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3.1: Introduction

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  • In Chapter 1, we pointed out that much of chemical engineering is concerned with keeping track of molecular species during processes in which chemical reactions and mass transport take place. However, before attacking the type of problems described in Chapter 1, we wish to consider the special case of single component systems. The study of single component systems will provide an opportunity to focus attention on the concept of control volumes without the complexity associated with multi‐component systems. We will examine the accumulation of mass and the flux of mass under relatively simple circumstances, and this provides the foundation necessary for our subsequent studies.

    There is more than one way in which the principle of conservation of mass for single component systems can be stated. Provided that a body is not moving at a velocity close to the speed of light (Hurley and Garrod, 1978), one attractive form is;

    \[the mass of a body is constant \nonumber\]

    however, we often express this idea in the rate form leading to an equation given by

    \[\left\{\begin{array}{l}{\text { time rate of }} \\ {\text { change of the }} \\ {\text { mass of a body }}\end{array}\right\}=0 \label{3-1}\]

    The principle of conservation of mass is also known as the axiom for the conservation of mass. In physics, one uses the word axiom to describe an accepted principle that cannot be derived from a more general principle. Axioms are based on specific experimental observations, and from those specific observations we construct the general statement given by Equation \ref{3‐1}.

    As an example of the application of Equation \ref{3‐1}, we consider the motion of the cannon ball illustrated in Figure 3‐1. Newton’s second law requires that the force

    Figure 3‐1. Cannon ball

    acting on the cannon ball be equal to the time rate of change of the linear momentum of the solid body as indicated by

    \[\mathbf{f}=\frac{d}{d t}(m \mathbf{v}) \label{3‐2}\]

    We now apply Equation \ref{3‐1} in the form

    \[\frac{d m}{d t}=0 \label{3‐3}\]

    to find that the force is equal to the mass times the acceleration.

    \[\mathbf{f}=m \frac{d \mathbf{v}}{d t}=m \mathbf{a} \label{3‐4}\]

    Everyone is familiar with this result from previous courses in physics and perhaps a course in engineering mechanics.