Chapter 2, Problem 2.29P

Interpretation Introduction

(a)

Interpretation:

What are the units of constants 200 and 10.

Concept introduction:

Experiments with seed crystals of different sizes show that the rate of nucleation varies with the seed crystal diameter as,

$\begin{array}{l}\text{r}\left(\text{crystals}\text{/}\text{min}\right)\text{=}\text{200}\text{D}\text{-}\text{10}{\text{D}}^{\text{2}}\\ \text{D=}\text{Crystal}\text{diameter,}\text{r}\text{=}\text{Crystals}\text{formation}\text{rate}\end{array}$

It is assumed that the given equation is valid and therefore dimensionally homogeneous. So, the dimension of the left hand side and right hand side of the equation is equal. In addition, the dimensions in the two sections of the left hand side are equal.

Interpretation Introduction

(b)

Interpretation:

The crystal nucleation rate to a crystal diameter of 0.050 inch should be calculated.

Concept introduction:

Experiments with seed crystals of different sizes show that the rate of nucleation varies with the seed crystal diameter as,

$\begin{array}{l}\text{r}\left(\text{crystals}\text{/}\text{min}\right)\text{=}\text{200}\text{D}\text{-}\text{10}{\text{D}}^{\text{2}}\\ \text{D=}\text{Crystal}\text{diameter,}\text{r}\text{=}\text{Crystals}\text{formation}\text{rate}\end{array}$

Interpretation Introduction

(c)

Interpretation:

Derive a formula for r (crystals/s) in terms of D (inches).

Concept introduction:

Experiments with seed crystals of different sizes show that the rate of nucleation varies with the seed crystal diameter as,

$\begin{array}{l}\text{r}\left(\text{crystals}\text{/}\text{min}\right)\text{=}\text{200}\text{D}\text{-}\text{10}{\text{D}}^{\text{2}}\\ \text{D=}\text{Crystal}\text{diameter,}\text{r}\text{=}\text{Crystals}\text{formation}\text{rate}\end{array}$

Interpretation Introduction

(d)

Interpretation:

Explain what is the equation gives away with its empirical nature.

Concept introduction:

Experiments with seed crystals of different sizes show that the rate of nucleation varies with the seed crystal diameter as,

$\begin{array}{l}\text{r}\left(\text{crystals}\text{/}\text{min}\right)\text{=}\text{200}\text{D}\text{-}\text{10}{\text{D}}^{\text{2}}\\ \text{D=}\text{Crystal}\text{diameter,}\text{r}\text{=}\text{Crystals}\text{formation}\text{rate}\end{array}$

It is assumed that the given equation is valid and therefore dimensionally homogeneous. So, the dimension of the left hand side and right hand side of the equation is equal. In addition, the dimensions in the two sections of the left hand side are equal.