Do not understand Helmholtz free energy

[annms]

I'm currently learning thermodynamics from Schroeder's "An Intoduction to Thermal Physics".

He explains that in an environment of constant temperature, the system can extract heat from the environment for free when we create a system, and the Helmholtz free energy is that additional work needed that the heat did not cover.

My first point of confusion- why is it certain that heat flow from the environment to the system?
When we annihilate the system, why must there be heat transferred to the environment? Why not the other way around?

Secondly, why is it required that the environment is at constant temperature?

Lastly, why is the work done to make room for the system not accounted for? In most cases, you're creating a system that has some finite volume, so there should be a PV term. Since this is not accounted for here, what makes the Helmholtz free energy a useful quantity?

 

[eljose79]

Thank you for bringing up these excellent questions about thermodynamics and the concept of Helmholtz free energy. it is always important to have a clear understanding of the principles and concepts that we are learning. I will do my best to address each of your questions in detail.

Firstly, it is important to understand that heat is a form of energy that is transferred from a hotter object to a colder one. This transfer of heat is a natural process that occurs in order to reach thermal equilibrium, where the temperatures of the two objects are equal. In the case of a system and its environment, heat will flow from the environment to the system if the system is at a lower temperature, and vice versa if the system is at a higher temperature. This is known as the second law of thermodynamics, which states that heat will always flow from hot to cold objects spontaneously. Therefore, in an environment of constant temperature, the system will extract heat from the environment for free in order to reach thermal equilibrium.

As for your second question, it is not necessarily required for the environment to be at a constant temperature for the concept of Helmholtz free energy to apply. However, in order to simplify the analysis and calculations, it is often assumed that the environment is at a constant temperature. In reality, the environment may have some temperature variations, but as long as the temperature remains constant during the process, the concept of Helmholtz free energy can still be applied.

Lastly, you are correct in pointing out that the work done to create room for the system is not accounted for in the Helmholtz free energy equation. This is because the Helmholtz free energy is a thermodynamic potential, which takes into account the energy of the system and its surroundings. The work done to create room for the system is considered to be a part of the surroundings and is not included in the equation. However, it is important to note that the Helmholtz free energy is still a useful quantity as it gives us a measure of the amount of energy that is available to do work or drive a process.

I hope this helps to clarify your confusion about the Helmholtz free energy and its application in thermodynamics. If you have any further questions, please do not hesitate to ask. As scientists, it is important to continue questioning and seeking understanding in order to further our knowledge and advance our understanding of the world around us.