Concept of continuum - thermodynamics:
Sol: Even the simplification of matter into molecules, atoms, electrons, etc. is too complex a picture for many problems of thermodynamics. Thermodynamics doesn't make any hypotheses about the structure of the matter of system. The volumes of system considered are quite large as compared to molecular dimensions. The system can be regarded as continuum. The system is supposed to contain continuous distribution of matter. There are no voids and cavities present. The pressure, temperature, density and other properties are average values of action of several molecules and atoms. This kind of idealization is a must for solving most of the problems. The laws and concepts of thermodynamics are not dependent of structure of matter.
In accordance to this concept there is minimum limit of volume up to which the property remains continuum. Below this volume, there is sudden change in the value of the property. This type of region is called as region of discrete particles and the region for which the property are maintain is called as region of continuum. The volume up to which continuum properties are maintained is called as continuum limit.
For Example: If we measure the density of a substance for a large volume (ν1), the value of density is(ρ1). If we go on reducing the volume by v', below which ratio äm/äv deviates from its actual value and value of äm/äv is large or small.
Thus according to this concept design could be defined as