The Gibbs-Duhem equation is a fundamental thermodynamic equation that relates the changes in pressure, temperature, and composition of a multicomponent system. It is a key equation in chemical engineering, materials science, and other fields that deal with complex systems.
The Gibbs-Duhem equation states that the total differential of the Gibbs free energy of a system is equal to the sum of the products of the changes in the number of moles of each component and the partial molar Gibbs free energy of that component:
dG = -SdT + VdP + ∑iμidni
where:
- G is the Gibbs free energy
- S is the entropy
- T is the temperature
- V is the volume
- P is the pressure
- μi is the partial molar Gibbs free energy of component i
- dni is the change in the number of moles of component i
In other words, the Gibbs-Duhem equation tells us that the change in the Gibbs free energy of a system is due to changes in temperature, pressure, and composition.
The Gibbs-Duhem equation has a wide range of applications. Some of the most common applications include:
The Gibbs-Duhem equation is a fundamental equation in thermodynamics. It provides a general relationship between the thermodynamic properties of a multicomponent system. The Gibbs-Duhem equation is essential for understanding the behavior of complex systems and for predicting the effects of changes in temperature, pressure, and composition.
dG = -SdT + VdP + ∑iμidni
The Gibbs-Duhem equation is a fundamental equation in thermodynamics. It provides a general relationship between the thermodynamic properties of a multicomponent system. The Gibbs-Duhem equation is essential for understanding the behavior of complex systems and for predicting the effects of changes in temperature, pressure, and composition.
The Gibbs-Duhem equation can be used to:
The Gibbs-Duhem equation is a powerful tool that can be used to gain insights into the behavior of complex systems.
Temperature (K) | Pressure (atm) | Volume (cm3/g) |
---|---|---|
273.15 | 1 | 1.000 |
298.15 | 1 | 1.005 |
373.15 | 1 | 1.043 |
Component | Partial Molar Gibbs Free Energy (J/mol) |
---|---|
A | 100 |
B | 200 |
C | 300 |
Temperature (K) | Pressure (atm) | Phase |
---|---|---|
273.15 | 1 | Solid |
273.15 | 0.006 | Liquid |
373.15 | 1 | Gas |
What We Can Learn from These Stories:
The Gibbs-Duhem equation is a fundamental equation in thermodynamics. It provides a general relationship between the thermodynamic properties of a multicomponent system. The Gibbs-Duhem equation is essential for understanding the behavior of complex systems and for predicting the effects of changes in temperature, pressure, and composition.
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