Equalities in Mechanics

  1. If we encounter an equality in mathematics, we consider each variable of the equality to have equal weight. That is, each variable can be expressed in terms of other variables. However, an equality becomes significant in mechanics only if we express a physical quantity that is difficult to measure in terms of physical quantities that are easy to measure. For example, [Zem, p.227, (9-20)] is a mathematical equality. In contrast, [Zem, p.228, (9-21)] is a mechanical equality [Zem, p.228, l.1-l.12].

  2. How we extract useful information from the sublimation equation given in [Zem, p.264, l.4].
        Vapor pressures of solids are usually measured over only a small range of temperature [Zem, p.260, l.1]. Using these measurements and the sublimation equation, we can obtain the vapor-pressure constant i' [Zem p.264, l.20]. Then we are able to calculate the vapor pressure of a substance at temperatures at which P is too small to measure [Zem, p.264, l.7-l.10].

  3. To sharpen an equality requires a more refined theory.
        The equation given in [Zem, p.289, l.-13] contains an unknown constant s0. This constant cannot be specified within the theory of thermodynamics. It requires a more refined theory, statistical mechanics, to find its value [Zem, p.289, (11-29)].

  4. (The law of corresponding states)
        We would like to put the Van der Waals equation [Hua1, p.40, (2.28)] into a universal form [Hua1, p.41, (2.33)] so that it is valid for all substances.

  5. Links {1}.