Deprecated: Non-static method TplHelper::tplStyles() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/component.php on line 19

Deprecated: Non-static method TplHelper::parseColor() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/helper.php on line 24

Deprecated: Non-static method TplHelper::html2rgba() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/helper.php on line 384

Deprecated: Non-static method TplHelper::parseColor() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/helper.php on line 25

Deprecated: Non-static method TplHelper::html2rgba() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/helper.php on line 384

Deprecated: Non-static method TplHelper::parseColor() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/helper.php on line 26

Deprecated: Non-static method TplHelper::html2rgba() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/helper.php on line 384

Deprecated: Non-static method TplHelper::parseColor() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/helper.php on line 27

Deprecated: Non-static method TplHelper::html2rgba() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/helper.php on line 384

Deprecated: Non-static method TplHelper::parseColor() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/helper.php on line 30

Deprecated: Non-static method TplHelper::html2rgba() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/helper.php on line 384

Deprecated: Non-static method TplHelper::loadCSS() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/component.php on line 25
Subregione 2c
Deprecated: Non-static method TplHelper::displayFavicons() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/component.php on line 47

Deprecated: Non-static method TplHelper::googleFonts() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/component.php on line 50

Deprecated: Non-static method TplHelper::googleAnalytics() should not be called statically, assuming $this from incompatible context in /htdocs/public/www/templates/kallyas/component.php on line 53
Essica Srl
Via E.Mattei, 15
35020 Maserà di Padova - ITALY
Email: essica.info@tin.it
URL: www.essica.it

Subregione 2c

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


Equazione inversa T(p,h) subregione 2c

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

 (24)

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 20c:

TABELLA 20c
Valori dei coefficenti e degli esponenti dell’equazione inversa T(p,h) relativa alla subregione 2c come da eq. (24)

i
Ii
Ji
ni
1
-7
0
-0.323 683 985 552 42 x 1013
2
-7
4
0.732 633 509 021 81 x 1013
3
-6
0
0.358 250 899 454 47 x 1012
4
-6
2
-0.583 401 318 515 90 x 1012
5
-5
0
-0.107 830 682 174 70 x 1011
6
-5
2
0.208 255 445 631 71 x 1011
7
-2
0
0.610 747 835 645 16 x 106
8
-2
1
0.859 777 225 355 80 x 106
9
-1
0
-0.257 457 236 041 70 x 105
10
-1
2
0.310 810 884 227 14 x 105
11
0
0
0.120 823 158 659 36 x 104
12
0
1
0.482 197 551 092 55 x 103
13
1
4
0.379 660 012 724 86 x 101
14
1
8
-0.108 429 848 800 77 x 102
15
2
4
-0.453 641 726 766 60 x 10-1
16
6
0
0.145 591 156 586 95 x 10-12
17
6
1
0.112 615 974  072 30 x 10-11
18
6
4
-0.178 049 822 406 86 x 10-10
19
6
10
0.123 245 796 908 32 x 10-6
20
6
12
-0.116 069 211 309 84 x 10-5
21
6
16
0.278 463 670 885 54 x 10-4
22
6
20
-0.592 700 384 741 76 x 10-3
23
6
22
0.129 185 829 918 78 x 10-2

Intervallo di validità

L’equazione (24) è valida solo per la subregione 2c e quindi sono escluse le regioni in fase vapore metastabile. La pressione piu bassa per l’eq.(24) 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. (24) e l’eq. (15) devono soddisfare i seguenti criteri:

|ΔT|tol = 25 mK   ;  |ΔT|max = 23.7 mK  ;  ΔTrms = 10.4 mK  

Test calcolo computer

La seguente tabella 22c contiene i valori di verifica relativi alla eq. (24).

TABELLA 22c
Valori delle temperature calcolati con l’eq. (24) in funzione di p e h

p (MPa)
h (kJ·kg-1)
T (K)
40
2700
0.743 056 411 x 103
60
2700
0.791 137 067 x 103
60
3200
0.882 756 860 x 103

Equazione inversa T(p,s) subregione 2c

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

 (27)

dove: θ=T/T*,   p=p/p*, e σ=s/s* con T*=1 K, p*=1 MPa, e s*=2.9251 kJ·kg-1·K-1.

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

TABELLA 21c
Valori dei coefficenti e degli esponenti dell’equazione inversa T(p,s) relativa alla regione 2c come da eq. (27)

i
Ii
Ji
ni
1
-2
0
0.909 685 010 053 65 x 103
2
-2
1
0.240 456 670 884 20 x 104
3
-1
0
-0.591 623 263 871 30 x 103
4
0
0
0.541 454 041 280 74 x 103
5
0
1
-0.270 983 084 111 92 x 103
6
0
2
0.979 765 250 979 26 x 103
7
0
3
-0.469 667 729 594 35 x 103
8
1
0
0.143 992 746 047 23 x 102
9
1
1
-0.191 042 042 304 29 x 102
10
1
3
0.532 991 671 119 71 x 101
11
1
4
-0.212 529 753 759 34 x 102
12
2
0
-0.311 473 344 137 60
13
2
1
0.603 348 408 946 23
14
2
2
-0.427 648 397 025 09 x 10-1
15
3
0
0.581 855 972 552 59 x 10-2
16
3
1
-0.145 970 082 847 53 x 10-1
17
3
5
0.566 311 756 310 27 x 10-2
18
4
0
-0.761 558 645 845 77 x 10-4
19
4
1
0.224 403 429 193 32 x 10-3
20
4
4
-0.125 610 950 134 13 x 10-4
21
5
0
0.633 231 326 609 34 x10-6
22
5
1
-0.205 419 896 753 75 x 10-5
23
5
2
0.364 053 703 900 82 x 10-7
24
6
0
-0.297 598 977 892 15 x 10-8
25
6
1
0.101 366 185 297 63 x 10-7
26
7
0
0.599 257 196 923 51 x 10-11
27
7
1
-0.206 778 701 051 64 x 10-10
28
7
3
-0.208 742 781 818 86 x 10-10
29
7
4
0.101 621 668 250 89 x 10-9
30
7
5
-0.164 298 282 813 47 x 10-9

Intervallo di validità

L’equazione (27) è valida solo per la subregione 2c e quindi sono escluse le regioni in fase vapore metastabile. La pressione piu bassa per l’eq.(27) 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. (27) e l’eq. (15) devono soddisfare i seguenti criteri:

|ΔT|tol = 25 mK   ;    |ΔT|max = 19.0 mK  ;  ΔTrms = 8.3 mK

Test calcolo computer

La seguente tabella 23c contiene i valori di verifica relativi alla eq. (27).

TABELLA 23c
Valori delle temperature calcolati con l’eq. (27) in funzione di p e s

p (MPa)
s (kJ·kg-1·K-1)
T (K)
20
5.75
0.697 992 849 x 103
80
5.25
0.854 011 484 x 103
80
5.75
0.949 017 998 x 104