Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev

Thermodynamics

Civil Engineering (CE) : Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev

The document Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Thermodynamics.
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The approach based on the use of the compressibility factors can be applied to the present instance to evolve generalized correlations for computing enthalpy and entropy changes for gases. We start with the Pitzer-type expression for the compressibility factor: 

Z =Z0 +ω Z                     ..(2.25)

Differentiating with respect to the reduced temperature we get:

Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev                      ..(5.55)

Thus using eqn. 5.54 we may recast eqns. 5.37 and 5.38 as follows: 

Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev                   ..(5.56)

 

Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev                   ..(5.57)

Both the above equations may be rewritten individually as follows: 

Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev                   ..(5.58)

 

Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev                   ..(5.59a) 

And 

Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev                   ..(5.59b)
 

Similarly: 

Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev                   ..(5.60)

Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev                   ..(5.61a)

 

Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev                   ..(5.61b)

 

The term  Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev in eqn. 5.59a constitutes the first order enthalpy departure, and Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev (in eqn. 5.59b) the second order (with respect to simple fluids) enthalpy departure at specified Tr and Pr. The same is true for the corresponding entropic terms provided by eqns. 5.61a and 5.61b.

The evaluation of the integrals in eqns. 5.59 to 5.62 may be carried out assuming an EOS. The most widely used approach is that of Lee and Kesler who employed a modified form of the BWR EOS (eqn. 2.17) to extend their generalized correlation to residual property estimation. Figs. 5.1 and 5.2 respectively provide values of (HR)0/RTC an (HR)1/RTC respectively. Similar plots for the entropy terms (SR)0 / R, an ( SR)1 /R are also available; however, here the plot of the entire entropy term (− SR) as function of Tr and Pr is shown in fig. 5.3. Table of values of all the above (eqns. 5.59 to 5.62) are also available as functions of T r and P r Fig. at discrete intervals 


Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev
Fig. 5.1 Correlation of  Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev drawn from tables of Lee-Kesler (Source: AIChE  J., pp. 510-527, 1975)

 

Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev
Fig. 5.2 Correlation of Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev drawn from tables of Lee-Kesler (Source: AIChE  J., pp. 510-527, 1975)

 

Generalized Correlations for Computing dH and dS for a Real Gas Civil Engineering (CE) Notes | EduRev
Figure 5.3 Generalized entropy departure functions using corresponding states.

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