Question about derivations of thermodynamic properties

In summary, the terms discussed refer to properties of a mixture in the ideal gas state at a given temperature and composition. The integration from specific volume to infinity is necessary to correct for properties at finite specific volume. The terms involving chemical potentials are for pure substances at a specified reference state.
  • #1
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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  • #2
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
 

1. What is a thermodynamic property?

A thermodynamic property is a physical characteristic of a system that can be measured or calculated and is used to describe its state. Examples of thermodynamic properties include temperature, pressure, and energy.

2. What are the three laws of thermodynamics?

The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transferred or converted from one form to another. The second law states that the total entropy of a closed system will always increase over time. The third law states that the entropy of a perfect crystal at absolute zero temperature is zero.

3. How are thermodynamic properties related to each other?

Thermodynamic properties are related to each other through various equations and relationships, such as the ideal gas law and the laws of thermodynamics. These relationships allow us to understand how changes in one property can affect other properties of a system.

4. What is a derivation of a thermodynamic property?

A derivation of a thermodynamic property is a mathematical process used to derive a relationship between different thermodynamic properties. This can involve manipulating equations and applying the laws of thermodynamics to find a new equation or relationship between properties.

5. Why are derivations of thermodynamic properties important?

Derivations of thermodynamic properties are important because they allow us to understand the underlying principles and relationships between different properties. This can help us to make predictions and solve problems in thermodynamics, and also provides a deeper understanding of how energy and matter behave in different systems.

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