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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.
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 )
5.5 Pathway for calculating ΔH and ΔS for Real Gases
• For step ‘a’ the change of enthalpy is given by: 
• For step ‘b’ the change of enthalpy is given by: 
• For step ‘c’ the change of enthalpy is given by: 
Therefore, the overall change of enthalpy is given by:
Using eqn. 3.8: 
......(5.63)
The same considerations apply for computing the change of entropy between the two states:
Using eqn. 4.21: 
......(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 −U1 = (H2 − P2V2 ) −(H1 − P1V1 )
Or: U2 −U1 = (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 V1 and V2 applying the generalized compressibility factor approach. One may, however, also use the generalized residual property charts for internal energy for the same purpose
Figure 5.6 Generalized internal energy departure functions using corresponding states
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FAQs on Computation of ΔH and ΔS for a Gas using Generalized Departure Functions - Additional Documents & Tests for Civil Engineering (CE)
| 1. What is the computation of ΔH for a gas using generalized departure functions? |  |
Ans. The computation of ΔH (enthalpy change) for a gas using generalized departure functions involves determining the difference in enthalpy between the final and initial states of the gas. Generalized departure functions are mathematical models used to describe the thermodynamic properties of gases, and they can be used to calculate the enthalpy change based on the temperature and pressure of the gas.
| 2. How are ΔH and ΔS related in the context of a gas? | |
Ans. ΔH (enthalpy change) and ΔS (entropy change) are related in the context of a gas through the Gibbs free energy equation, ΔG = ΔH - TΔS. This equation expresses the relationship between the change in free energy (ΔG), enthalpy change (ΔH), and entropy change (ΔS) of a system. It indicates that for a spontaneous process (ΔG < 0), the enthalpy change and entropy change must have the correct relationship based on the temperature (T).
| 3. How can generalized departure functions be used in civil engineering? | |
Ans. Generalized departure functions can be used in civil engineering to analyze and design systems involving gases, such as ventilation systems, air conditioning systems, and gas pipelines. By utilizing these functions, civil engineers can accurately determine the thermodynamic properties of gases, including enthalpy, entropy, and other relevant parameters, for the design and optimization of such systems.
| 4. What factors influence the computation of ΔH and ΔS for a gas? | |
Ans. The computation of ΔH and ΔS for a gas is influenced by several factors, including the initial and final states of the gas (temperature and pressure), the specific gas being considered, and the assumptions made in the mathematical model used for the computation. It is essential to consider these factors accurately to obtain reliable and meaningful results.
| 5. Are there any limitations or challenges associated with using generalized departure functions for gas analysis? | |
Ans. Yes, there are limitations and challenges associated with using generalized departure functions for gas analysis in civil engineering. Some of these include the accuracy and reliability of the mathematical models employed, the availability and accuracy of experimental data used to validate the models, and the complexity of the calculations involved. It is crucial to carefully evaluate the applicability and limitations of these functions before utilizing them in real-world engineering applications.
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