Question

The statement given above which suggests us to calculate α from the expression α = √K_a/c  and than compare its value with 0.1 looks a little odd. How can we compare the value of α (which is derived after making the assumption) with 0.1 and then claim that it is correct if α ≤ 0.1? Can you suggest the validity of this statement?

Answer 1

 The actual expression for calculating the value of α is, Ka = Cα²/1-α  If we make the assumption that α  is very small compared to one and ignore it in the denominator, we get, K_a = Cα² . By ignoring the α in the denominator, we increase the value of the denominator. This will consequently increase the value of the numerator (since the ratio is a constant) consequently the value of α   calculated after the assumption will be greater than the actual value of α . If this value of α   is less than or equal to 0.1 then it means that the actual value of α   will be much less compared to 0.1. Therefore the assumption is valid. If this value of α is greater than 0.1, than the actual value of α may be greater, equal to or less than 0.1. So here we cannot predict and so we do not make the assumption.