Spontanelity of any process can be predicated withthe help of DeltaS_("total").But this requires calculation of changes in system as will as surrounding. If some criteria (depanding upon the system only) can be developed for checking spontaneity unde specific conditions, then that would be a more useful parameter.The criteria can be derived from Clausius inequality. T ds ge q,(gt sign for irreversible process= sign for rev. process) or T dsgtdU-W for an irreversible process or T dS_(sys)gt dU_(sys)+p dV [consider no non-PV work] If U and V are constant, T dS_(sys)gt0 or (dS)_(u.v)gt0 for spontaneous process if V and T are constant T dS gt dU or dU-T dS lt 0 As temperature is constant, dU-d(TS)lt0 or d(U-TS)lt0 Another state function A(Helmholtz's function)=U-TS A decrease in Helmholtz function (A) under constant volume and temperature is the criteria of spontaneity of a process. If a state function G is defined such as G=H-TS, then dG must decrease for a spontaneou process (involving only PV work ) occuring at