What is a thermodynamic function
In order for your coffee to taste good in the morning, the milk has to mix properly with the coffee. For this we need thermodynamic potentials. We'll explain what that is in this post.
But what are these thermodynamic potentials? You are probably already familiar with potentials from mechanics. They are used similarly in thermodynamics. You can think of a thermodynamic potential as the driving force for a state of equilibrium. The state variables change until equilibrium is established. In mechanics we had a state of equilibrium when the potential energy no longer changes over the location, i.e. the derivative is equal to zero. We now do the same thing, only that we want to look at the change over time.
And what potential is there now? To do this, we consider what types of balance we know. The best known balance is the mechanical one. Let us now consider a closed piston with two different pressures on each side. The piston will now move until the pressure is the same on both sides. In doing so, the volume of both chambers will change. That means the pressure is the driving force for the equalization process and we have found our first potential.
Next we consider thermal equilibrium. For this we look at the flask again, only this time the temperature is different. A heat flow now flows between the two chambers until the temperature is the same. So the temperature is our second potential.
The last thing we know is the material balance. So now it's about the composition. For this we consider a chamber that is separated in the middle. There are gases of different compositions on both sides. If we remove the separation, the two gases will mix until the composition is the same. That means we are now looking for the driving force for material equilibrium. We define ourselves as:
It is called chemical potential. Each component has a defined chemical potential that influences the amount of substance n. If we look at the fundamental equation, we see that, analogously, the temperature T has an influence on the entropy S and the pressure p has an influence on the volume V:
If we consider mixtures, we can complete our fundamental equation:
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