Mathematical relations between the various functions of state

Mathematical relations between the various functions of state 

By combining (2 G4)-(2 G7) with the defininj equations for //, A and C/, further expressions may be obtained. For example, 

Now 7 is a function of state and thus forms an exact differential. It is also known experimentally to bo a smooth function of the variables 8y V and n, , except at points of phase change. If we disregard such points, the second partial differential of U with respect to any pair of variables is independent of tho order of differentiation. 

IJpS and V aa thi oo Cartoaian co-ordinates. V, as a function of 6 and Vp is a surface in tho throo-dimonaional space. 6VldS)y is tho gradient, ffy of this surface with respect to at any plane of constant V. Wo can now think of 

Additional reciprocity relations which give the temperature tuid pressure coefEicients of fif may also be obtained. Thus from (2 61) 

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