Boiling Line

The saturated vapor pressure is a very important parameter of LM coolants for safety estimations. It is directly related to the latent heat of evaporation. The boiling temperature increases (with the decreas­ing rate) when pressure increases. At low pressures, where the vapor behaves as a perfect gas and the evaporation enthalpy (AHe) is practically constant, it follows from the Clausius-Clapeyron equation that temperature dependence of the saturated vapor pres­sure is about exponential:

ps(T) =ps, i exp(-AHe/RT) [2]

R = 8.314J mol-1 K-1 is the universal gas constant.

Equation [2] can provide approximate values for equilibrium-saturated vapor pressures over a wide range of temperature due to the relatively small variation of AHe with temperature at low pressures. At high pressures, closer fits of the experimental results can be obtained by adding supplementary temperature-dependent terms:

ln(ps(T))= A + T + C ln(T) + DT [3]

Very often this correlation is used without the last term.

Evaluation of data on the temperature depen­dence of the saturation vapor pressure of sodium in a wide range of temperatures was performed many

times3,8,43,44 and correlations of type [3] were pro­posed that can describe the temperature dependence of the Na saturation pressure in a wide temperature range with an uncertainty of 1-25%. In the recent compilation of IAEA,26 a polynomial of the fifth order was proposed for the saturation pressure of Na constructed on the bases of the recommended data presented in Bystrov et al, Browning and Potter,44 and Vargaftik and Voljak.45 In the review of Fink and Leibowitz,22 a detailed analysis of previous compilations was performed and a correlation of type [3] proposed in Browning and Potter44 was selected, which allows to calculate the Na saturated vapor pressure with an uncertainty of <3% in the temper­ature range from 864 K to the region close to T:(Na). The uncertainty increases at lower temperatures and reaches 24% at T = 400 K. This correlation is recommended for high temperatures in the current work and its coefficients are given in Table 4.

Not many data exist on the saturation vapor pres­sure of lead. In 1973, they were reviewed by Hultgren eta/.,5 who analyzed different sources and presented a table with the recommended data in the temperature range of 298.15-2100 K. Later, Kubaschewski and Alcock46 reanalyzed the available data on the Pb satu­ration vapor pressure and proposed a correlation of type [3]. In more recent compilations23,27,33,47,48 and in the present work, the simpler correlation of type [2] or the correlation of type [3] with the coefficients from

Table 4 Coefficients of the correlation [3] for the tem­perature dependence of the saturated vapor pressure (in MPa) of Na, Pb, and Pb-Bi(e)

Parameter

Unit

Na

Pb

Pb-Bi(e)

TM,0

K

371.0

600.6

398

TB,0

K

1155

2021

1927

A

ln(MPa)

11.9463

16.7488

21.9575

B

K

-12633.73

-23325

-24053

C

-0.4672

-0.985

-1.6402

Dx 10-4

k-1

3.3274

image395
Подпись: Figure 2

Kubaschewski and Alcock46 are recommended for the saturated vapor pressure of lead (see Table 4).

Data on the saturated vapor pressure of Pb-Bi(e) are very limited in number49-51 and in the tempera­ture range (508-1023 K), and a larger dispersion exists between them, especially at lower tempera­tures. Therefore, they can be described with correla­tion [2]. Nevertheless, in order to take into account the formation of Bi2 molecules in the Pb-Bi vapor phase, Morita et al5 proposed to use a four-term correlation [3] for temperature interval 700-2000 K. The coefficients are included in Table 4; the coeffi­cient D was corrected to obtain TB = 1927 K at ps = 0.101 325 MPa (1 atm).

At low temperatures, the saturated vapor pressure of the considered LM can be estimated with the same or better uncertainty with eqn [2]; the coefficients recommended in the compilations33,34 for Na, Pb,

and Pb-Bi(e) are given in Table 5.

Figure 3, in which the saturated vapor pressure is plotted as a function of temperature, illustrates the

Table 5 Coefficients of the correlation [2] for the temperature dependence of the saturated vapor pressure of Na, Pb, and Pb-Bi(e)

Parameter

Unit

Na

Pb

Pb-Bi(e)

TM,0

K

371.0

600.6

398

TB,0

K

1155

2021

1927

ps, i

109 Pa

4.43

5.76

12.2

A He

kJ

102.6

184.0

187.5

correlation [2] for Na, Pb-Bi(e), and Pb in the tem­perature range of TM0 to TB0.

It should be noticed that for Na and Pb, the uncer­tainty of this correlation is about 7-10% when the temperature is 50-100 °C higher than normal melt­ing temperature and lower than normal boiling tem­perature. The uncertainty increases rapidly beyond this interval, at lower and higher temperatures. For Pb-Bi(e), the uncertainty of this correlation is about 10% at temperatures higher than 1500 K; however, it becomes more than 50% when temperature decreases below 1000 K.24,34 At lower temperatures, the saturated pressure is too low to be measured correctly. The values of AHe presented in Table 5 are slightly higher but in satisfactory agreement with AHB 0 presented in Table 2.