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Thus for a complete cycle of a Carnot engine, the two quantities Q / T associated with the absorption and rejection of heat by the working fluid of the engine sum to zero The working fluid of a cyclic engine periodicallyreturns to its initial state, and its properties, eg, temperature, pressure, and internal energy, return to their initial values Indeed, a primary characteristic of a property is that the sum of its changes is zero for any complete cycle Thus for a Carnot cycle Eq (59) suggests the existence of a property whose changes are given by the quantities Q / T Our purpose now is to show that Eq (59), applicable to the reversible Carnot cycle, also applies to other reversible cycles The closed curve on the P V diagram of Fig 54 represents an arbitrary reversible cycle traversed by an arbitrary fluid Divide the enclosed area by a series of reversible adiabatic curves; since such curves cannot intersect (Pb 51), they may be drawn arbitrarily close to one another Several such curves are shown on the figure as long dashed lines Connect adjacent adiabatic curves by two short reversible isotherms which approximate the curve of the arbitrary cycle as closely as possible The approximation clearly improves as the adiabatic curves are more closely spaced When the separation becomes arbitrarily small, the original cycle is faithfully represented Each pair of adjacent adiabatic curves and their isothermal connecting curves represent a Carnot cycle for which Eq (59) applies Each Carnot cycle has its own pair of isotherms TH and Tc and associated heat quantities QH and Qc These are indicated on Fig 54 for a representative cycle When the adiabatic curves are so closely spaced that the isothermal steps are infinitesimal, the heat quantities become d Q H and d Q c , and Eq (59) for each Carnot cycle is written:.

Because computers are computers and people are people, they generally have different requirements when it comes to getting their data into a usable format. XML is an attempt to arrange data in a structure that is usable for both people and software. XML has really come into vogue in recent years, but its roots are quite old. It s derived from SGML (Standard Generalized Markup Language), as is HTML (cousins!). SGML in turn came from GML (Generalized Markup Language), a metalanguage (a language that describes another language) designed by IBM back in the 1960s. So, blame IBM if you want to, but either way, you will come in regular contact with XML as you develop .NET applications. I might as well tell you right from the start: either you will love XML, or you will hate it, but probably both. It s a strange beast, this XML, as you would expect from any acronym that takes letters from the middle of the words it represents ( eXtensible Markup Language ). XML represents an alphabet of data manipulation technologies, an alphabet which strangely has seven Xs. But enough of the teasing; let s extend our understanding of this basic .NET technology.

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In this equation TH and Tc, absolute temperatures of the working fluid of the Carnot engines, are also the temperatures traversed by the working fluid of the arbitrary cycle Summation of all quantities d Q / T for the Carnot engines leads to the integral:

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where the circle in the integral sign signifies integration over the arbitrary cycle, and the subscript "rev" indicates that the cycle is reversible Thus the quantities d Q,,/ T sum to zero for the arbitrary cycle, exhibiting the characteristic of a property We therefore infer the existence of a property whose differential changes for the arbitrary cycle are given by these quantities The property is called entropy (en'-tro-py), and its differential changes are:

As with variable definitions, classes are defined using one of the access modifier keywords: Public, Private, Protected, Friend, or Protected Friend. Flip back to 6, in the Variables section, if you need a refresher course. The .NET Framework Class Libraries (FCLs) are simply loaded with classes and objects, and they are all pretty much defined with this simple keyword: Class.

where S t is the total (rather than molar) entropy of the system Alternatively,

Points A and B on the P V diagram of Fig 55 represent two equilibrium states of a particular fluid, and paths ACB and ADB show two arbitrary reversible processes connecting these points Integration of Eq (511) for each path gives: and

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