The Second Moment of E t —Mixing

Let s calculate the second moments for these two reactors. For the CSTR, 

The second moment about the mean is a much better indicator of mixing that the second moment about the origin. The second moment about the mean, also known as the variance, is defined as 

For a CSTR, t = r and = t. For a PFR, t = r and = 0. These values of clearly reflect the major difference in mixing between the two ideal, continuous reactors. 

The values of and/ri forthisdistiibutionfunction were found to be lOminand 104 min, respectively, in Example 10-S. Moreover, fii =t = r. The variance will be calculated from Eqn. (10-27). 

The value of cr is proportional to the width of the E t) curve. For an ideal CSTR, aft = 1, whereas for an ideal PFR, tr/r = 0. For this example, r/r = 0.20. The distribution of residence times is not vray broad compared to the mean residence time. 

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