In recent years, hopanes and modified hopanes (nor and homo derivatives), collectively termed hopanoids, have come to be recognized as ubiquitous in sedimentary organic matter of varied origin (303). [Pg.783]

It is assumed throughout that an expression for the rate of reaction in terms of the local thermodynamic variables is available. The derivation of such expressions is no easy task (see for example Hougen and Watson, 1947) and there are some commercial reactions for which no sound kinetic expression is known. Nor is it always easy to get at those that are being used, for often a company will guard [Pg.10]

Here the first term represents ff and the second term the effect of 5 . Eq. (8.19) represents one of the many empirical ways in which Eq. (8.18) can be made to work in practice (Miodownik 1977). However, this expression does not lend itself easily to a derivation of the associated value of Cp nor to an explicit formulation of 6AG /5T. Therefore, most alternative expressions have been based on approximate analytical expressions for the magnetic specific heat. However, all such expressions also incorporate the functions og 0 +1) and r and are a far cry from the original methods of graphical integration. [Pg.255]

The first derivative on the right-hand side of equation (2.53) must be zero because subsystems 1 and 2 have been defined to be independent of each other. Therefore, (50/5 ) in the second term of equation (2.53) must also equal zero in order for this equation to be true for all conditions. In a similar manner, starting with the equivalent equations involving the derivative of 0 /0, one can show that (50/5zi) = 0. If one substitutes this last result into equation (2.52), one gets (50 /5zi) = 0, and the conclusion that 0 is independent of ri. From a similar treatment, one can also show that (5 2/5c2) = 0, so that 02 is independent of r2. Thus, since the two ratios i/0 and 2/0 are independent of r neither 0, 0i, nor 0 can depend upon the c variables. [Pg.75]

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