Free energy ideal gas

Ideal Gas Free Energy Functions [G°/(RT)] for Detonation Products... 

In the united atom limit—that is, when all bond lengths are equal to zero— the ideal gas free energy functional is of course just given by... 

A different approach is to express the ideal gas free energy functional in terms of the molecular density, pM(R), instead of the site densities. In this case the ideal gas functional is known exactly ... 

The ideal gas data in these tables were calculated directly from a statistical mechanical description of the isolated molecules. In terms of the quantities defined in these tables, jL02(T,p°)=[H°(T) H°(Tr) TS(T) [H°(0) H°(Tr). This expression is derived by noting that the chemical potential of an ideal gas is equal to the ideal gas free energy, G = H TS. 

From tables of the ideal gas free energy function,... 

The alcoholysis of urea affords stepwise acyclic carbonates through the formation of an alkyl carbamate intermediate (Scheme 7.2). The reaction of urea with alcohols to carbamate is exothermic, whereas the subsequent reaction-carbamate to carbonate-is endothermic. Thus, the ideal gas free energy, AG, is positive for the latter step, which means that a low yield of carbonates would be expected [12],... 

The ideal gas free energy functional is defined exactly from statistical mechanics, dropping the temperature-dependent terms that do not affect the fluid structure. Free energy functional contribution due to the excluded volume of the segments is calculated from Rosenfeld s (1989) DFT for a mixture of hard spheres. The functional derivatives of these free energy functional contributions, which are actually required to solve the set of Euler-Lagrange equations, are straightforward. 

It is instructive to consider some other possible versions [7,31,32,52]. The combination of the DH limiting law for the ionic tree energy with the ideal gas free energy does not yield a phase transition. This is also true, if the electrostatic energy is used instead of the tree energy. In both cases, however, phase transitions are obtained with the vdW hard-core tree energy or the Camahan-Starling hard sphere term. However, then the critical density and the critical temperature come out nearer to that of vdW fluids [7],... 

Ideal-gas free energies A and G are, however, p or V dependent. Consider Helmholtz energy first. From the fundamental differential Equation (4.79),... 

From tables of the ideal gas free energy function, miel we get AG /RT = E(G7RT) -= -1-81. for the above reaction at 2500 K. According to equation 18 ... 

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