Clausius Theorem
Clausius Theorem, a fundamental concept in thermodynamics, states that heat cannot spontaneously flow from a colder body to a hotter body. It provides a basis for the second law of thermodynamics, which governs the direction of heat transfer and the efficiency of heat engines. The theorem has wide-ranging applications in engineering, including the design and optimization of energy systems.
5 Key excerpts on "Clausius Theorem"
eBook - ePub- Emile Meyerson(Author)
- 2013(Publication Date)
- Routledge(Publisher)
...The way in which Clapeyron stated the teachings of his master was doubtless an additional cause, as has been already remarked. Finally, from the time of the researches of Mayer and of Joule, the fact that Carnot believed that he ought to limit himself to the conservation of heat (although at that time he had already conceived of heat as motion) (2) contributed equally to this neglect. But we shall see later that this lack of recognition can also be explained, perhaps, by the action of a more profound cause. Clausius, who at the beginning of his work was unacquainted with that of his illustrious predecessor, discovered the principle anew; he had, besides, the great merit of proving that it could be brought into agreement with that of the conservation of energy;(3) finally, he stated it more precisely, as especially applicable to the phenomena of thermodynamics, in order to guard it against certain objections. Clausius, moreover, was himself led later on to modify his first statement, and other modifications have been proposed since. It was with the work of Clausius that the principle definitely entered the domain of science, where its enormous importance and its great fertility were soon recognized. That is why it is sometimes designated by the name of the principle of Clausius or yet again by that of the principle of Carnot-Clausius, although Clausius himself, recognizing the incontestable rights of his predecessor, assigned to it only the name of Carnot. The principle is formulated by Duhem in these words: “The transformation value of a modification is equal to the diminution that a certain magnitude, connected with all the properties which fix the state of the system, but independent of its motion, undergoes through this modification.”(4) This magnitude is what is called the entropy of the system, and its conception for heat phenomena is closely related to that of temperature, and this results in investing this property with a very particular and essential rôle...
eBook - ePub- V. Babu(Author)
- 2019(Publication Date)
- CRC Press(Publisher)
...Note that this statement does not specify how much heat has to be rejected. The Clausius statement of the second law may be formally written as follows: “It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a cold to a hot body”. In other words, the COP of a reverse heat engine cannot be infinity. An informal and quite popular version of this statement is: A refrigerator does not work until it is turned on. Both the Kelvin-Planck and the Clausius statements emphasize three conditions to be met for the law to be applicable and these are shown above in italics. Even if one of these conditions is not met, then the law is silent on the viability of such a device. Let us examine this through the arrangement shown in Fig. 3.1. The desired effect in this case is the lifting of the weight and the input given is electrical work from the battery and so an efficiency relating these two may easily be defined. Under ideal circumstances, it is not difficult to realize that the efficiency of this arrangement can be quite close to 100 percent. The arrangement has access to a single reservoir (the ambient) and produces useful work (raising of a weight). Does this violate the Kelvin-Planck statement? The answer to this question is that Kelvin-Planck statement is not applicable in this case, since the arrangement does not execute a cyclic process. One important point about these two statements of the second law as well as the statement of the first law, Eqn. 4.1, is that they are based on extensive observations alone and without any proof. However, no instance of a violation of any of these statements has been reported so far † 8.3.1 Equivalence of the two statements Since the Kelvin-Planck statement is applicable to direct heat engines and the Clausius statement is applicable to reverse heat engines, the possibility that a device may violate one but not the other, if real, would be a vexing dilemma...
eBook - ePub- D. Paul Mehta, Albert Thumann(Authors)
- 2021(Publication Date)
- River Publishers(Publisher)
...All forms of energy, including work, can be converted to heat, but the converse is not generally true. The Kelvin-Planck statement of the second law of thermodynamics says essentially the following: Only a portion of the heat from a heat work cycle, such as a steam power plant, can be converted to work. The remaining heat must be rejected as heat to a sink of lower temperature (to the atmosphere, for instance). The Clausius statement, which also deals with the second law, states that heat, in the absence of some form of external assistance, can only flow from a hotter to a colder body. THE CARNOT CYCLE The Carnot cycle is of interest because it is used as a comparison of the efficiency of equipment performance. The Carnot cycle offers the maximum thermal efficiency attainable between any given temperatures of heat source and sink. A thermodynamic cycle is a series of processes forming a closed curve on any system of thermodynamic coordinates. The Carnot cycle is illustrated on a temperature-entropy diagram, Figure 6-2A, and on the Mollier diagram for superheated steam, Figure 6-2B. The cycle consists of the following: Heat addition at constant temperature, resulting in expansion work and changes in enthalpy. Adiabatic isentropic expansion (change in entropy is zero) with expansion work and an equivalent decrease in enthalpy. Constant temperature heat rejection to the surroundings, equal to the compression work and any changes in enthalpy. Adiabatic isentropic compression returning to the starting temperature with compression work and an equivalent increase in enthalpy. The Carnot cycle is an example of a reversible process and has no counterpart in practice. Nevertheless, this cycle illustrates the principles of thermodynamics...
eBook - ePub- H. W. Liepmann, A. Roshko(Authors)
- 2013(Publication Date)
- Dover Publications(Publisher)
...CHAPTER 1 Concepts from Thermodynamics 1.1 Introduction The basis of any physical theory is a set of experimental results. From these special primary observations, general principles are abstracted, which can be formulated in words or in mathematical equations. These principles are then applied to correlate and explain a group of physical phenomena and to predict new ones. The experimental basis of thermodynamics is formalized in the so-called principal laws. The law of conservation of energy, which thermodynamics shares with mechanics, electrodynamics, etc., is one of these principal laws. It introduces the concept of internal energy of a system. The other principal laws of thermodynamics introduce and define the properties of entropy and temperature, the two concepts which are particular and fundamental for thermodynamics. The principles laid down in these fundamental laws apply to the relations between equilibrium states of matter in bulk. For instance, thermodynamics yields the relation between the specific heats at constant pressure and at constant volume; it relates the temperature dependence of the vapor pressure to the latent heat of evaporization; it gives upper bounds for the efficiency of cyclic processes, etc. Fluid mechanics of perfect fluids, i.e., fluids without viscosity and heat conductivity, is an extension of equilibrium thermodynamics to moving fluids. The kinetic energy of the fluid has now to be considered in addition to the internal energy which the fluid possesses when at rest. The ratio of this kinetic energy per unit mass to the internal energy per unit mass is a characteristic dimensionless quantity of the flow problem and in the simplest cases is directly proportional to the square of the Mach number. Thermodynamic results are taken over to perfect fluid flow almost directly. Fluid mechanics of real fluids goes beyond classical thermodynamics...
eBook - ePub- Mike Pauken(Author)
- 2011(Publication Date)
- For Dummies(Publisher)
...The steam can then be used in a power plant to generate additional electricity. The heat rejected by one heat engine can be the heat source for another heat engine operating at lower temperatures. (One man’s trash is another man’s treasure.) I describe cogeneration and combined cycles in a bit more detail in Chapter 18. Chilling with the Clausius Statement on Refrigeration Heat naturally flows from hot sources to cold sinks. Until the invention of the first refrigeration machine, you couldn’t do much about the natural flow of heat. You just had to sweat it out during the summer until winter came. All that has changed, but moving heat from a cold reservoir up to a warmer reservoir comes with a price, as you may know if you’ve paid a huge electric bill in the summer for air conditioning. Thermodynamically, a refrigerator is very much like a heat engine operating in reverse. It uses work to move heat from a low-temperature reservoir, such as the inside of your refrigerator, to a high-temperature reservoir, like your kitchen. Examples of refrigeration machines include air conditioners and heat pumps. A heat pump is basically an air conditioner that can pump heat from the outdoors to the inside of a house during the winter. It works best in areas with mild winters (I explain why in Chapter 13). The following sections discuss how the second law of thermodynamics applies to refrigeration cycles and provides a brief introduction on how the refrigeration cycle works. I go into more depth and discuss how to analyze refrigeration cycles in Chapter 13. Characterizing refrigerators Because heat naturally flows from hot to cold temperatures, making it flow in the opposite direction takes some effort. This observation is expressed as the Clausius statement of the second law of thermodynamics: It’s impossible for a refrigerator to move heat from a colder reservoir to a warmer reservoir without a work input...
