Thermodynamics Kelvin statement

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. 

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. 

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. 

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... 

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. 

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.)... 

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) ... 

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. 

When an enzyme-catalyzed biochemical reaction operating in an isothermal system is in a non-equilibrium steady state, energy is continuously dissipated in the form of heat. The quantity J AG is the rate of heat dissipation per unit time. The inequality of Equation (4.13) means that the enzyme can extract energy from the system and dissipate heat and that an enzyme cannot convert heat into chemical energy. This fact is a statement of the second law of thermodynamics, articulated by William Thompson (who was later given the honorific title Lord Kelvin), which states that with only a single temperature bath T, one may convert chemical work to heat, but not vice versa. 

The size of the kelvin, the SI temperature unit with symbol K, is defined by the statement that the triple point of pure water is exactly 273.16 K. The practical usefulness of the thermodynamic scale suffers from the lack of convenient instruments with which to measure absolute temperatures routinely to high precision. Absolute temperatures can be measured over a wide range with the helium-gas thermometer (appropriate corrections being made for gas imperfections), but the apparatus is much too complex and the procedure much too cumbersome to be practical for routine use. 

We begin here the discussion of the Second Law of Thermodynamics. This law has been enunciated in many different forms, the most prominent being the formulations by Kelvin and by Planck. These will be presented later as consequences of the approach derived below. Undoubtedly, the most elegant statement of this Law was provided by Caratheodory in the following form ... 

Re Entry [63], Ref. [63]) In Ref. [63], Dr. Peter Atkins doesn t seem to explicitly state that negative Kelvin temperatures are hotter than ooK, not colder than OK. He admits the possibility of attaining OK via noncyclic processes, but as we showed in Sect. 3. of this chapter purely dynamic — as opposed to thermodynamic — limitations may contravene. On pp. 103-104 of Ref. [63], he correctly states that the third law of thermodynamics is "not really in the same league" as the zeroth, first, and second laws, and that "hints of the Third Law of Thermodynamics are already present in the consequences of the second law," but that the Third Law of Thermodynamics is "the final link in the confirmation that Boltzmann s and Clausius s definitions refer to the same property." But his statement that "we need to do an ever increasing, and ultimately infinite, amount of work to remove energy from a body as heat as its temperature approaches absolute zero" neglects the rapid decrease in specific heat as absolute zero is approached as discussed in Sect. 2. of this chapter. 

This T, the thermodynamic or absolute temperature, is here a function of S, V and x. But it s easy to show that if T were a function of temperature and entropy, or if it were a function of temperature and anything else, we could violate Kelvin s statement. So T depends only on the empirical temperature, and this dependence must be the same for all systems in order for the entropy of a composite to equal the sum of the entropies of the subsystem. In order for Clausius statement to hold in the case of irreversible processes, the equal sign of rfQ = TdS becomes <, and we have Clausius inequality TdS,rwKere T is the... 

In most treatises on thermodynamics, it is usual to refer to the laws of thermodynamics. The conservation of energy is referred to as the First La of Thermodynamics, and this principle was discus.sed in detail in Chapter 3. The positivc-dehniie nature of entropy generation used in Chapter 4, or any of the other statements such as those of Clausius or Kelvin and Planck, are referred to as the Second Law of Thermodynamics. The principle of consers ation of mass precedes the development of thermodynamics. and therefore is not considered to be a law of thermodynamics. 

This experience is embodied in the second law of thermodynamics. It is impossible for a system operating in a cycle and connected to a single heat reservoir to produce a positive amount of work in the surroundings. This statement is equivalent to that proposed by Kelvin in about 1850. 

The main purpose of this book is to present a rigorous and logical discussion of the fundamentals of thermodynamics and to develop in a coherent fashion the application of the basic principles to a number of systems of interest to chemists. The concept of temperature is carefully discussed, and special emphasis is placed on the appropriate method for the introduction of molecular weights into thermodynamics. A new treatment of the second law of thermodynamics is presented which demonstrates that Caratheodory s principle is a necessary and sufficient consequence of the physical statements of Clausius and Kelvin. 

The kelvin temperature unit could be defined in terms of an exact value of the Boltzmann constant k by the statement The kelvin, the unit of thermodynamic temperature, is scaled such that the Boltzmann constant is exactly 1.3806505 x 10 joule per kelvin. 

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 work of Carnot, published in 1824, and later the work of Clausius (1850) and Kelvin (1851), advanced the formulation of the properties of entropy, temperature, and the second law. Clausius introduced the word entropy. The second law is a statement of existence of stable equilibrium states and distinguishes thermodynamics from mechanics and other fields of physics. The many stable equilibrium states and various other equilibrium and nonequilibrium states contemplated in thermodynamics are not contemplated in mechanics (Gyftopoulos and Beretta, 2005). The second law is a qualitative statement on the accessibility of energy and the direction of progress of real processes. For example, the efficiency of a reversible engine is a function of temperature only, and efficiency cannot exceed unity. These statements are the results of the first and second laws, and can be used to define an absolute scale of temperature that is independent of any material properties used to measure it. A quantitative description of the second law emerges by determining entropy and entropy production in irreversible processes. 

The second law of thermodynamics dictates that certain processes are irreversible. For example, heat travels in a direction of decreasing temperature. There are two commonly cited equivalent qualitative statements to the second law. The Kelvin-Planck statement states that it is impossible to construct any cyclic device that receives heat from a single thermal reservoir and converts it entirely into work. According to the Clausius statement, it is impossible to construct a device, which operates in a cycle that produces no other effect on the environment other than the transfer of heat from a low temperature reservoir to a higher temperature reservoir. Both of the Kelvin-Planck and Clausius statements of the second... 

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 plan of the remaining sections of this chapter is as follows. In Sec. 4.3, a h)q)o-thetical device called a Carnot engine is introduced and used to prove that the two physical statements of the second law (the Clausius statement and the Kelvin-Planck statement) are equivalent, in the sense that if one is true, so is the other. An expression is also derived for the efficiency of a Carnol engine for Ihe purpose of defining thermodynamic temperature. Section 4.4 combines Carnot cycles and the Kelvin-Planck statement to derive the existence... 

It is now possible to justify the statement in Sec. 2.3.5 that the ideal-gas temperature scale is proportional to the thermodynamic temperature scale. Both Eq. 4.3.13 and Eq. 4.3.15 equate the ratio TJT to —qc/qh, but whereas Tc and Th refer in Eq. 4.3.13 to the ideal-gas temperatures of the heat reservoirs, in Eq. 4.3.15 they refer to the thermodynamic temperatures. This means that the ratio of the ideal-gas temperatures of two bodies is equal to the ratio of the thermod5mamic temperatures of the same bodies, and therefore the two scales are proportional to one another. The proportionality factor is arbitrary, but must be unity if the same unit (e.g., kelvins) is used in both scales. Thus, as stated on page 41, the two scales expressed in kelvins are identical. 

Clapeyron s paper used indicator diagrams and calculus for a rigorous proof of Carnot s conclusion that the efficiency of a reversible heat engine depends only on the temperatures of the hot and cold heat reservoirs. However, it retained the erroneous caloric theory of heat. It was not until the appearance of English and German translations of this paper that Clapeyron s analysis enabled Kelvin to define a thermodynamic temperature scale and Clausius to introduce enffopy and write the mathematical statement of the second law. 

There are several ways of defining the second law of thermodynamics, but a very useful statement, according to Kelvin and Planck, is as follows ... 

Statements of the Second Law Thermodynamic Operation of Heat Engines Kelvin and Planck Statements Temperature Scale Operation of Heat Engines... 

The second law of thermod5mamics is stated through the Kelvin-Planck statement and the Clausius statement. The Inequality of Clausius is a consequence of the second law of thermod5mamics, and it is stated for a system undergoing a thermodynamic cycle as... 

The second law of thermodynamics has historically been a mysterious concept, and the basic idea has been verbalized by Clausius, Kelvin, Planck, and others for those who think in words. One simple statement by Rudolph Clausius (1822-1888) was... 

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