Metastable Versus Equilibrium States

The problem statement provides us with the value of y (0.30) at some time t (20 min), and also the value of n (3.1) from which data it is possible to compute the value of the constant k. In order to perform this calculation, some algebraic manipulation of Equation 10.17 is necessary. First, we rearrange this expression as follows  

Taking natural logarithms of both sides leads to 

Incorporating values cited above for y, n, and t yields the following value for k  

At this point, we want to compute fg.s —the value of f for y = 0.5—which means that it is necessary to establish a form of Equation 10.17 in which t is the dependent variable. This is accomplished using a rearranged form of Equation 10.17a as 

substituting into this expression the value of k determined above, as well as the value of n cited in the problem statement (viz., 3.1), we calculate as follows  

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