## Basic Equation for Region

This section contains all details relevant for the use of the equations for region 5 of IAPWS-IF97. Information about the consistency at the boundary between regions 2 and 5 is summarized in Section 10. The results of computing-time comparisons between IAPWS-IF97 and IFC-67 are given in Section 11. The estimates of uncertainty of the most relevant properties can be found in Section 12.

The basic equation for this high-temperature 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

where * = p/p and * = T*/ Twith R given by Eq. (1).

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

where * = p/p* and * = T*/ T with p* = 1 MPa and T* = 1000 K. The coefficients n° and n° 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 37 contains the coefficients n° and exponents J° of Eq. (33).

i |
jo |
n° |
i J |
? r° |

1 |
0 |
- 0.131 799 836 742 01 x 102 |
4- |
2 0.369 015 349 803 33 |

2 |
1 |
0.685 408 416 344 34 x 101 |
5- |
1 - 0.311 613 182 139 25 x 101 |

3 |
- 3 |
- 0.248 051 489 334 66 x 10"1 |
6 |
2 - 0.329 616 265 389 17 |

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

where n = p/p* and t= T*/ T with p* = 1 MPa and T* = 1000 K. The coefficients m and exponents Ij and Jt of Eq. (34) are listed in Table 38.

All thermodynamic properties can be derived from Eq. (32) by using the appropriate combinations of the ideal-gas part yo, Eq. (33), and the residual part yr, Eq. (34), of the dimensionless Gibbs free energy and their derivatives. Relations between the relevant thermodynamic properties and yo and yr and their derivatives are summarized in Table 39. All required derivatives of the ideal-gas part and of the residual part of the dimensionless Gibbs free energy are explicitly given in Table 40 and Table 41, respectively.

i |
Ii |
Ji |
ni |

1 |
1 |
0 |
- 0.125 631 835 895 92 x ir3 |

2 |
1 |
1 |
0.217 746 787 145 71 x 10_2 |

3 |
1 |
3 |
- 0.459 428 208 999 10 x 10"2 |

4 |
2 |
9 |
- 0.397 248 283 595 69 x 10"5 |

5 |
3 |
3 |
0.129 192 282 897 84 x 1r6 |

Table 39. Relations of thermodynamic properties to the ideal-gas part and the residual part yx of the dimensionless Gibbs free energy and their derivatives a when using Eq. (32)

Property

Relation

Specific internal energy u = g- T(dg!d T) - p(dgdp) t

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