Question

This given equation represents which law: \(E=K_k\ ln \frac {d_1}{d_2}\)

• A. Rittinger’s law
• B. Bond’s law
• C. Fick's law
• D. Kick’s law

Answer 1

The Correct Option is D

The correct option is (D): Kick’s law.

Answer 2

Each size-reduction (comminution) law relates the energy needed for grinding to particle size in a different mathematical form, so the given equation can be matched by comparing its structure to the standard form of each law:

1. Rittinger's law: Rittinger's law states that the energy required for size reduction is proportional to the newly created surface area, expressed as \(E=K_R\left(\dfrac{1}{d_2}-\dfrac{1}{d_1}\right)\). This involves a difference of reciprocals of the diameters, not a logarithm, so it does not match the given equation.
2. Bond's law: Bond's law expresses energy in terms of the difference of the reciprocal square roots of the diameters, \(E=K_B\left(\dfrac{1}{\sqrt{d_2}}-\dfrac{1}{\sqrt{d_1}}\right)\). This square-root form is structurally different from the given logarithmic equation.
3. Fick's law: Fick's law describes the rate of diffusion of a substance in terms of a concentration gradient, \(J=-D\dfrac{dC}{dx}\); it is a diffusion law and has no connection to comminution energy or particle diameters at all.
4. Kick's law: Kick's law states that the energy required is proportional to the logarithm of the ratio of the initial to the final particle size, written as \(E=K_k \ln\dfrac{d_1}{d_2}\). This is an exact structural match to the equation given in the question.

Since the given equation is a natural logarithm of the size ratio rather than a difference of reciprocals or reciprocal square roots, it corresponds specifically to Kick's law.

Therefore, the correct answer is Kick's law.