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Thermodynamic properties, including entropy, belong to a chemical substance; to be more precise, the concept of a thermodynamic phase is needed. A phase is in general a solution of individual components (pure substances). Let us consider the example of a burning candle, starting with surrounding air. Air is a gaseous phase — a gaseous solution containing two chief components, oxygen (O2) and nitrogen (N2). The latter are pure substances.
A candle flame is also a gaseous solution, but it contains many components that react with each other. Therefore, its composition varies in different zones of the flame. Furthermore, tiny particles of carbon are formed during combustion, which give the candle its characteristic color. Thus, a candle flame should be considered a suspension — a gas in which small particles of a solid substance are dispersed. Thermodynamically, we speak of two phases: the gaseous solution itself and the glowing carbon particles.
In thermodynamics, a phase is described by a single fundamental equation of state, and in this sense, different coal particles belong to the same phase. Along this way, it is important to separate extensive quantities (internal energy and entropy) from intensive quantities (temperature, pressure, and concentration). Extensive quantities are summed up, and thus the total internal energy and entropy of all coal particles will be the sum over all particles, although in this case we must not forget about the surface energy.
The candle material typically includes paraffin and stearin; the paraffin consists of alkanes ranging from C18H38 (octadecane) to C35H72 (pentatriocontane). The melt is a homogeneous solution and thus a single thermodynamic phase, while the solid candle body has a complex composite structure containing microparticles of different phases. From a thermodynamic standpoint, the different microparticles must be sorted into different thermodynamic phases; thus, the thermodynamics of the solid candle is rather complex.
This book will focus for simplicity on the thermodynamics of individual substances. Therefore, thermodynamics of solutions and thermodynamics of solid candle will not be considered. Surface effects will also be ignored, as usually the surface energy is negligible. The comparison of thermodynamics and statistical mechanics normally is made exactly at such a level. It will also be sufficient to reveal the logical structure of classical thermodynamics.
In this part of the book to discuss the conceptual model, a drawing from Sadi Carnot’s book ‘Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power‘ is employed:
This belongs to the famous cycle for finding the maximum efficiency of a steam engine. Now, I describe the figure in general only. It depicts a cylinder with a piston containing a chemical substance. The substance mass remains constant; such a thermodynamic system is called a closed system. It is assumed that the cylinder and piston have ideal thermal properties (zero heat capacity) and do not undergo deformation. Therefore, their properties are considered to have no effect on the interaction of the substance with the external environment. The piston sets the external pressure, and two other bodies, A and B, at the bottom of the figure will be used as thermostats to control temperature of the system. When the cylinder does not touch any of these bodies, there is no heat transfer between the substance and environment. When the cylinder is connected to one of the thermostats, there is heat transfer.
Physical quantities from mechanics are employed without any discussion: volume (length), pressure, and work, including methods for measuring them. The development of barometers paralleled the development of thermometry, but this belonged to hydrostatics, a branch of mechanics. Therefore, we start with a discussion of temperature; this was the first non-mechanical physical quantity. Temperature in thermodynamics and its relationship to thermometry are examined. The thermal equation of state, which plays a major role in thermometry, is also considered. Note that temperature plays a significant role in continuum mechanics, as material properties are functions of temperature.
The development of thermometry led to separation of the concept of heat from the concept of temperature. Calorimeters have been developed — instruments to measure the amount of heat released in a process. However, heat happened not to be a function of a substance state. A calorimeter measures the amount of heat, but we cannot say that a substance possesses heat at a given state. The development of thermodynamics is related to the maximum efficiency of a steam engine and the interconversion of heat and work. Instead of heat and work, which are not functions of state, two new physical quantities have been introduced: internal energy and entropy; both characterize the state of a substance.
We will consider the calculation of internal energy and entropy from experimental data (the equation of state and calorimetry). New thermodynamic properties such as enthalpy and Gibbs energy happens to be more convenient for practical work. It will be considered how thermodynamic tables are compiled from experimental data. Thermodynamic tables includes entropy of a substance and they are used to compute equilibrium composition.
Classical thermodynamics provides also equilibrium criteria (the Clausius inequality). The existence of this inequality raises many questions. Often it is said that classical thermodynamics is applicable only to equilibrium states, and such a statement basically denies the Clausius inequality. We will use two simple examples to examine how classical thermodynamics makes it possible to consider non-equilibrium states and thus to employ equilibrium criteria to compute equilibrium composition.
Thermodynamics doesn’t explicitly include time, but in many cases this is an advantage, as it allows for the fast solution of practical problems. An example of estimating the temperature of a candle flame is considered (the adiabatic flame temperature). This will require minimal thermodynamics of solutions, which in the case of an ideal gas solution will be understandable on an intuitive level.
In conclusion, the entropy of non-equilibrium states in classical thermodynamics is examined in more detail – this will be necessary when discussing the relationships between thermodynamics and statistical mechanics. A brief overview of irreversible thermodynamics is given and its relationship to classical thermodynamics and continuum mechanics is discussed.
Next: Chapter 1. Temperature and Thermal Equation of State
Additional information
In Russian. Physical quantity and empirical fact: The relationship between the measurement of a physical quantity and the theory of physics – the example of measuring length. Measurement errors allow us to speak of empirical science, separated from the worldview.