From the macroscopic perspective, the description of matter is simplified by considering it to be distributed continuously throughout a region. The correctness of this idealization, known as the continuum hypothesis, is inferred from the fact that for an extremely large class of phenomena of engineering interest the resulting description of the behavior of matter is in agreement with measured data.
When substances can be treated as continua, it is possible to speak of their intensive thermodynamic properties “at a point.” Thus, at any instant the density at a point is defined as
r lim amb (1.3) VSV¿ V
where V is the smallest volume for which a definite value of the ratio exists. The volume V contains enough particles for statistical averages to be significant. It is the smallest vol- ume for which the matter can be considered a continuum and is normally small enough that it can be considered a “point.” With density defined by Eq. 1.8, density can be described mathematically as a continuous function of position and time.
The density, or local mass per unit volume, is an intensive property that may vary from point to point within a system. Thus, the mass associated with a particular volume V is determined in principle by integration
Factor Prefix Symbol
1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h
102 centi c
103 milli m
106 micro 109 nano n 1012 pico p
and not simply as the product of density and volume.
The specific volume v is defined as the reciprocal of the density, v 1r. It is the volume
per unit mass. Like density, specific volume is an intensive property and may vary from point to point. SI units for density and specific volume are kg/m3 and m3/kg, respectively. How- ever, they are also often expressed, respectively, as g/cm3 and cm3/g.
In certain applications it is convenient to express properties such as a specific volume on a molar basis rather than on a mass basis. The amount of a substance...