Thermodynamic Systems: Basic Concepts

Thermodynamic Systems: Basic Concepts
1.1 Introduction
The word “Thermodynamics” originates from its Greek roots (therme, heat; dynamis, force). As a subject it is concerned with quantification of the inter-relation between energy and the change of state of any real world system. The extent of such change of state due to transfer of energy to or from the system is captured through the basic equations of thermodynamics which are derived starting from a set of fundamental observations known as “Laws of Thermodynamics”. The laws are essentially ‘postulates’ that govern the nature of interaction of real systems and energy. They are products of human experiential observations to which no exceptions have been found so far, and so are considered to be “laws”. The scope of application of the laws of thermodynamics ranges from the microscopic to the macroscopic order, and indeed to cosmological processes. Thus, all processes taking place in the universe, whether in non-living or living systems, are subject to the laws of thermodynamics.

Historically speaking, thermodynamics, is an extension of Newtonian mechanics which considered mechanical forces (or energy) as the agent of change of state of a body (anything possessing mass), the state being defined by its position and momentum with respect to a frame of reference. With the discovery steam power which propelled the so-called ‘Industrial Revolution’ of the 18th century, it became evident that not only the direct application of mechanical energy can change the state of a system, but that fluids themselves can act as reservoir of energy, which can be harnessed to effect changes in the real world to human advantage. It was this observation that laid the foundations of thermodynamics, which now constitutes a generalized way of understanding and quantifying all changes that occur during processes taking place in the universe as a result of application of energy in any form.

1.2 Thermodynamic System: Select Definitions
It may be evident from the foregoing introduction, that for the purpose of any thermodynamic analysis it is necessary to define a ‘system’. A system, in general, is any part of the universe which may be defined by a boundary which distinguishes it from the rest of the universe. Such a thermodynamic system is usually referred to as control volume as it would possess a volume and would also contain a definite quantity of matter. The system boundary may be real or imaginary, and may change in shape as well as in size over time, i.e., increase or decrease.

A system can either be closed or open. A closed system does not allow any transfer of mass (material) across its boundary, while an open system is one which does. In either case energy transfer can occur across the system boundary in any of its various forms; for example, heat, work, electrical / magnetic energy, etc. However, for most real world systems of interest to chemical engineers the primary forms of energy that may transfer across boundaries are heat and work. In contrast to closed or open systems, a system which is enclosed by a boundary that allows neither mass nor energy transfer is an isolated system.

All matter external to the system constitutes the surroundings. The combination of the system and surroundings is called the universe. For all practical purposes, in any thermodynamic analysis of a system it is necessary to include only the immediate surroundings in which the effects are felt.

A very common and simple example of a thermodynamic system is a gas contained in a piston-and-cylinder arrangement derived from the idea of steam engines, which may typically 
Fig. 1.1 Example of simple thermodynamic system
exchange heat or work with its surroundings. The dotted rectangle represents the ‘control volume’, which essentially encloses the mass of gas in the system, and walls (including that of the piston) form the boundary of the system. If the internal gas pressure and the external pressure (acting on the moveable piston) is the same, no net force operates on the system. If, however, there is a force imbalance, the piston would move until the internal and external pressures equalize. In the process, some net work would be either delivered to or by the system, depending on whether the initial pressure of the gas is lower or higher than the externally applied pressure. In addition, if there is a temperature differential between the system and the surroundings the former may gain or lose energy through heat transfer across its boundary. 
This brings us to a pertinent question: how does one characterize the changes that occur in the system during any thermodynamic process? Intuitively speaking, this may be most readily done if one could measure the change in terms of some properties of the system. A thermodynamic system is, thus, characterized by its properties, which essentially are descriptors of the state of the system. Change of state of a system is synonymous with change in the magnitude of its characteristic properties. The aim of the laws of thermodynamics is to establish a quantitative relationship between the energy applied during a process and the resulting change in the properties, and hence in the state of the system.  

1.3 Types of Energies associated with Thermodynamic Processes
We know from the fundamentals of Mechanics, that the energy possessed by a body by virtue of its position or configuration is termed potential energy (PE). The potential energy of a body of mass mwhich is at an elevation z from the earth’s surface (or any particular datum) is given by: 
where, g is the acceleration due to gravity (= 9.81 m/s2).
The energy possessed by a body by virtue of its motion is called the kinetic energy (KE). For a body of mass m moving with a velocity u, the kinetic energy of the body is given by: 
It follows that, like any mechanical body, a thermodynamic system containing a fluid, in principle may possess both PE and KE. It may be noted that both PE and KE are expressed in terms of macroscopic, directly measurable quantities; they, therefore, constitute macroscopic, mechanical forms of energy that a thermodynamic system may possess. As one may recall from the basic tenets of mechanics, PE and KE are inter-convertible in form.  

It may also be noted that PE and KE are forms of energy possessed by a body as a whole by virtue of its macroscopic mass. However, matter is composed of atoms /molecules which have the capacity to translate, rotate and vibrate. Accordingly, one ascribes three forms intra-molecular energies: translational, rotational and vibrational.  Further, energy is also associated with the motion of the electrons, spin of the electrons, intra-atomic (nucleus-electron, nucleus-nucleus) interactions, etc. Lastly, molecules are also subject to inter-molecular interactions which are electromagnetic in nature, especially at short intermolecular separation distances. All these forms of energy are microscopic in form and they cannot be readily estimated in terms of macroscopically measurable properties of matter. It needs to be emphasized that the microscopic form of energy is distinct from PE and KE of a body or a system, and are generally independent of the position or velocity of the body. Thus the energy possessed by matter due to the microscopic modes of motion is referred to as the internal energy of the matter. The microscopic variety of energy forms the principal consideration in case of transformations that occur in a thermodynamic system. Indeed, as mentioned earlier, it is the realization that matter or fluids possessed useful form of microscopic energy (independent of macroscopic KE or PE) that formed the basis of the 18th century Industrial Revolution.

As we will see later, the majority of practical thermodynamic systems of interest are the ones that do not undergo change of state that entails significant change in its macroscopic potential and kinetic energies. Thus, it may be intuitively obvious that in a very general sense, when a thermodynamic system undergoes change of state, the attendant change in the internal energy is responsible for the energy leaving or entering the system. Such exchange of energy between a thermodynamic system and its surroundings may occur across the system boundary as either heat or work or both. 
Thermodynamic Work:
Work can be of various forms: electrical, magnetic, gravitational, mechanical, etc. In general work refers to a form of energy transfer which results due to changes in the external macroscopic physical constraints on a thermodynamic system. For example, electrical work results when a charge moves against an externally applied electrical field. As we will see later, it is mechanical work that is most commonly encountered form in real thermodynamic systems, for example a typical chemical plant. In its simplest form, such work results from the energy applied to expand the volume of a system against an external pressure, or by driving a piston-head out of a cylinder against an external force. In both the last examples, work transfer takes place due to the application of a differential (or finite) force applied on the system boundary; the boundary either contracts or expands due to the application of such a force. In effect this results in the applied force acting over a distance, which results in mechanical energy transfer.

Consider the system in fig.1.2, where a force F acts on the piston and is given by pressure x piston area. Work is performed whenever this force translates through a distance. 
Fig. 1.2 Illustration of Thermodynamic Work
Thus for a differential displacement ‘dx’ of the piston the quantity of work is given by the equation:

Here is the force acting along the line of the displacement x. If the movement takes place over a finite distance, the resulting work is obtained by integrating the above equation. By convention, work is regarded as positive when the displacement is in the same direction as the applied force and negative when they are in opposite directions.Thus, for the above example, the equation 1.4 may be rewritten as:
If the piston area ‘A’ is constant, then:
As may be evident from eqn. 1.6, when work is done on a system (say through compression) the volume decreases and hence the work term is positive. The reverse is true when the system performs work on the surroundings (through expansion of its boundary). 

We invoke here the common observation that when a hot and a cold object are contacted, the hot one becomes cooler while the cold one becomes warmer. It is logical to argue that this need be due to transfer of ‘something’ between the two objects. The transferred entity is called heat. Thus, heat is that form of energy that is exchanged between system and its surrounding owing to a temperature differential between the two. More generally, heat is a form of energy that is transferred due to temperature gradient across space. Thus heat always flows down the gradient of temperature; i.e., from a higher to a lower temperature regions in space. In absence of such temperature differential there is no flow of heat energy between two points. Heat flow is regarded to be positive for a thermodynamic system, if it enters the latter and negative if it leaves.

Like work, heat is a form of energy that exists only in transit between a system and its surrounding. Neither work nor heat may be regarded as being possessed by a thermodynamic system. In a fundamental sense, the ultimate repositories of energy in matter are the atoms and molecules that comprise it. So after transit both work and heat can only transform into the kinetic and potential energy of the constituent atoms and molecules.

1.4 Thermodynamic Equilibrium
In general change of state of a thermodynamic system results from existence of gradients of various types within or across its boundary. Thus a gradient of pressure results in momentum or convective transport of mass. Temperature gradients result in heat transfer, while a gradient of concentration (more exactly, of chemical potential, as we shall see later) promotes diffusive mass transfer. Thus, as long as internal or cross-boundary gradients of any form as above exist with respect to a thermodynamic system it will undergo change of state in time. The result of all such changes is to annul the gradient that in the first place causes the changes. This process will continue till all types of gradients are nullified. In the ultimate limit one may then conceive of a state where all gradients (external or internal) are non-existent and the system exhibits no further changes. Under such a limiting condition, the system is said to be in a state of thermodynamic equilibrium. For a system to be thermodynamic equilibrium, it thus needs to also satisfy the criteria for mechanical, thermal and chemical equilibrium.

Types of Thermodynamic Equilibrium
A thermodynamic system may exist in various forms of equilibrium: stable, unstable and metastable. These diverse types of equilibrium states may be understood through analogy with a simple mechanical system as depicted in fig. 1.3 – a spherical body in a variety of gradients on a surface.  
Fig. 1.3 Types of Mechanical Equilibrium
Consider the body to be initially in state ‘I’. If disturbed by a mechanical force of a very small magnitude the body will return to its initial state. However, if the disturbance is of a large magnitude, the body is unlikely to return to its initial state. In this type of situation the body is said to be in unstableequilibrium. Consider next the state ‘II’; even a very small disturbance will move the body to either positions ‘I’ or ‘III’. This type of original equilibrium state is termed metastable. Lastly, if the body is initially in state ‘III’, it will tend to return to this state even under the influence of relatively larger disturbances. The body is then said to be in a stable equilibrium state. If ‘E’ is the potential energy of the body and ‘x’ is the effective displacement provided to the body in the vertical direction, the three equilibrium states may be described by the following equations:
Stable Equilibrium: (1.7)
Unstable Equilibrium: (1.8)
Metastable Equilibrium: (1.9)

The above arguments may well be extended to understand equilibrium states of thermodynamic systems, which are relatively more complex in configuration. The disturbances in such cases could be mechanical, thermal or chemical in nature. As we shall see later (section 6.3), for thermodynamic systems, the equivalent of (mechanical) potential energy is Gibbs free energy. The considerations of change of Gibbs free energy are required to understand various complex behaviour that a thermodynamic system containing multiple phases and components (either reactive or non-reactive) may display under the influence of changes brought about by exchange of energy across its boundary.

1.5 The Phase Rule
Originally formulated by the American scientist Josiah Willard Gibbs in the 1870’s, the phase rule determines the number of independent variables that must be specified to establish the intensive state of any system at equilibrium. The derivation of the general phase rule is shown in chapter 6, but here we state it without proof:
Here, F = degrees of freedom of the thermodynamic system in question; N = Number of components; π = number of co-existing phases, and r = number of independent reactions that may occur between the system components. For a non-reactive system, the phase rule simplifies to:

In the most general sense a thermodynamic system may be multiphase and multi-component in nature. A phase is a form of matter that is homogeneous in chemical composition and physical state. Typical phases are solids, liquids and gases. For a multiphase system, interfaces typically demarcate the various phases, properties changing abruptly across such interfaces. Various phases can coexist, but they must be in equilibrium for the phase rule to apply. An example of a three-phase system at equilibrium is water at its triple point (~ 00C, and 0.0061 bar), with ice, water and steam co-existing. A system involving one pure substance is an example of a single-component system. On the other hand mixtures of water and acetone, have two chemically independent components. 
The intensive state of a system at equilibrium is established when its temperature, pressure, and the compositions of all phases are fixed. These are therefore, regarded as phase-rule variables; but they are not all independent. The degrees of freedom derivable from the phase rule gives the number of variables which must be specified to fix all other remaining phase-rule variables. Thus, means the number of intensive properties (such as temperature or pressure), which are independent of other intensive variables. For example, for a pure component gaseous system, phase rule yields two degrees of freedom. This implies that if one specifies temperature and pressure, all other intensive properties are then uniquely determined these two variables. Similarly for a biphasic system of a pure component – say water and steam – there is only one degree of freedom, i.e., either temperature or pressure may be specified to fix all other intensive properties of the system. At the triple point the degrees of freedom is zero, i.e., any change from such a state causes at least one of the phases to disappear.