A New Approach to the Calculation of Work Index and the Potential Energy of a Particulate Material
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Abstract
The work index W<sub>i</sub> was defined by F. Bond as the specific energy (kWh/ton) required to reduce a particulate material from infinite grain size to 100 microns. The calculation is based on the size-energy relationship <i>e</i><sub>1,2</sub>=C.(1/x<sub>2</sub><sup>n</sup>–1/x<sub>1</sub><sup>n</sup> ) , which for n = 0.5, x<sub>1</sub> = ∞ and x<sub>2</sub> =100, by definition gives e∞, 100 = <i>W</i><sub>i</sub> and consequently C=10<i>W</i><sub>i</sub>. In theory, for a given material the value found for <i>W</i><sub>i</sub>.should be constant regardless of the measured sizes x<sub>1</sub> and x<sub>2</sub> used to calculate the constant C by measuring the energy <i>e</i><sub.1,2</sub>. In practice this is not so due to the fact that n ≠ 0.5 and many correction factors have been proposed to overcome this inadequacy experienced by accepting n= 0.5. The present paper proposes a simple way to calculate the appropriate exponent n using conventional grinding procedures. The same calculation can be used to calculate the true value of Wi and attribute a potential energy state to a material at any size.
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