CONCEPT OF CONTINUUM

In Macroscopic approach of thermodynamics the substance is considered to be continuous whereas

every matter actually comprises of myriads of molecules with intermolecular spacing amongst them.

For analyzing a substance in aggregate it shall be desired to use laws of motion for individual molecules

and study at molecular level be put together statistically to get the influence upon aggregate. In statistical

thermodynamics this microscopic approach is followed, although it is often too cumbersome for practical

calculations.

In engineering thermodynamics where focus lies upon the gross behaviour of the system and

substance in it, the statistical approach is to be kept aside and classical thermodynamics approach be

followed. In classical thermodynamics, for analysis the atomic structure of substance is considered to

be continuous. For facilitating the analysis this concept of continuum is used in which the substance is

treated free from any kind of discontinuity. As this is an assumed state of continuum in substance so the

order of analysis or scale of analysis becomes very important. Thus, in case the scale of analysis is large

enough and the discontinuities are of the order of intermolecular spacing or mean free path then due to

relative order of discontinuity being negligible it may be treated continuous.

In the situations when scale of analysis is too small such that even the intermolecular spacing or

mean free path are not negligible i.e. the mean free path is of comparable size with smallest significant

dimension in analysis then it can not be considered continuous and the microscopic approach for

analysis should be followed. For example, whenever one deals with highly rarefied gases such as in

rocket flight at very high altitudes or electron tubes, the concept of continuum of classical thermodynamics

should be dropped and statistical thermodynamics using microscopic approach should be followed.

Thus, in general it can be said that the assumption of continuum is well suited for macroscopic approach

where discontinuity at molecular level can be easily ignored as the scale of analysis is quite large. The

concept of continuum is thus a convenient fiction which remains valid for most of engineering problems

where only macroscopic or phenomenological informations are desired.

Introduction

Thermodynamics involves the storage, transformation, and transfer of energy.

Energy is stored as internal energy (due to temperature), kinetic energy (due to

motion), potential energy (due to elevation), and chemical energy (due to chemical

composition); it is transformed from one of these forms to another; and it is transferred

across a boundary as either heat or work. We will present equations that

relate the transforma tions and transfers of energy to properties such as temperature,

pressure, and density. The properties of materials thus become very important.

Many equations will be based on experimental observations that have been presented

as mathematical statements, or laws: primarily the fi rst and second laws of

thermodynamics.

The mechanical engineer’s objective in studying thermodynamics is most often

the analysis of a rather complicated device, such as an air conditioner, an engine, or

a power plant. As the fl uid fl ows through such a device, it is assumed to be a continuum

in which there are measurable quantities such as pressure, temperature, and

velocity. This book, then, will be restricted to macroscopic or engineering thermodynamics.

If the behavior of individual molecules is important, statistical thermodynamics

must be consulted.