Subtopic: Bond work index and differential equation of size reduction
Question Statement:
Which of the following statements regarding size reduction principles is/are TRUE?
Options:
(A) The general differential equation of comminution is $\frac{dE}{dx} = -\frac{K}{x^n}$, where $n = 1$ gives Kick's law, $n = 1.5$ gives Bond's law, and $n = 2$ gives Rittinger's law
(B) Bond's Work Index ($W_i$) is the gross energy (in $\text{kWh/ton}$) required to reduce material from infinite feed size to $80\%$ passing $100\;\mu\text{m}$
(C) Energy efficiency of commercial grinding mills is typically under $1-5\%$, with the vast remainder dissipating as heat
(D) Fine grinding consumes significantly less specific energy than coarse crushing
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
1. Walker-Lewis generalized differential law yields Kick ($n=1$), Bond ($n=1.5$), Rittinger ($n=2$) (A is true).
2. Bond's exact definition of work index $W_i$ (B is true).
3. Most mechanical comminution energy is lost to friction, sound, and thermal heat dissipation (C is true).
4. Fine grinding creates enormous surface area and consumes exponentially more specific energy than coarse crushing (D is false).