Gibbs Free Energy, Maxwell Relations

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SUMMARY

The discussion focuses on deriving expressions for internal energy (U) and enthalpy (H) from the Gibbs Free Energy function G=G(P, T, N1, N2) using Maxwell Relations. The user successfully derived expressions for entropy, volume, and chemical potential but seeks clarity on U and H. Key equations include T=(dU/dS)V, -P=(dU/dV)S, and dG=-SdT-VdP+μ1dN1+μ2dN2. The user is advised to substitute S=(H-G)/T to find H and to consider specific conditions for simplification.

PREREQUISITES
  • Understanding of Gibbs Free Energy and its dependencies
  • Familiarity with Maxwell Relations in thermodynamics
  • Knowledge of partial derivatives and their applications in thermodynamic equations
  • Basic concepts of internal energy and enthalpy
NEXT STEPS
  • Study the derivation of internal energy expressions from Gibbs Free Energy
  • Explore the application of Maxwell Relations in thermodynamic systems
  • Learn about the implications of partial molar Gibbs Free Energy
  • Investigate the relationship between enthalpy and other thermodynamic potentials
USEFUL FOR

Students and professionals in thermodynamics, particularly those studying physical chemistry or chemical engineering, will benefit from this discussion as it addresses key concepts in energy transformations and state functions.

albertov123
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Homework Statement


We have a Gibbs Free Energy function G=G(P, T, N1, N2) I am not writing the whole function because I just want a push in the right direction. Find expressions for the entropy, volume, internal energy, enthalpy and chemical potential.

Homework Equations


Maxwell Relations
T=(dU/dS) V and Ni constant
-P=(dU/dV) S and Ni constant
T=(dH/dS) P and Ni constant
V=(dH/dP) S and Ni constant

The Attempt at a Solution


I have found entropy, volume and chemical potential (partial molar gibbs free energy) functions using related equations. But I'm not sure on how to derive internal energy and enthalpy expressions.
If I try to make use of above equations, for an example first equation dU=TdS so U=T.dS
but also from second equation dU=-PdV so U=-PdV

Can both be correct at the same time? I think they would yield different equations.

If I am going absolutely wrong, do you have any idea on how to find U and H expressions. What other relations could be used?
 
Physics news on Phys.org
For H, start with dG=-SdT-VdP+μ1dN1+μ2dN2, and substitute S=(H-G)/T. Then consider dP=0, dN's = 0.
 

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