Planck statement of the second law

The Kelvin-Planck statement of the Second Law also focuses on cyclic devices and limitations. It may be stated as ... 

Like the engine-based statements, Caratheodory s statement invokes limitations. From a given thermodynamic state of the system, there are states that cannot be reached from the initial state by way of any adiabatic process. We will show that this statement is consistent with the Kelvin-Planck statement of the Second Law. 

We wish to show that no points to the leftbb of 2 on the isotherm 62 are accessible from point 1 via any adiabatic path, reversible or irreversible. Suppose we assume that some adiabatic path does exist between 1 and 2. We represent this path as a dotted curve in Figure 2.11a. We then consider the cycle I —>2 —> 1 — 1. The net heat associated with this cycle would be that arising from the last step 1 — 1, since the other two steps are defined to be adiabatic. We have defined the direction 1 — 1 to correspond to an absorption of heat, which we will call qy. From the first law, the net work vv done in the cycle, is given by w = —q, since AU for the cycle is zero. Thus, for this process, iv is negative (and therefore performed by the system), since qy is positive, having been absorbed from the reservoir. The net effect of this cycle, then, is to completely convert heat absorbed at a high temperature reservoir into work. This is a phenomenon forbidden by the Kelvin-Planck statement of the Second Law. Hence, points to the left of 2 cannot be reached from point 1 by way of any adiabatic path. 

Furthermore, in the four steps of the cycle (Fig. 6.8) three are adiabatic (one irreversible, two reversible). Hence, Qcycie is identical with Q of the isothermal step, that is, Q of Equation (6.104). If g > 0, then W < 0 that is, work would have been performed by the system. In other words, if Q were positive, we would have carried out a cyclical process in which heat at a constant temperature had been converted completely into work. According to the Kelvin-Planck statement of the second law, such a process cannot be carried out. Hence, Q cannot be a positive number. As Q must be either negative or zero, it follows from Equation (6.104) that... 

An essential step in the Caratheodory formulation of the second law of thermodynamics is a proof of the following statement Two adiabatics (such as a and b in Fig. 6.12) cannot intersect. F rove that a and b cannot intersect. (Suggestion Assume a and b do intersect at the temperature Ti, and show that this assumption permits you to violate the Kelvin-Planck statement of the second law.)... 

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. 

Kelvin-Planck statement of the second law of thermodynamics is as follows It is impossible to construct an engine to work in a cyclic process whose sole effect is to convert all the heat supplied to it into an equivalent amount of work. ... 

The first statement is the Kelvin-Planck statement of the second law of thermodynamics. As a corollary, it is not possible to affect a cyclic process that can convert heat absorbed by a system completely into work done by the system. Mathematically stated, the second law of thermodynamics can be written as... 

The Kelvin-Planck statement of the second law It is impossible to constmct a heat engine whose only effect, when it operates in a cycle, is heat transfer from a heat reservoir to the engine and the performance of an equal quantity of work on the surroundings. Both the Clausius statement and the Kelvin-Planck statement assert that certain processes, although they do not violate the first law, are nevertheless impossible. 

We can use the logical tool of reductio ad absurdum to prove the equivalence of the Clausius and Kelvin-Planck statements of the second law. 

The ratio Tc / Th is positive but less than one, so the efficiency is less than one as deduced earlier on page 111. This conclusion is an illustration of the Kelvin-Planck statement of the second law A heat engine cannot have an efficiency of unity—that is, it cannot in one cycle convert all of the energy transferred by heat from a single heat reservoir into work. The example shown in Fig. 4.5 on page 108, with e = 1/4, must have Td 7h = 3/4 (e.g., Tc = 300 K and T = 400 K). 

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. 

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