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3.1: Introduction to Two-Phase Equilibria

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  • There is more than one way in which the principle of conservation of mass for single component systems can be stated. One attractive form is1;

    the mass of a body is constant

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

    \[\begin{Bmatrix} \text{time rate of} \\ \text{change of the} \\ \text{mass of a body}\end{Bmatrix} = 0 \label{1}\]

    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{1}.

    As an example of the application of Equation \ref{1}, we consider the motion of the cannon ball illustrated in Figure \(\PageIndex{1}\).

    Figure \(\PageIndex{1}\): Cannon ball

    Newton’s second law requires that the force acting on the cannon ball be equal to the time rate of change of the linear momentum of the solid body as indicated by

    \[\mathbf{f}= \frac{d}{dt} \left(m\mathbf{v}\right) \label{2}\]

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

    \[\frac{dm}{dt} =0 \label{3}\]

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

    \[\mathbf{f} = m\frac{d\mathbf{v}}{dt} = m \mathbf{a} \label{4}\]

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

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