Kelvin statement

Does the Kelvin statement apply to rocket performance Or to engines operating on a single stroke ... 

Thus, a net amount of work has been done by the system from heat obtained from a heat reservoir at the temperature of step 2, without at the same time transferring heat from a hot to a cold reservoir. This violates the Kelvin statement of the Second Law. Therefore, the assumption that the two adiabatic reversible paths may intersect is disproven. 

There are several formulations of the second law of thermodynamics.The so-called Clausius statement says that in spontaneous processes heat cannot fiow from a lower-temperature body to a higher-temperature body. The Thomson (Lord Kelvin) statement says that heat cannot be completely converted into work. 

The Kelvin statement is named for William Thomson, Lord Kelvin, already mentioned In Chapters 1 and 2. 

There are two important physical statements of the second law of thermodynamics. The Kelvin statement involves cyclic processes, which are processes in which the final state of the system is the same as its initial state It is impossible for a system to undergo a cyclic process whose sole effects are theflow of an amount of heatfrom the surroundings to the system and the performance of an equal amount of work on the surroundings. In other words, it is impossible for a system to undergo a cyclic process that turns heat completely into work done on the surroundings. 

The Clausius statement is It is impossible for a process to occur that has the sole effect of removing a quantity of heat from an object at a lower temperature and transferring this quantity of heat to an object at a higher temperature. In other words, heat cannot flow spontaneously from a cooler to a hotter object if nothing else happens. The Clausius statement of the second law is closely related to ordinary experience. The Kelvin statement is less closely related, and it is remarkable that the statements are equivalent to each other and to the mathematical statement of the second law, which establishes that the entropy is a state function. 

No violation of either physical statement of the second law of thermodynamics has ever been observed in a properly done experiment. We regard the second law as a summary and generalization of experimental fact. A machine that would violate the Kelvin statement of the second law and turn heat completely into work in a cyclic process is called a perpetual motion machine of the second kind. 

From the Kelvin statement of the second law, the efficiency must be less than unity, so that qj, must be negative. It is not possible to run a Carnot engine without exhausting some heat to a cool reservoir. 

Kelvin s statement of the second law of thermodynamics is that heat put into a system that undergoes a cyclic process cannot be completely converted into work done on the surroundings. Clausius statement of this law is that heat cannot flow from a cooler to a hotter body if nothing else happens. The mathematical statement of the second law was shown to be a consequence of the Kelvin statement. It asserts that S, the entropy, is a state function if we define... 

In spite of the fact that the general statement of this principle has been shown to be false from all standpoints, it must be admitted that its enunciation was quite in harmony with the spirit of the times the great physicists Lord Kelvin (1851) and Helmholtz (1847) had previously formulated an identical principle in connection with galvanic cells. Thomsen and Berthelot went wrong, not in tlieir enunciation of the so-called theorem as a working hypothesis, but rather in their... 

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

The Clausius and Kelvin-Planck statements and the Carnot principle reflect a historical interest in increasing the efficiency of engines. While the... 

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. 

The conclusion that can be reached from the Nernst heat theorem is that the total entropy of the products and the reactants in a chemical reaction must be the same at 0 Kelvin. But nothing in the statement requires that the entropy of the individual substances in the chemical reaction be zero, although a value of zero for all reactants and products is an easy way to achieve the result of equation (4.17). 

Kelvin-Planck statement of Second Law 57 Klotz. I. M. 217. 254. 256 krypton, heat capacity 577-8... 

Two classically important statements have been provided. The first statement, due to Lord Kelvin, is that it is not possible by a cyclic process to take heat from a reservoir and convert it into work without at the same time transferring heat from a hot to a cold reservoir. This statement of the second law is related to equilibria when it is realized that work can be obtained from a system only when the system is not already at equilibrium. The statement recognizes that the spontaneous process is the flow of heat from a higher to a lower temperature and that only from such a spontaneous process can the work be acquired. The second important classic statement, due to Clausius, is that it is not possible to transfer heat from a cold to a hot reservoir without at the same time converting a certain amount of work into heat. The operation of a refrigerator readily illustrates this statement... 

What kind of solution was expected from physicists As we have seen, many chemists, from Lavoisier on, expected that fundamental chemical problems would be accessible to mathematical solution, meaning not just precise quantification or geometrical explanation but algebraic formulation on mechanical principles. 32 For all the resentment of statements by Kelvin or Boltzmann that chemistry could be reduced to vortex atoms or the kinetics of atoms,33 many nineteenth-century chemists shared Kekule s vague presentiment... 

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 ... 

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. 

Carnot s principle (4.10) may not seem particularly compelling from experience. However, we can easily derive some consequences from (4.10) that are indeed more obvious statements about the irreversibility of natural events, and hence provide compelling inductive proof of the truth of Carnot s principle. These derivative principles were first obtained by Thomson (Kelvin) and Clausius. 

As defined by (4.19) or (4.21), it is easy to recognize that TK is an absolute (strictly non-negative) quantity. Furthermore, one can see from (4.19) that the highest possible efficiency ( —> 1) is achievable only at the absolute zero of the Kelvin scale (7"cK —> 0). In addition, the lowest efficiency of converting heat to work ( —> 0) occurs when the two reservoirs approach the same temperature (7j —> 7"cK), consistent with the statement of Kelvin s principle in Section 4.4. Such limits on engine efficiency can be used to paraphrase the three laws of thermodynamics in somewhat whimsical form as follows (the ultimate formulation of the no free lunch principle) ... 

A numerical evaluation of the Fermi energy lor a simple metal having one or two conduction electrons per atom yields a value of approximately ID-11 erg. or a few electron volts. The equivalent temperature. E,/b. is several lens of thousands of degrees Kelvin. Thus, except in extraordinary circumstances, when dealing with metals. bT -SC ( i.e.. the energy range or partially filled states is small, and the Fermi surface is well defined by the foregoing statement. It must be noted, however, that this is not necessarily true for semiconductors where the number of free electrons per unit volume may be very much smaller. 

Most models to calculate the pore size distributions of mesoporous solids, are based on the Kelvin equation, based on Thomson s23 (later Lord Kelvin) thermodynamical statement that the equilibrium vapour pressure (p), over a concave meniscus of liquid, must be less than the saturation vapour pressure (p0) at the same temperature . This implies that a vapour will be able to condense to a liquid in the pore of a solid, even when the relative pressure is less than unity. This process is commonly called the capillary condensation. 

From the discussion of heat engines, the second law of thermodynamics states that it is impossible to achieve heat, taken from a reservoir, and convert it into work without simultaneous delivery of heat from the higher temperature to the lower temperature (Lord Kelvin). It also states that some work should be converted to heat in order to make heat flow from a lower to a higher temperature (Principle of Clausius). These statements acknowledge that the efficiency of heat engines could never be 100% and that heat flow from high temperatures to low temperatures is not totally spontaneous. Simply, the second law states that natural processes occur spontaneously toward the direction in which less available work can be used. 

As you can see from Figure 11.19 on page 442, the volume of a gas increases or decreases by a fixed increment when subjected to a change in temperature. The algebraic statement of Charles law depends on using absolute, or Kelvin, temperatures. This law is stated as V a T, where T is measured in kelvins. (Figure 11.18 uses Charles law to explain how a thermometer works.)... 

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