# Confused by some aspects of thermodynamics

• secret2
In summary, the conversation discusses the concept of thermodynamics and the conditions for equilibrium in a sub-system. It also mentions the use of a partition function to find the equation of state. The use of "natural" arguments to calculate free energy and the relationship between partition function and thermodynamic quantities is also mentioned.

#### secret2

I am quite confused by some aspects of thermodynamics. First of all, I just wonder, when the textbook says that "when the constraints are temperature, volume and particle number, minimise F for equilibrium" (and similar statements for G and H), does it mean that the temperature, volume and particle number of the sub-system (i.e. excluding the reservoir) is fixed?

And also, if Z, the partition function, is given, how should I proceed to find the equation of state?

Thank you. :tongue2:

Because
$$dF \leq -SdT -PdV + \mu dN$$
then at fixed volume , temperature, and particle number, the free energy can only decrease, if we are at non-equilibrium. Thus temperature, volume, and particle number called "natural" arguments for the free energy.

If you know a partition function, you can calculate free energy. After that you can find pressure, enthropy, and thermodynamic potential using the thermodynamic identities

I can understand your confusion about some aspects of thermodynamics. Let me try to clarify a few things for you.

Firstly, when the textbook mentions minimizing F, G, and H for equilibrium, it is referring to the free energy, Gibbs free energy, and enthalpy, respectively. These are thermodynamic potentials that represent the amount of energy available to do work in a system. In order for a system to be in equilibrium, these potentials must be minimized. This means that the system has reached a state where it has the lowest possible energy and is stable.

Now, when it comes to the constraints of temperature, volume, and particle number, it is important to note that these are referring to the constraints of the entire system, including the reservoir. This means that the temperature, volume, and particle number of the sub-system and the reservoir combined must be fixed in order for equilibrium to be achieved.

As for finding the equation of state, it is important to note that the partition function, Z, is a function of temperature, volume, and particle number. Therefore, by manipulating the partition function, you can obtain the equation of state for a given system. However, this process can be complex and may involve using statistical mechanics techniques.

I hope this helps to clarify some of your confusion. Thermodynamics can be a challenging subject, but with practice and a deeper understanding of the concepts, it can become more manageable. Keep asking questions and seeking clarification, and you will eventually gain a better grasp on the subject.

## 1. What is thermodynamics and why is it important?

Thermodynamics is a branch of physics that deals with the study of energy and its transformations in systems. It is important because it provides a framework for understanding and predicting the behavior of various physical systems, including chemical reactions, heat engines, and refrigerators.

## 2. Why is thermodynamics often considered confusing or difficult to understand?

Thermodynamics can be confusing because it deals with abstract concepts and mathematical equations that may not be intuitive to everyone. It also involves a lot of terminology that can be overwhelming for beginners.

## 3. What are some key concepts in thermodynamics?

Some key concepts in thermodynamics include the laws of thermodynamics, which describe the behavior of energy in systems, and the concepts of heat, work, and entropy. Other important concepts include internal energy, enthalpy, and free energy.

## 4. How does thermodynamics relate to other branches of science?

Thermodynamics has widespread applications in many fields, including chemistry, physics, engineering, and biology. It is also closely related to other branches of science, such as statistical mechanics, which helps explain thermodynamic behavior at a molecular level.

## 5. What are some real-life applications of thermodynamics?

Thermodynamics has many practical applications, including the design and operation of power plants, engines, and refrigeration systems. It is also crucial in understanding weather and climate patterns, as well as the behavior of materials and chemical reactions.

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