Matter Exists in Space and Time

Basic Thermodynamics ~ J. Pohl ©

www.THERMOspokenhere.com (2-A010)

This section re-introduces some fundamental terms and methods of science that form the basis of Engineering Thermodynamics. Topics are of high-school-level difficulty. To assist students in learning beginning-level thermodynamics; some review to set things straight is required. Principal topics of Section 1 are:

Fundamental Abstracts: The accumulated observations of ourselves are categorized into our "knowledge." From time to time, the essence of "all we know" is formulated as an abstract, being something we all agree that we know. One abstract is "life." While each of us supposes to know what life is, all of us have had very different life experiences. This section is a refresher of what we know. Some examples with rationales (geometry, algebra, assumption and calculation) are listed.

Eratosthanes: the assumption "Earth is spherical" is used.
(A - B)² = A² -2AB + B²: The areas of plane figures equal the sum of the areas of their parts. The useful idea is to break things into smaller pieces, solve all pieces then sum the solutions.
Theorem of Pythagoras: Geometry, with sine and cosine definitions, leads to a useful algebraic result.
Drilling Rig Visibility: Calculations involving very large and small numbers can be difficult.
(-1) x (-1) = 1 : This commonly used fact is a consequence of algebra.

Newton's System: BODY: The physical entity (or object) of Newton's analytic studies was matter having mass but having no extent. This model of mass is called the BODY (point mass or particle). We use "uppercase" notation, BODY, to emphasize that the BODY under consideration has been carefully selected and "set apart" from the rest of the physical world. The mental, analytical act of "setting apart" is the essential part of system specification (more later).

The BODY has mass, momentum, position and velocity but by our assumption, its size is zero. No actual mass has zero size, of course. Nonetheless analytic studies of events are facilitated by the model (of physical reality), BODY. Finally, Newton's Laws of motion address BODY as the system model; much worthwhile has resulted.

Position: the First Vector: Newton used vector mathematics to establish his Laws of Motion (1687). Logically a beginning knowledge of vectors, vectors spaces and vector algebra is needed to understand his ideas. Position is the location in space of our system, the BODY. Examples of this section relate to representation of space as an origin, coordinates and a unit vector basis.

Pharaoh's Engineers: The Great Pyramid is analyzed by use of vectors.
Crank, Rod and Piston: Vector analysis of the engine "drive-train" results in the Laws of Sines and Cosines
Ladder Boom Rescue: Vector analysis is methodological. Every vector has a component and a magnitude-direction form.
High Wire Apparatus: Vector calculations deal with three dimensions readily.
Trigonometry Laws: To derive these again is worth the time.

Velocity: the First Derivative To explain velocity, Newton needed first to explain vectors then he needed to explain calculus. Newton used vectors and calculus because he needed that mathematics.

Newton's Second Law of Motion: Newton's system was the simplest of all perspectives of matter ~ the BODY. By his definitions, a BODY has mass (quantity of matter) and momentum (quantity of motion). We use the notations, m_BODY and mV_BODY, for mass and momentum, respectively.