General Solution for Two Degrees of Freedom and Relationship to Jacobian Methods

2 GENERAL SOLUTION FOR TWO DEGREES OF FREEDOM AND RELATIONSHIP TO JACOBIAN METHODS 

In order to obtain the ratio V = —fi/A of coefficients from the vector equation (12.12) in its most general form, let A) and B) represent arbitrary vectors in the two-dimensional space, corresponding to thermodynamic variables A, B, respectively. The successive scalar products of these vectors with (12.12) then lead to the linear equations 

Solving for the 2 x 2 inverse matrix in (12.20), we obtain the desired ratio in the form 

Representative applications of this equation are illustrated in Sidebar 12.7. 

From the definition Cv = TidSf dT )v and (12.22), we obtain the general expression 

The general solution (12.22) reduces to the simpler forms considered previously when we introduce special choices for the variables A and B. Thus, the particular choices  

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