Basic Concepts of Relevant Thermodynamics and Thermodynamic Variables

Abstract

A macroscopic or a mesoscopic system contains many microscopic constituents, such as atoms and molecules, with a huge number of degrees of freedom to describe their motion. Thermodynamics seeks to describe properties of matter in terms of only a few variables, arguably being the all-around, basic area of sciences and engineering, including biology. Thermodynamics and thermodynamic variables characterize states of matter and their transitions phenomenologically without recourse to microscopic constituents. In this chapter we summarize what we believe to be the essentials that will serve as references throughout the book. The link between this phenomenological description and microscopic mechanics is provided by statistical mechanics beginning next chapter. When a macroscopic system is brought to equilibrium , where its bulk properties become time-independent, they can completely be described by a few variables descriptive of the state, called the state variables . For example, the macroscopic properties of an ideal gas or of an ideal solution at equilibrium can be described by the pressure or the osmotic pressure $p$, volume V, and absolute temperature T; e.g., for a mole of them, the equation of state is $pV = RT$, where the R is the universal gas constant. The thermodynamic state variables are either extensive or intensive. Extensive variables are proportional to the size of the system under consideration; intensive variables are independent of the system size; for example, the gas’ volume V and internal energy E are extensive, whereas the pressure $p$ and the temperature T are intensive. Here, we briefly summarize the universal relations beginning with the first law of thermodynamics. By a universal relation we mean the relation independent of the systems’ microscopic details. We introduce the basic thermodynamic potentials from which we can find the various thermodynamic variables. From the second law of thermodynamics, we discuss nature of the processes leading to equilibrium, which are governed by variational principles for the thermodynamic potentials relevant to ambient thermodynamic conditions.