Consistency at the Saturation Line

The consistency investigations along the vapor-liquid saturation line were performed for the properties ps , Ts , and g. The calculations concern the following basic equations and ranges of the saturation line, see Fig. 1; the way of calculating the inconsistencies Aps , ATs , and Ag is also given:

• Equations (7), (15) and (30) on the saturation line for temperatures from Tt = 273.15 K to 623.15 K.

The calculation of ps and of Ts from Eqs. (7) and (15) is made via the Maxwell criterion (phase-equilibrium condition) for given values of T or p. The g values are determined for given T values and corresponding ps values from Eq. (30).

• Equations (28) and (30) on the saturation line for temperatures from 623.15 K to Tc = 647.096 K.

The calculation of ps and Ts from Eq. (28) is made via the Maxwell criterion for given temperatures or pressures, respectively. The inconsistency hg corresponds to the difference g(p', T) - g"(p", T) which is calculated from Eq. (28) after p' and p" are determined from Eq. (28) by iteration for given T values and corresponding ps values from Eq. (30).

• Equations (7), (15) and (28) on the saturation line at 623.15 K. This is the only point on the saturation line where the validity ranges of the fundamental equations of regions 1 to 3 meet each other.

All three properties ps and Ts and g are calculated via the Maxwell criterion from the corresponding equations.

The results of these consistency investigations along the saturation line are summarized in Table 44. In addition to the permitted inconsistencies corresponding to the Prague values [13], the actual inconsistencies characterized by their maximum and root-mean-square values, IAmax and A^rms , for the two sections of the saturation line are given for x = ps, Ts and g. It can be seen that the inconsistencies between the basic equations for the corresponding singlephase region and the saturation-pressure equation are extremely small. This statement also holds for the fundamental equations, Eqs. (7), (15), and (28), among one another and not only in relation to the saturation-pressure equation, Eq. (30), see the last column in Table 44.

Table 44. Inconsistencies between the basic equations valid at the saturation line

Inconsistency A x

Prague value

1 Ax\ max AxRMS a

1 A x\ max A xRMS a

T = 623.15 K Eqs. (7),(15)/(28)

IAps | /%

0.05

0.0069 0.0033

0.0026

0.0015

0.0041

|a Ts| /%

0.02

0.0006 0.0003

0.0003

0.0002

0.0006

Ia g\/(kj kg-1)

0.2

0.012 0.006

0.002

0.001

0.005

a The A^rms values (see Nomenclature) were calculated from about 3000 points evenly distributed along the two sections of the saturation line.

a The A^rms values (see Nomenclature) were calculated from about 3000 points evenly distributed along the two sections of the saturation line.

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