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For a change of state from an initial state 1 to a final state 2 with a constant amount of matter, the first law can be formulated as follows:

(1.42)

      where,

As is clear in Eq. (1.42), we broaden the definition of energy to include kinetic and potential energies in addition to internal energy. An important consequence of the first law is that the internal energy change resulting from a process is independent of the thermodynamic path followed by the system, and of the paths followed by the processes, for example, heat transfer and work. In turn, the rate at which the internal energy content of the system changes is dependent only on the rates at which heat is added and work is done (when kinetic and potential energies are neglected).

      1.4.19 The Second Law of Thermodynamics

      As mentioned earlier, the first law is the energy‐conservation principle. The second law of thermodynamics (SLT) is instrumental in determining the inefficiencies of practical thermodynamic systems, and indicates that it is impossible to have 100% efficiency in energy conversion. The classical statements, such as the Kelvin–Plank statement and the Clausius statement, help us formulate the second law:

       The Kelvin–Plank statement: It is impossible to construct a device operating in a cycle (e.g. heat engine), that accomplishes only the extraction of heat from some source and its complete conversion to work. This statement describes the impossibility to have a heat engine with a thermal efficiency of 100%.

       The Clausius statement: It is impossible to construct a device operating in a cycle (e.g. refrigerator and heat pump), that transfers heat from a low‐temperature (cooler) region to a high‐temperature (hotter) region.

A simple way to illustrate the implications of both the first and second laws is a desktop game that consists of several pendulums (made of metal balls), one in contact with the other. When you raise the first of the balls, you give energy to the system in the form of potential energy. Releasing this ball allows it to gain kinetic energy at the expense of potential energy. When this ball hits the second ball, a small elastic deformation transforms the kinetic energy again into a form of potential energy. The energy is transferred from one ball to the other. The last ball again gains kinetic energy, which allows it to rise. The cycle continues, with the ball rising every time to a slightly lower level, until it finally stops. The first law concerns why the balls keep moving, while the second law explains why they do not do it forever. In this game, the energy is lost in the form of sound and heat, causing the decline in motion.

      The second law also states that the entropy in the universe always increases. As mentioned before, entropy is a measure of degree of disorder, and every process happening in the universe increases the entropy of the universe to a higher level. The entropy of a state of a system is proportional to (depends on) its probability, which gives us an opportunity to define the second law in a broader manner as “the entropy of a system increases in any heat transfer or conversion of energy within a closed system.” That is why all energy transfers or conversions are irreversible. From the entropy perspective, the basis of the second law is the statement that the sum of the entropy of a system changes and that of its surroundings must always be positive. Recently, much effort has been invested in minimizing the entropy generation (irreversibilities) in thermodynamic systems and applications.

      Moran and Shapiro [3] noted that the second law and deductions from it are useful because they provide a means for

       predicting the direction of processes;

       establishing conditions for equilibrium;

       determining the best performance of thermodynamic systems and applications;

       quantitatively evaluating the factors that preclude the attainment of the best theoretical performance level;

       defining a temperature scale, independent of the properties of the substance; and

       developing tools for evaluating some thermodynamic properties, for example, internal energy and enthalpy, using available experimental data.

      Consequently, the second law is the linkage between entropy and the usefulness of energy. The second law analysis has found applications in a wide variety of disciplines, for example, chemistry, economics, ecology, environment, and sociology, far removed from engineering thermodynamics applications.

      1.4.20 Reversibility and Irreversibility

      These two concepts are highly important to thermodynamic processes and systems. Reversibility is defined by the statement that only for a reversible process can both a system and its surroundings be returned to their initial states. Such a process is only theoretical. The irreversibility during a process describes the destruction of useful energy or availability. Without new inputs, both the system and its surroundings cannot be returned to their initial states because of the irreversibilities that have occurred, for example, friction, heat transfer or rejection, and electrical and mechanical effects. For instance, an actual system provides an amount of work that is less than the ideal reversible work, so the difference between these two values gives the irreversibility of that system. In real applications, there are always such differences, and therefore real processes and cycles are always irreversible.

Table 1.4 Relations among essergy, availability, exergy, and free energy.

      Source: Szargut et al. [4].

Name	Function	Remarks
Essergy		Formulated for the special case in 1878 by Gibbs and in general in 1962, and changed from available energy to exergy in 1963, and from exergy to essergy (i.e. essence of energy) in 1968 by Evans
Availability	E + P0V − T0S − (E0 + P0V0 − T0S0)	Formulated by Keenan in 1941 as a special case of the essergy function
Exergy	E + P0V − T0S − (E0 + P0V0 − T0S0)	Introduced by Darrieus in 1930 and Keenan in 1932; called the availability in steady flow by him, and exergy by Rant in 1956 as a special case of essergy
Free energy	Helmholtz: E – TS	Introduced by von Helmholtz and Gibbs in 1873 as the Legendre transforms of energy to yield useful alternate criteria of equilibrium, as measures of the potential work of systems representing special cases of the essergy function
	Gibbs: E + PV – TS

      1.4.21 Exergy

Exergy is defined as the maximum amount of work (also called availability, see Table

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