Universe = system (Ur) and reservoir (Ur,Tr) constrained by U0=Ur+Us

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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

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

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

The Tds equations

Thermodynamic potentials and equilibrium