Projected area: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
Newer edit →
Removed cylinder projected area formula. It relied on {\beta}, the angle between surface normal and plane normal . Cylinders do not have just one normal.
 
it wanted curlies that it didn't care for in the preview. Weird.
Line 1: Line 1:
Hello! I am Gene. I am satisfіed that I ϲan unite to [http://theamazingspider-man2movie.blogspot.com/ Watch The Amazing Spider-Man 2 Full Movie] entire world. I live in Iceland, in the region. I ԁream to gߋ to the various nations, to оbtain acquainted with interesting people.
The '''Lee-Kesler method'''
<ref>Lee B.I., Kesler M.G., "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., 21(3), 510-527, 1975
</ref>
allows the estimation of the [[saturated vapor pressure]] at a given temperature for all components for which the [[critical pressure]] P<sub>c</sub>, the [[critical temperature]] T<sub>c</sub>, and the [[acentric factor]] ω are known.
 
== Equations ==
<math> \ln P_r = f^{(0)} + \omega \cdot f^{(1)} </math>
 
<math> f^{(0)}=5.92714 - \frac{6.09648}{T_r} - 1.28862 \cdot \ln T_r + 0.169347 \cdot T_r^6 </math>
 
<math> f^{(1)}=15.2518 - \frac{15.6875}{T_r}-13.4721 \cdot \ln T_r + 0.43577 \cdot T_r^6 </math>
 
with
 
<math>P_r=\frac{P}{P_c}</math> ([[reduced pressure]]) und <math>T_r=\frac{T}{T_c}</math> ([[reduced temperature]]).
 
== Typical errors ==
The prediction error can be up to 10% for polar components and small pressures and the calculated pressure is typically too low. For pressures above 1&nbsp;bar, that means, above the normal boiling point, the typical errors are below 2%.
<ref>Reid R.C., Prausnitz J.M., Poling B.E., "The Properties of Gases & Liquids", 4. Auflage, McGraw-Hill, 1988
</ref>
 
== Example calculation ==
For [[benzene]] with
* T<sub>c</sub> = 562.12 K<ref name="Brunner">Brunner E., Thies M.C., Schneider G.M., J.Supercrit.Fluids, 39(2), 160-173, 2006</ref>
* P<sub>c</sub> = 4898 kPa<ref name="Brunner" />
* T<sub>b</sub> = 353.15 K<ref>Silva L.M.C., Mattedi S., Gonzalez-Olmos R., Iglesias M., J.Chem.Thermodyn., 38(12), 1725-1736, 2006</ref>
* ω = 0.2120<ref>[[Dortmund Data Bank]]</ref>
 
the following calculation for T=T<sub>b</sub> results:
 
* T<sub>r</sub> = 353.15 / 562.12 = 0.628247
* f<sup>(0)</sup> = -3.167428
* f<sup>(1)</sup> = -3.429560
* P<sub>r</sub> = exp( f<sup>(0)</sup> + ω f<sup>(1)</sup> ) = 0.020354
* P = P<sub>r</sub> * P<sub>c</sub> = 99.69 kPa
 
The correct result would be P = 101.325 kPa, the normal (atmospheric) pressure. The deviation is -1.63 kPa or -1.61 %.
 
It is important to use the same absolute units for T and T<sub>c</sub> as well as for P and P<sub>c</sub>. The unit system used (K or R for T) is irrelevant because of the usage of the reduced values T<sub>r</sub> and P<sub>r</sub>.
 
== References ==
<references/>
 
{{DEFAULTSORT:Lee-Kesler Method}}
[[Category:Thermodynamic models]]

Revision as of 18:58, 4 October 2013

The Lee-Kesler method [1] allows the estimation of the saturated vapor pressure at a given temperature for all components for which the critical pressure Pc, the critical temperature Tc, and the acentric factor ω are known.

Equations

ln⁡Pr=f(0)+ω⋅f(1)

f(0)=5.92714−6.09648Tr−1.28862⋅ln⁡Tr+0.169347⋅Tr6

f(1)=15.2518−15.6875Tr−13.4721⋅ln⁡Tr+0.43577⋅Tr6

with

Pr=PPc (reduced pressure) und Tr=TTc (reduced temperature).

Typical errors

The prediction error can be up to 10% for polar components and small pressures and the calculated pressure is typically too low. For pressures above 1 bar, that means, above the normal boiling point, the typical errors are below 2%. [2]

Example calculation

For benzene with

  • Tc = 562.12 K[3]
  • Pc = 4898 kPa[3]
  • Tb = 353.15 K[4]
  • ω = 0.2120[5]

the following calculation for T=Tb results:

  • Tr = 353.15 / 562.12 = 0.628247
  • f(0) = -3.167428
  • f(1) = -3.429560
  • Pr = exp( f(0) + ω f(1) ) = 0.020354
  • P = Pr * Pc = 99.69 kPa

The correct result would be P = 101.325 kPa, the normal (atmospheric) pressure. The deviation is -1.63 kPa or -1.61 %.

It is important to use the same absolute units for T and Tc as well as for P and Pc. The unit system used (K or R for T) is irrelevant because of the usage of the reduced values Tr and Pr.

References

  1. ↑ Lee B.I., Kesler M.G., "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., 21(3), 510-527, 1975
  2. ↑ Reid R.C., Prausnitz J.M., Poling B.E., "The Properties of Gases & Liquids", 4. Auflage, McGraw-Hill, 1988
  3. ↑ 3.0 3.1 Brunner E., Thies M.C., Schneider G.M., J.Supercrit.Fluids, 39(2), 160-173, 2006
  4. ↑ Silva L.M.C., Mattedi S., Gonzalez-Olmos R., Iglesias M., J.Chem.Thermodyn., 38(12), 1725-1736, 2006
  5. ↑ Dortmund Data Bank
Retrieved from "https://en.formulasearchengine.com/index.php?title=Projected_area&oldid=23236"