The Zeroth and First Laws of Thermodynamics

Law The body of rules governing the affairs of man within a com-munity or among states common law the law of natiotts. Often plural Principles of conduct perceived to be of natural origin. 

Just as Society is built upon the foundation of its laws, so is a field of Science. There is, however, a difference Society s laws express man s collective wisdom Science s laws express Nature s wisdom . Thus the Laws of Thermodynamics express Nature s wisdom, as of course perceived by humans, and were developed in two stages  

observations of a variety of physical phenomena led men to conclude that there is a common reason behind all of them, dictated by Nature and not by the way they are carried out. They arrived, thus, at a verbal statement of this common reason such as, Energy is Conserved . 

Second, this verbal statement was expressed analytically so that quantitative results can be obtained. Thus, Energy is Conserved becomes Q AU W. 

These analytical statements of the laws led eventually to the development of a framework of equations that are used to solve all thermodynamic problems. 

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Although the mathematical and conceptual tools provided by the zeroth and first laws of thermodynamics are very useful, we need more. There is a major question that these laws cannot answer Will a given process occur spontaneously Nothing in the previous chapters addresses spontaneity, which is an important concept. Thermodynamics helps to understand the spontaneity of processes—but only once we add more of its tools. These tools are called the second and third laws of thermodynamics. 

Thermodynamics is a science in which the storage, transformation, and transfer of energy E and entropy S are studied. Thermodynamics is governed by four basic laws called (1) the zeroth law of thermodynamics, (2) the first law of thermodynamics, (3) the second law of thermodynamics, and (4) the third law of thermodynamics. 

The zeroth law of thermodynamics involves some simple definition of thermodynamic equilibrium. Thermodynamic equilibrium leads to the large-scale definition of temperature, as opposed to the small-scale definition related to the kinetic energy of the molecules. The first law of thermodynamics relates the various forms of kinetic and potential energy in a system to the work which a system can perform and to the transfer of heat. This law is sometimes taken as the definition of internal energy, and introduces an additional state variable, enthalpy. 

This relation for temperature is often referred to as the zeroth law of thermodynamics. However, in the spirit of Rudolph Clausius, we will view thermodynamics in terms of two fundamental laws of nature that are represented by the first and second laws of thermodynamics. 

By the standard methods of statistical thermodynamics it is possible to derive for certain entropy changes general formulas that cannot be derived from the zeroth, first, and second laws of classical thermodynamics. In particular one can obtain formulae for entropy changes in highly di.sperse systems, for those in very cold systems, and for those associated, with the mixing ofvery similar substances. 

I mentioned temperature at the end of the last chapter. The concept of temperature has a great deal to do with thermodynamics, and at first sight very little to do with microscopic systems such as atoms or molecules. The Zeroth Law of Thermodynamics states that Tf system A is in thermal equilibrium with system B, and system B is in thermal equilibrium with system C, then system A is also in thermal equilibrium with system C . This statement indicates the existence of a property that is common to systems in thermal equilibrium, irrespective of their nature or composition. The property is referred to as the temperature of the system. 

In previous chapters we looked at the way heat travels from hot to cold, as described by the so called minus-oneth law of thermodynamics, and the way net movements of heat cease at thermal equilibrium (as described by the zeroth law). Although this transfer of heat energy was quantified within the context of the first law, we have not so far been able to describe why such chemical systems occur. Thermodynamic changes only ever proceed spontaneously in one direction, but not the other. Why the difference ... 

Two systems in thermal contact eventually arrive at a state of thermal equilibrium. Temperature, as a universal function of the state and the internal energy, uniquely defines the thermal equilibrium. If system 1 is in equilibrium with system 2, and if system 2 is in equilibrium with system 3, then system 1 is in equilibrium with system 3. This is called the zeroth law of thermodynamics and implies the construction of a universal temperature scale (stated first by Joseph Black in the eighteenth century, and named much later by Guggenheim). If a system is in thermal equilibrium, it is assumed that the energy is distributed uniquely over the volume. Once the energy of the system increases, the temperature of the system also increases (dU/dT> 0). 

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. 

The formalism of the statistical mechanics agrees with the requirements of the equilibrium thermodynamics if the thermodynamic potential, which contains all information about the physical system, in the thermodynamic limit is a homogeneous function of the first order with respect to the extensive variables of state of the system [14, 6-7]. It was proved that for the Tsallis and Boltzmann-Gibbs statistics [6, 7], the Renyi statistics [10], and the incomplete nonextensive statistics [12], this property of thermodynamic potential provides the zeroth law of thermodynamics, the principle of additivity, the Euler theorem, and the Gibbs-Duhem relation if the entropic index z is an extensive variable of state. The scaling properties of the entropic index z and its relation to the thermodynamic limit for the Tsallis statistics were first discussed in the papers [16,17],... 

Tne zerutti law of thermodynamics just states tnanemperatuie exists, it s called the zeroth law because after the first, second, and third laws were already established It was realized that they depended upon a law that established the existence of temperature. 

By what may seem a rather long route, the existence of a property of a system—the entropy—has been demonstrated. The existence of this property is a consequence of the second law of thermodynamics. The zeroth law defined the temperature of a system the first law, the energy and the second law, the entropy. Our interest in the second law stems from the fact that this law has something to say about the natural direction of a transformation. It denies the possibility of constructing a machine that causes heat to fiow from a cold to a hot reservoir without any other effect. In the same way, the second law can identify the natural direction of a chemical reaction. In some situations the second law declares that neither direction of the chemical reaction is natural the reaction must then be at equilibrium. The application of the second law to chemical reactions is the most fruitful approach to the subject of chemical equilibrium. Fortunately, this application is easy and is done without interminable combinations of cyclic engines. 

Physically, how could we obtain such an ensemble First, consider the laboratory temperature bath , sketched in Fig. 4.2. Experimentally, the system of interest is placed in the temperature bath where it can exchange energy with the bath. Now, if the bath is infinite in extent (infinite reservoir), the bath temperature remains constant. The so-called zeroth law of thermodynamics states that two systems in thermal contact with each other (i.e., energy flows freely between the two systems) will have the same temperature at equilibrium (i.e., at long contact times) thus, T = Tg if the contact time is sufficiently large. After a sufficiently long time, when the bath temperature and system temperature have equilibrated, the thermodynamic properties... 

Thermometry is based on the principle that the temperatures of different bodies may be compared with a thermometer. For example, if you find by separate measurements with your thermometer that two bodies give the same reading, you know that within experimental error both have the same temperature. The significance of two bodies having the same temperature (on any scale) is that if they are placed in thermal contact with one another, they will prove to be in thermal equilibrium with one another as evidenced by the absence of any changes in their properties. This principle is sometimes called the zeroth law of thermodynamics, and was first stated as follows by J. C. Maxwell (1872) Bodies whose temperatures are equal to that of the same body have themselves equal temperatures. ... 

Thermodynamics is now the framework that links the various functions of state. All our experimental experience can be distilled into the three laws of thermodynamics (or four, if one counts the zeroth law already mentioned in Sect. 1.1.3). Not so precisely, these three laws have been characterized as follows "In the heat-to-work conversion game the first law says you cannot win the best you can do is break even. The second law says you can break even only at absolute zero of temperature and the third law, finally, says you can never reach absolute zero." Indeed, one finds that it is difficult to win in thermodynamics. 

The need to formulate the zeroth law was felt after the first law and the second law were established. The zeroth law was regarded to be more fundamental than the other laws. So it was pushed at the start of the thermodynamic laws and thus numbered by zero. There is still some discussion about its status in relation to the other three laws. 

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