Modern Engineering Thermodynamics

2.9 The Continuum Hypothesis 43
Surrounding
fluid, S
Glass, G
Zeroth law;
T G = T S
and
T M = T G
therefore,
T M = T S
Mercury, M
FIGURE 2.6
The zeroth law of thermodynamics applied to a mercury in a glass thermometer.
2.9 THE CONTINUUM HYPOTHESIS
While we recognize today the existence of the atomic nature of matter, we have not found an effective way to
apply the basic laws of physics to large aggregates of atomic particles except by a statistical averaging technique.
This is because the number of molecules in even a cubic centimeter of gas at standard atmospheric pressure
and temperature is so large (about 10 20 ) that we cannot simultaneously solve all the equations of
motion for each molecule. The statistical averaging process taken over large numbers of molecules produces a
continuum model for matter, and the continuum hypothesis simply states that large systems made up of many
discrete molecules or atoms may be treated as though they were made up of a continuous (i.e., nonmolecular)
material.
The continuum approach to thermodynamics works well so long as the dimensions of the systems being
analyzed are much larger than the dimensions of the molecules themselves and so long as the time interval over
which a process takes place is very much greater than the average time between molecular collisions. The
continuum thermodynamics breaks down when these conditions are violated, such as in the rarefied gas of
outer space. When continuum thermodynamics breaks down, another type of thermodynamics, called statistical
thermodynamics, can be used to solve problems.
The vast majority of engineering problems can be solved with continuum concepts, and they are the main focus
of this text. Two other technical terms are used to express these ideas, microscopic and macroscopic.
When we deal with differential quantities in continuum analysis, such as dx/dt, we do not infer that the differentials
shrink down to molecular dimensions and thus invalidate the continuum concept. Also, when we speak of
evaluating thermodynamic properties at a point in a continuum system, we extrapolate the continuum concept
in a mathematical sense only. The resulting mathematical functions and relations developed in macroscopic
system analysis are not valid in, and cannot be accurately applied to, microscopic systems.
MICROSCOPIC SYSTEM ANALYSIS
Microscopic system analysis is the analysis of systems at the atomic level. This is the domain of statistical thermodynamics.
MACROSCOPIC SYSTEM ANALYSIS
Macroscopic system analysis is the analysis of systems at the continuum level (i.e., molecular dimensions and time scales
do not enter into the analysis). This is the domain of classical and nonequilibrium thermodynamics.