Switching from Entropy to Free Energy

Switch from Maximum Entropy to Minimum Free Energy 

In Chapter 7 we reasoned with the principle that systems tend toward states of maximum entropy. We considered systems with known or zero energy exchange across their boundaries. That logic helped explain gas expansion, particle mixing, and the interconversion of heat and work in engines. If we continued no further, we would miss much of the power of thermodynamics for physics, chemistry, and biology. 

For processes in test tubes in laboratory heat baths, or processes open to the air, or processes in biological systems, it is not the work or heat flow that you control at the boundaries. It is the temperature and the pressure. This apparently slight change in conditions actually requires new thermodynamic quantities, the free energy and the enthalpy, and new extremum principles. S stems held at constant temperature do not tend toward their states of maximum entropy. They tend toward their states of minimum free energy. 

In Chapter 7, U, V, and N were the independent variables. Independent variables represent quantities that you can measure or control at the boundary of the system. You choose independent variables based on the type of boundaries enclosing the system. In Example 7.2 two otherwise isolated objects were 

Consider a process in a system that we will call the test tube, immersed in a heat bath. The system need not be a real test tube in a water jacket. It could be molecules in a solvent or air in the atmosphere. Heat bath refers to any surroundings of a system that hold the temperature of the system constant. This arrangement controls the temperature T, not the energy U, at the boundary around the subsystem. If the test tube plus heat bath are isolated from the greater surroundings, equilibrium will be the state of maximum entropy for the total system. However, we are not interested in the state of the total system. We are interested in what happens in the test tube itself. We need a new extremum principle that applies to the test tube, where the independent variables are (T,V,N). 

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