We’ve all heard the old saying, You can’t add apples and oranges (Fig. 7–3).
This is actually a simplified expression of a far more global and fundamental
mathematical law for equations, the law of dimensional homogeneity,
stated as
Every additive term in an equation must have the same dimensions.
Consider, for example, the change in total energy of a simple compressible
DIMENSIONAL HOMOGENEITY
We’ve all heard the old saying, You can’t add apples and oranges (Fig. 7–3).
This is actually a simplified expression of a far more global and fundamental
mathematical law for equations, the law of dimensional homogeneity,
stated as
Every additive term in an equation must have the same dimensions.
Consider, for example, the change in total energy of a simple compressible
closed system from one state and/or time (1) to another (2), as illustrated in
Fig. 7–4. The change in total energy of the system ( E) is given by Change of total energy of a system:
where E has three components: internal energy (U), kinetic energy (KE), and potential energy (PE). These components can be written in terms of the system mass (m); measurable quantities and thermodynamic properties at each of the two states, such as speed (V), elevation (z), and specific internal
energy (u); and the known gravitational acceleration constant (g),
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