Alternative Statement of the Second Law

In addition to the statement we have been using, several alternative ways exist to express the second law. One that will be particularly useful is the Kelvin-Planck statement  

It is impossible to construct a machine that, operating in a cycle, will take heat from a 

If such a machine could be constmcted, it would be a perpetual-motion machine of the second kind.  

TABLE 6.1. Coupling of Two Camot Cycles with Different Efficiencies 

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It can be shown that Equation 4.6 can also be derived from Equation 4.8, so Equation 4.8 is an alternate statement of the second law. 

Let us conclude this section by quoting some alternative statements of the second law in colloquial form ... 

An alternative statement of the second law, due to Lord Kelvin (William Thomson, 1824-1907) and Max Planck (1858-1947), is that it is not possible to construct a device operating in a cycle that results in no effect other than, the production of work by tran.sferring heat from a single body. A schematic diagram of a Kelvin-Planck device is shown below. 

Another (alternative) statement of the Second Law is that for an isolated system ... 

An interesting alternative demonstration of Equation (7.75) can be carried out on the basis of isothermal cycles and of the Kelvin-Planck statement of the second law. Consider two possible methods of going from State a to State b, a spontaneous change of state, in an isothermal fashion (Fig. 7.1) (1) a reversible process and (2) an irreversible process. 

Let us now attempt to re-express the Gibbs criterion of equilibrium in alternative analytical and graphical forms that are more closely related to Clausius-like statements of the second law. For this purpose, we write the constrained entropy function S in terms of its... 

There are several implications of the above statement. The first obvious one is that there will be no entropy change on a chemical reaction at 0 K if each of the reacting substances is in a perfect state, to produce one or more products in perfect states. In fact, it was this observation that led to the formulation of-the third law. A second implication, which is less obvious and is sonietimes used as an alternative statement of the third law, is... 

Summary. The Second Law was postulated as a simple general statement on heat exchange in cyclic processes. It was demonstrated that when this statement is combined with the properties of thermodynamic systems and universe introduced in Sect. 1.2 the existence of the absolute temperature and entropy follows, even out of equilibrium. The entropy should satisfy an inequality (1.21) which can be viewed as an alternative form of the Second Law and is called the entropy inequality. However, enttopy need not be unique especially in complex (nonequilibrium) systems or processes and even the ttansferability of the proof of its existence at such conditions remains unclear. Even in such cases the supposed existence of entropy can give important information on possible behavior which can be subjected to experimental testing. 

The Kelvin and Planck statements of the second law (Section 1.11) deal with the impossibility of operating thermal engines under certain prescribed conditions from these assumptions, the second law may then be deduced. There is no logical objection to such a procedure, but it does seem somewhat unsatisfactory to base a universally applicable law on principles pertaining to the operation of heat engines. The reverse procedure, outlined in Section 1.11 does provide what appears to be a better alternative here the characteristics of cychcaUy operated heat engines are derived as a consequence of the second law. 

The traditional formulation of the second law is given by (2.3.5) and (2.3.7) however, there is an alternative that may be useful, especially for open systems. Again, the statement is in two parts a definition of entropy plus an assertion that entropy is not conserved because we now explicitly include entropy changes in the boundary. The definition takes the form of the stuff equation (1.4.1) with Figure 1.7,... 

Much of the preliminary discussion above has been lacking in precision. However, aU that we require for a systematic treatment of the second law is the fact, which is securely based on experience, that it is impossible to carry out Joule s experiment in reverse (Statement A below). As a postulate, to be justified later, we shall also assume the existence of reversible paths. On this basis the development of the second law may be carried out in several different ways. In the following we shall describe the traditional method, as used by dausiuef and Poincar, which depends on the use of heat engines. The main alternatives are the methods of Planck, which depends on the existence of perfect gases, and of Bom and Carathto-dory, II which is based on the properties of Pfaffian differential expressions. 

Second Law of Thermodynamics The law that states that the entropy in a closed system never decreases. An alternative statement is that processes that are thermo-dynamicahy favored at constant temperature and pressure involve a decrease in free energy. 

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