Thermodynamics---Lesson 6

Statistical Mechanics

Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. Statistical mechanics, sometimes called statistical physics, can be viewed as a subfield of physics and chemistry.
It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum) at the microscopic level. In particular, it can be used to calculate the thermodynamic properties of bulk materials from the spectroscopic data of individual molecules.
This ability to make macroscopic predictions based on microscopic properties is the main advantage of statistical mechanics over thermodynamics. Both theories are governed by the second law of thermodynamics through the medium of entropy. However, entropy in thermodynamics can only be known empirically, whereas in statistical mechanics, it is a function of the distribution of the system on its micro-states.

Kinetic Theory

Kinetic theory (or kinetic theory of gases) attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecular composition and motion. Essentially, the theory posits that pressure is due not to static repulsion between molecules, as was Isaac Newton's idea, but due to collisions between molecules moving at different velocities. Kinetic theory is also known as the kinetic-molecular theory or the collision theory.
The theory for ideal gases makes the following assumptions:
The gas consists of very small particles, each of which has a mass or weight in SI units, kilograms.
The number of molecules is large such that statistical treatment can be applied.
These molecules are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container.
The collisions of gas particles with the walls of the container holding them are perfectly elastic.
The interactions among molecules are negligible. They exert no forces on one another except during collisions.
The total volume of the individual gas molecules added up is negligible compared to the volume of the container. This is equivalent to stating that the average distance separating the gas particles is relatively large compared to their size.
The molecules are perfectly spherical in shape, and elastic in nature.
The average kinetic energy of the gas particles depends only on the temperature of the system.
Relativistic effects are negligible.
Quantum-mechanical effects are negligible. This means that the inter-particle distance is much larger than the thermal de Broglie wavelength and the molecules can be treated as classical objects.
The time during collision of molecule with the container's wall is negligible as comparable to the time between successive collisions.
The equations of motion of the molecules are time-reversible.