# Thermodynamical potentials: some hand-waving please

• jonas_nilsson
In summary, the conversation discusses the connections between statistical physics and thermodynamics, specifically in verifying old-school thermodynamical results. The speaker expresses a lack of "feeling" for thermodynamical potentials and asks for others to share their understanding of what they really describe. The conversation also mentions the process of conjuring a rabbit in a hat as an analogy for understanding thermodynamic processes, such as assembling molecules and extracting energy from the surrounding environment.
jonas_nilsson
Hello!

I am right now occupied with statistical physics, and of course the connections to thermodynamics are always there. We are especially verifying the old-school thermodynamical results. This leads to a lot of talking about thermodynamical potentials, but I feel that I and most of the students lack a "feeling" for them.

I would appreciate if some people could do some hand-waving and tell me what "feeling" they have developed for the thermodynamical potentials. What do they really describe? I'm sure it would help us out also with the theoretical stuff.

Jonas

Suppose you wanted to conjure a rabbit in your hat. For one thing, you would have to assemble the molecules:

$$dU=\mu dN$$

But you would also have to do the work to make room for the rabbit:

$$dU = \mu dN + P dV$$ (Enthalpy)

And you can extract some energy from the surrounding air to help you:

$$dU = \mu dN + P dV - T ds$$ (Gibbs free energy)

, thank you for bringing up this topic. Thermodynamical potentials can be a difficult concept to grasp, but they are essential to understanding the behavior of thermodynamic systems.

In simple terms, thermodynamical potentials are mathematical functions that describe the state of a system in terms of its thermodynamic variables, such as temperature, pressure, and volume. These potentials are useful because they allow us to analyze and predict the behavior of a system without having to consider all of its individual particles.

For example, the internal energy of a system can be described by the Helmholtz free energy potential, while the enthalpy can be described by the Gibbs free energy potential. These potentials provide information about the energy and work that can be extracted from a system, as well as its equilibrium conditions.

One way to think about thermodynamical potentials is to imagine them as maps. Just like a map can show the terrain and features of a physical landscape, thermodynamical potentials can show the landscape of a thermodynamic system. They provide a simplified representation of the system, allowing us to understand its behavior and make predictions.

Another helpful analogy is to think of thermodynamical potentials as energy reservoirs. Just like a reservoir holds a certain amount of water, the thermodynamical potential holds a certain amount of energy that can be accessed and utilized by the system. This energy can change depending on the system's conditions, such as temperature or pressure, and can be used to do work.

I hope this hand-waving explanation has helped give you a better understanding of thermodynamical potentials. They are a fundamental concept in thermodynamics and are crucial for understanding the behavior of physical systems. Keep exploring and asking questions, and you will continue to develop a deeper "feeling" for them.

## 1. What are thermodynamical potentials?

Thermodynamical potentials are mathematical functions used to describe the state of a thermodynamic system. They represent the amount of energy required to drive a system towards a particular state.

## 2. What is the purpose of using thermodynamical potentials?

Thermodynamical potentials provide a convenient way to study and analyze the behavior of thermodynamic systems. They allow us to calculate important quantities such as entropy, internal energy, and free energy.

## 3. What is the difference between internal energy and free energy?

Internal energy is the total energy contained within a system, including both its kinetic and potential energy. Free energy, on the other hand, is the amount of energy that is available to do work. It takes into account both the internal energy and the energy lost to the environment.

## 4. How are thermodynamical potentials related to each other?

There are several different thermodynamical potentials, including internal energy, free energy, enthalpy, and Gibbs free energy. These potentials are all related to each other through mathematical equations, and each one is useful for different types of thermodynamic systems.

## 5. Can thermodynamical potentials be applied to real-world systems?

Yes, thermodynamical potentials are used extensively in the study of real-world systems, such as chemical reactions, phase changes, and heat engines. They provide a theoretical framework for understanding and predicting the behavior of these systems and have many practical applications in industries such as energy production and materials science.

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