Confused by some aspects of thermodynamics

[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:

 

[shyboy]

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

 

[Graeme Robinson]

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.