# Thermodynamic potentials

by Lojzek
Tags: potentials, thermodynamic
 P: 249 I have some questions about thermodynamic potentials (internal energy U, enthalpy H, Helmholz free energy F, Gibbs free energy G): 1. The differentials of potentials: dU<=TdS-pdV dH<=TdS+Vdp dF<=-SdT-pdV dH<=-SdT+Vdp Do this equations apply only for a single homogeneous system or can they be used for a system composed of several different subsystems? Example: Let's have N subsystems, each respecting the equation dUi<=TidSi-pidVi Considering U=$$\sum$$Ui S=$$\sum$$Si V=$$\sum$$Vi, does it always follow that dU<=TdS-pdV? I think I can prove this if all pressures and temperatures are equal. Can this equation also be used if pressures and temperatures of subsystems are not equal? In this case, should we use the outside temperature and pressure for the equation corresponding to the whole system? Can similar generalization be used for other potentials? 2. In which cases the can we get inequalities like dU