Thermodynamics---Lesson 4

Statistical Thermodynamics

In thermodynamics, statistical thermodynamics is the study of the microscopic behaviors of thermodynamic systems using probability theory. Statistical thermodynamics, generally, provides a molecular level interpretation of thermodynamic quantities such as work, heat, free energy, and entropy. Statistical thermodynamics was born in 1870 with the work of Austrian physicist Ludwig Boltzmann, much of which was collectively published in Boltzmann's 1896 Lectures on Gas Theory.
Boltzmann's original papers on the statistical interpretation of thermodynamics occupy about 2,000 pages in the proceedings of the Vienna Academy and other societies. The term "statistical thermodynamics" was proposed for use by the American thermodynamicist Willard Gibbs in 1902. According to Gibbs, the term "statistical", in the context of mechanics, i.e. statistical mechanics, was first used by the Scottish
Classical thermodynamics vs. statistical thermodynamics
As an example, from a classical thermodynamics point of view we might ask what is it about a thermodynamic system of gas molecules, such as ammonia NH3, that determines the free energy characteristic of that compound? Classical thermodynamics does not provide the answer. If, for example, we were given spectroscopic data, of this body of gas molecules, such as bond length, bond angle, bond rotation, and flexibility of the bonds in NH3 we should see that the free energy could not be other than it is. To prove this true, we need to bridge the gap between the microscopic realm of atoms and molecules and the macroscopic realm of classical thermodynamics. From physics, statistical mechanics provides such a bridge by teaching us how to conceive of a thermodynamic system as an assembly of units. More specifically, it demonstrates how the thermodynamic parameters of a system, such as temperature and pressure, are interpretable in terms of the parameters descriptive of such constituent atoms and molecules.
In a bounded system, the crucial characteristic of these microscopic units is that their energies are quantized. That is, where the energies accessible to a macroscopic system form a virtual continuum of possibilities, the energies open to any of its submicroscopic components are limited to a discontinuous set of alternatives associated with integral values of some quantum number.





Chemical Thermodynamics

In thermodynamics, chemical thermodynamics is the mathematical study of the interrelation of heat and work with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics. Chemical thermodynamics can be generally thought of as the application of mathematical methods to the study of chemical questions and is concerned with the spontaneity of processes.
The structure of chemical thermodynamics is based on the first two laws of thermodynamics. Starting from the first and second laws of thermodynamics, four equations called the "fundamental equations of Gibbs" can be derived. From these four, a multitude of equations, relating the thermodynamic properties of the thermodynamic system can be derived using relatively simple mathematics. This outlines the mathematical framework of chemical thermodynamics.
The primary objective of chemical thermodynamics is the establishment of a criterion for the determination of the feasibility or spontaneity of a given transformation. In this manner, chemical thermodynamics is typically used to predict the energy exchanges that occur in the following processes:
Chemical reactions
Phase changes
The formation of solutions
The following state functions are of primary concern in chemical thermodynamics:
Internal energy (U)
Enthalpy (H).
Entropy (S)
Gibbs free energy (G)
Most identities in chemical thermodynamics arise from application of the first and second laws of thermodynamics, particularly the law of conservation of energy, to these state functions.