1. Universe = system (Ur) and reservoir (Ur,Tr) constrained by U0=Ur+Us
Thermal exchange only
Universe = system (Ur) and reservoir (Ur,Tr) constrained by U0=Ur+Us
resevoir (Ur, Tr) U
system Us
Maximize total entropy by minimizing Helmholtz free energy

2. Thermal and mechanical exchange
Universe = system (Us, Vs) and reservoir (Ur, Vr, Tr) constrained by
U0=Ur+Us and V0=Vr+Vs
resevoir (Ur, Vr, Tr) U
system
Us, Vs V
Maximize total entropy by minimizing Gibbs free energy

3. Enthalpy
When considering phase transitions, it is useful to define a quantity h called ‘enthalpy’
Because h depends only on state variables, it too must be a state variable – hence its usefulness.
When a material changes phase (e.g. from a solid to a liquid) at constant temperature and pressure, latent heat l must be added. This heat of transformation is related simply to the enthalpy difference between the liquid and solid

5. The Tds equations

6. Thermodynamic potentials and equilibrium