Question about derivations of thermodynamic properties

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SUMMARY

This discussion focuses on the derivation of thermodynamic properties, specifically addressing terms from equations 3-47, 3-49, and 3-41 in the context of ideal gas mixtures. The integration from finite specific volume to infinite is clarified as necessary for correcting properties at finite volumes. Additionally, the discussion highlights the significance of analytical functions in deriving chemical potential expressions for pure substances at a given temperature relative to a reference state.

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  • Understanding of thermodynamic properties such as internal energy (U), enthalpy (H), and entropy (S).
  • Familiarity with ideal gas laws and their applications in thermodynamics.
  • Knowledge of mathematical integration techniques, particularly in the context of thermodynamic equations.
  • Basic concepts of chemical potential and its relevance in thermodynamic systems.
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  • Study the derivation of thermodynamic properties from the ideal gas law.
  • Learn about the integration of thermodynamic functions and its implications in finite and infinite specific volumes.
  • Research the concept of chemical potential and its calculation for pure substances.
  • Examine the role of analytical functions in thermodynamics and their applications in deriving various properties.
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Students and professionals in thermodynamics, chemical engineering, and physical chemistry who seek to deepen their understanding of the derivation of thermodynamic properties and their applications in ideal gas mixtures.

swmmr1928
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I don't understand how some terms are derived.
How did the last term of 3-47 originate?
How did 3-49 get so many terms from just one term in 3-41?
Why integrate from V to infinite? That is not intuitive.
Thas a functions are unusual because the absolute values of U,H,S cannot be computed. However, the analytical functions are needed to derive the expression for chemical potential?
 
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swmmr1928 said:
View attachment 82182
View attachment 82183
I don't understand how some terms are derived.
How did the last term of 3-47 originate?
How did 3-49 get so many terms from just one term in 3-41?
All the terms you are referring to are the properties of the mixture in the ideal gas state at the given temperature and composition.
Why integrate from V to infinite? That is not intuitive.
Infinite specific volume refers to the ideal gas limit. You need to do the integration to get the correction for the property at finite specific volume.
Thas a functions are unusual because the absolute values of U,H,S cannot be computed. However, the analytical functions are needed to derive the expression for chemical potential?
The terms involving the chemical potentials are for the pure substances at temperature T relative to a specified reference state.

Chet
 

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