130 INTRODUCTION TO IMMUNOCHEMICAL SPECIFICITY 



let us say F, such that Ft,p = j(V,S). We can get this rather simply 

 by the definition 



F = H - TS (14) 



It is easy to show that F is a function of V and 5" when P and T 

 are constant. So is TS, obviously : when T is constant it is a function 

 of 5" alone. From our original definition of H we have 



H = E -\- PV (15) 



When P is constant, PF is a function of V only. We saw above that 

 £ is a function of P and V only ; consequently, when P is constant, 

 £ is a function merely of V. Therefore, 



F = H - TS = E + PV - TS (16) 



is a function of V and S. Consequently, the thermodynamic function 

 F defined by this expression is a function of V and S. The new func- 

 tion is called the Gibbs free energy. 



When T and P are constant, we have from equation (16) 



A£p,r = A£ + PAF - rA5 (17) 



Now, from equation (3) above, we have Aii = AQ — Al>F. If we 

 ignore complications such as osmotic effects, the only work the system 

 does is mechanical, MV = P AV, and AE = AQ — P AV. Substitut- 

 ing this into equation (17), w^e obtain 



AFp,T = AQ - PAV -\- PAV - TAS (18) 



From the definition of entropy, AQ = T AS ior a. reversible process, 

 we find that for a reversible process, or at equilibrium, 



AFp,T = O (19) 



If the pressure does vary but the temperature continues to remain 

 constant, we have from equation (16) 



dF = dE + P dV + J' dP - T dS 



Again, dE = dQ - P dV = T dS - P dV, and we obtain 



dPr = VdP 



For a perfect gas we have PV = nRT, or V = nRT/P, so that 



