System Model: EXTENDED BODY

Next - X

Basic Thermodynamics ~ J. Pohl ©

www.THERMOspokenhere.com (27-A320)

Actual matter we see has size and shape and a distribution of mass over the domain of its existence. Nonetheless such masses are often and effectively modeled as having the boundary "of its reality" but with all of its mass concentrated "at a point." The location of that point is called the system center of mass. The point is usually interior to the physical boundary of the system. When the system density is uniform, the center of mass and the center of geometry are the same location. Now we have the system models, BODY and EXTENDED BODY. The utility of EXTENDED BODY as a system model will become evident.

We have persisted in writing the system models as uppercase, e.g., BODY. Our reasons are:

System as "BODY" is physical. It means a specific collection and amount of mass that has been selected by a "focused," selection process.
To select a system and model it as a BODY is to apply mental and/or actual observation of some physical setting and to imagine "extract from all of matter," some part to be a system.
Selection is focused. Done properly, one's mind visualizes a boundary encompassing the system.
Next, the physical matter, and its scenario is imagined to be extracted from totality to become the system or subject of analysis. It is removed from the physical space and placed in our "analysis space."
Finally a careful survey of the boundary, every portion thereof, is made to ascertain where and if so, in what manner, the surroundings (left behind in physical space) might effect or influence the event of consideration.
Those potential influences are notated on the sketch and in the operant equations.

The steps are the same for system specification, be it a BODY or EX-BODY (and other system models).

Body, Point Mass and Particle: Many persons consider these terms to be synonymous. In this writing "point mass" is another way of saying "body" but particle is a different idea.

The term particle is used to mean some part, component, subdivision, entity, etc., the concept of which facilitates the understanding of the nature of matter. Depending on the questions that a study seeks to answer, the system particles might be stars, planets, billiard balls, raindrops, molecules, atoms, ions, electrons, photons, mesons and so on. Thermodynamics defines the particle to be the largest system subdivision, the knowledge of whose individual behavior is sufficient to predict the statistical overall behavior of the group, i.e., the systems thermodynamic properties.

EXTENDED BODY: With the motion of planets in the solar system, it is acceptable that Jupiter or Mars might be considered a BODY ("mass located at a point") because their sizes are miniscule when compared to the space of their motions. However, the real objects of our everyday lives are not point masses. Common objects have extent. The simplest model of physical reality that has extent is the EXTENDED BODY.

In discussions of forces, physics texts invariably show normal, external, friction and gravity forces acting on some block or object as system. The model, EXTENDED BODY adds an aspect of the reality of size to the model BODY. With extended body, all of the mass is modeled (assumed) to be located at the mass center (which is often the geometric center) of space of the body. A border or surface for the mass is envisaged; the forces act at places on this border, all directed through the center of mass of the system.

The ideas expressed above are sufficient for us to do elementary calculations similar to what you have done in physics. The examples presented below provide a minor review of algebra, geometry and physics which are a beginning of thermodynamics. The general organization follows the principal properties of thermodynamic analysis: mass, momentum and energy.