
0.297 086 059 511 58 x 104
10
-3
11
-0.344 068 785 485 26 x 101
11
-3
12
0.388 155 642 491 15
12
-2
0
0.175 112 950 857 50 x 105
13
-2
1
-0.142 371 128 544 49 x 104
14
-2
6
0.109 438 033 641 67 x 101
15
-2
10
0.899 716 193 084 95
16
-1
0
-0.337 597 400 989 58 x 104
17
-1
1
0.471 628 858 183 55 x 103
18
-1
5
-0.191 882 419 936 79 x 101
19
-1
8
0.410 785 804 921 96
20
-1
9
-0.334 653 781 720 97
21
0
0
0.138 700 347 775 05 x 104
22
0
1
-0.406 633 261 958 38 x 103
23
0
2
0.417 273 471 596 10 x 102
24
0
4
0.219 325 494 345 32 x 101
25
0
5
-0.103 200 500 090 77 x 101
26
0
6
0.358 829 435 167 03
27
0
9
0.525 114 537 260 66 x 10-2
28
1
0
0.128 389 164 507 05 x 102
29
1
1
-0.286 424 372 193 81 x 101
30
1
2
0.569 126 836 648 55
31
1
3
-0.999 629 545 849 31 x 10-1
32
1
7
-0.326 320 377 784 59 x 10-2
33
1
8
0.233 209 225 767 23 x 10-3
34
2
0
-0.153 348 098 574 50
35
2
1
0.290 722 882 399 02 x 10-1
36
2
5
0.375 347 027 411 67 x10-3
37
3
0
0.172 966 917 024 11 x 10-2
38
3
1
-0.385 560 508 445 04 x 10-3
39
3
3
-0.350 177 122 926 08 x 10-4
40
4
0
-0.145 663 936 314 92 x 10-4
41
4
1
0.564 208 572 672 69 x 10-5
42
5
0
0.412 861 500 746 05 x 10-7
43
5
1
-0.206 846 711 188 24 x 10-7
44
5
2
0.164 093 936 747 25 x 10-8

Intervallo di validità

L’equazione (26) è valida solo per la subregione 2b e quindi sono escluse le regioni in fase vapore metastabile. La pressione piu bassa per l’eq.(26) ammonta a 611.153 Pa a cui corrisponde una temperatura di sublimazione pari a 273.15 K.

Tolleranza numerica

Per almeno 106 valori random calcolati in p ed in s la differenza ΔT tra le temperature calcolate con l’eq. (26) e l’eq. (15) devono soddisfare i seguenti criteri:

|ΔT|tol = 10 mK   ;    |ΔT|max = 6.5 mK  ;  ΔTrms = 2.8 mK

Test calcolo computer

La seguente tabella 23b contiene i valori di verifica relativi alla eq. (26).

TABELLA 23b
Valori delle temperature calcolati con l’eq. (26) in funzione di p e s

p (MPa)
s (kJ·kg-1·K-1)
T (K)
8
6
0.600 484 040 x 103
8
7.5
0.106 495 556 x 103
90
6
0.103 801 126 x 104