Discussion
Energy requirement (\(E\)) to produce a change (\(dX\)) in dimension \(X\) of a particular size can be expressed as \(\frac{dE}{dX} = -\frac{C}{X^{n}}\), where, \(c\) is constant and \(n\) according to Rittinger’s law is _______.
Answer: D
For Rittinger’s law, \(n = 2\).
The general size-reduction relation \(dE/dX = -C/X^{n}\) gives the three classical laws for different values of \(n\):
- \(n = 2\): Rittinger’s law. Integrating gives \(E = C(1/X_{2} - 1/X_{1})\), energy proportional to the new surface created; it suits fine grinding.
- \(n = 1\): Kick’s law, \(E = C\ln(X_{1}/X_{2})\), suited to coarse crushing.
- \(n = 1.5\): Bond’s law, \(E \propto 1/\sqrt{X_{2}} - 1/\sqrt{X_{1}}\), for intermediate sizes.
So 3/2 is Bond’s exponent, and 1/2 and \(\sqrt{2}\) correspond to none of the classical laws.
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