Free Energy Defines Another Extremum Principle

Free Energy Defines Another Extremum Principle 

Now we reason with the First and Second Laws of thermodynamics to find an expression that describes the condition for equilibrium in terms of the changes in the test tube alone. 

Because the entropy is extensive, the entropy change of the total system is the sum of the entropy changes of its parts  

Our aim is to relate dSbath to some property of the test tube system. Use the fundamental equation, dibath = (l/T)dU + f)/T)dV-(ij/T)dN = (l/TldUbath for a bath in which V and N are constant. Combine this with Equation (8.2) to get 

You now have an expression describing the approach to equilibrium in terms of the test tube subsystem alone. Define a quantity f, the Helmholtz free energy  

---

Free Energy Defines Another Extremum Principle... 

---