9. It can be shown that the power consumed by a closed batch comminution process is given by WW=1dtdA where is the efficiency of the process and A is the free energy of the ore. (a) Equation (2.12) is too general as it stands. Common practice is to assume that the free energy and efficiency depend on the size L of the particles according to a power-law relation, 1dLdA=LnK where K and n are constants. Show that for n=1, Equations (2.13) and (2.12) together imply W=KlnL1L2=KlnL2L1 This is called Kick's Law (1885). It holds that the work of communition depends solely on the size reduction ratio L2/L1, regardless of the original particle size. Kick's Law may be approximately true for relatively large particles. (b) An alternative assumption is that the energy of comminution is proportional to the new surface area produced. This is equivalent to the assumption that n=2 in Equation (2.13). Show that for n=2, Equations (2.13) and (2.12) together imply W=K(L21L11) This is called Rittinger's Law (1867). It is approximately true for relatively small particles. (c) Show that for n>1, Equations (2.13) and (2.12) together imply W=(n1K)(L2n11L1n11)