Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev

Thermodynamics

Civil Engineering (CE) : Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev

The document Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Thermodynamics.
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Computation of ΔH and ΔS for a Gas using Generalized Departure Functions

The residual function equations presented in the last section are particularly useful for estimating finite changes in enthalpy and entropy for real gases undergoing change in either closed or open system processes. We consider that a pure fluid changes state from (T1 ,P1 ) to (T2 , P2 ); shown schematically in fig. 5.4. 

 

Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev
Fig. 5.4 Schematic of a General Thermodynamic Process on P – T co-ordinates

Since the departure functions H R andS R capture deviations from ideal gas behaviour at the same temperature as the real gas, one can conceive of the pathway between states ‘1’ and ‘2’ to be decomposed into following steps (see fig 5.5):

a) Real gas state at (T1 ,P1 ) to ideal gas state (ig) at (T1 ,P1 )
b) Ideal gas state at (T1 ,P1 ) to ideal gas state at (T2,P2 )
c) Ideal gas state at (T2,P2 ) to real gas state at (T2,P2 )

 

Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev
5.5 Pathway for calculating ΔH and ΔS for Real Gases

 

• For step ‘a’ the change of enthalpy is given by:  Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev
• For step ‘b’ the change of enthalpy is given by:  Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev
• For step ‘c’ the change of enthalpy is given by:  Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev

 

Therefore, the overall change of enthalpy is given by:

Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev

Using eqn. 3.8:  Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev                  ......(5.63)

 

The same considerations apply for computing the change of entropy between the two states:

Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev

Using eqn. 4.21: Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev                  ......(5.64)

Generalized residual property relations may be used for calculation of change in internal energy i.e. U 2 −U1 for a process in the following manner:

U2 −U= (H2 − P2V2 ) −(H1 − P1V)

Or: U2 −U= (H2 −H1 ) −( P2V2 − P1V1 )                  ......(5.65)

The term (H2 −H1) can be calculated using eqn. 5.63, while the term ( P2V2 − P1V1 )

may be computed after obtaining Vand V2 applying the generalized compressibility factor approach. One may, however, also use the generalized residual property charts for internal energy for the same purpose 

Computation of ΔH and ΔS for a Gas using Generalized Departure Functions Civil Engineering (CE) Notes | EduRev
Figure 5.6 Generalized internal energy departure functions using corresponding states

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