THERMO Spoken Here! ~ J. Pohl © ~ 2019 (A9850-068)

1.26 Method, System and Numbers

The grandest abstract of thermodynamics is the universe which is defined to be all that exists in a physical sense. Everything that happens, happens inside the universe. Being infinitely vast, the universe extends well beyond the range or the localized volume of our engineering systems and events. Physical events of importance to human life occur in vanishingly small spaces in the universe. The impossibility of dealing with the entirety of the universe mandates a Newton's Systematic Approach.

Method: Some method must be used. Newton's Method is what is taught, the beginning. All of science, engineering education begins with arithmetic, algebra... Newton's methods.

System: is part of the whole. We do not study the entirety. The system must be "small." Its events are assumed independent of the vast rest. The system must be "large" so as to include significance to us. From Newton's ideas we have abstracts of "all there is" as:

  • Universe: The entirety of all physical matter known. An infinite amount of mass distributed in an infinite space. A system so large as to be impractical to study.
  • System: A finite amount of matter of the infinite universe specifically selected and noted for the purpose of study. System selection, the first step of any engineering or physics analysis, is an art.
  • Surroundings: System selection divides the universe into system matter, the matter whose change is to be observed or predicted and the remaining infinite matter not selected, which is called the surroundings.
(characteristics and properties)
BODY (or Extended Body)
time:t ~ [t]
position:P ~ [L]
velocity:V ~ [L/t]
mass:m ~ [m]
momentum:mV ~ [m L/t]

Change as Time and/or Event:

Time is the measure of change. Event is the idea of change, any manner of change, including assumed zero change or perma­nence. There is no permanence. Time is one measurement of event, in the sense of event initiation, duration and such. The event occurs principally with the system which usually has observable change. Surroundings might also change upon happening of a system event.

In General each property consists a name and a technical description. The property also has a dimension (or combination of dimensions) and at least one measurement process the measurement of which (taken for some material) are statistically the same unique number (or three, or nine numbers... depending upon the property).

Thus a property is more than a number or numbers and the same set of numbers must be obtained (subject to measurement accuracy) by different measurement processes.

With regard to numbers, physical properties are tensors. Each distinct physical property is ultimately described numerically by one number (the property being a scalar), or by 3 numbers (that property being a vector with the numbers determined relative to a space and time coordinate reference) or 9... numbers.

Tensors are classed by rank as rank zero, rank one, two or some larger integer. There are (3)RANK , that is three raised to the "rank" numbers, and appropriated dimensions, vector basis and so, associated with a physical tensor or system properties. The "numbers" of physical properties must be established by some measurement process.

1(3)1vectorposition, velocity, momentum,
area. {But not force. Force is a
vector but not a property}.
2(3)2tensormoment of inertial and material stress

Measurement and Properties: Measurement, the driving force of science, is the process of making matter and events quantitative. Whatever characteristic of a system that can be measured has the possibility of being named a property. Whatever cannot be measured is not a property. Measurement is property oriented, results in a number which has units. As a rule, numbers have units. Students at this level generally have adequate experience with ideas of measurement and property. The brief discussion below is focused on the needs of classical engineering thermodynamics, limited to simple, compressible substances with minor exceptions.

Measurable and Non-Measurable Properties:  While the idea "measurable properties," (or primary properties in some texts) might seems obvious, the fact that there are properties, physical characteristics of matter, which can be made quantitative but which cannot be measured. Non-measurable (or secondary) properties are made quantitative in relation to other properties that are measurable. There are subtle differences among types of properties but there are many steps of learning that can be accomplished with just a little of the subtly. Measurement itself has become a science. But limited to primary properties - that's all that can be measured. But before that, lets talk primary properties.

Qualifiers for properties of matter include the following distinctions and contrasts:

  • ENUMERATIVE or NATURAL:  These are the numbers of counting. They do not have dimensions. Sometimes natural or enumerative numbers are ascribed units. There is no dimension for "person" as in "the task required work of 6 persons." But the time of the task might be assigned a "pseudo-dimension" as say, "3hr/person A."
  • GEOMETRIC:   two and three dimensional reasoning, mensuration
  • SPATIAL:  time is the independent variable of position and velocity.
  • TEMPORAL:  These properties describe instances and sequences in time.
  • MEASURABLE:  Measurement is the power of science and science begins in a meager way with only what can be measured. Measaurement can be direct or indirect. (Eratosthenes).
  • NON-MEASURABLE:   Some properties of thermodynamics are not measurable. These are made quantitative by inference.
  • PRIMARY AND SECONDARY:  The distinction of primary measurements is that they basically are independent of inner detail of the matter. Primary properties are basic, those for which successful measurement devices are available including: mass, volume, length, density, pressure, temperature and others.
  • EXTENSIVE - INTENSIVE: (or specific)
    Properties with extent: mass (m), volume (L3), kinetic energy [E], potential energy [E], internal energy [E], enthalpy [E] and entropy [E/Θ].
    Properties made by division by system mass: kinetic energy (e=E/m), potential energy (e=E/m), internal energy (e=E/m), enthalpy (e=E/m) and entropy (e/m Θ).
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