Caloric entropy

L. Demetrius, Caloric restriction, metabolic rate, and entropy. J. Gerontol. A Biol. Set Med. Set 59(9), B902 B915 (2004). 

The value (3.6), while appreciable compared with the values of Table XVI-1, which are of the order of magnitude of two or more calorics per degree, is definitely less, so much less that it cannot possibly account for the whole entropy of fusion. Let us see what value of a we should have to take to get the whole entropy of fusion from this term. If we set a — 1, for instance, we have... 

Equations (1.18.13) represent the caloric equations of state. Note how the Maxwell relations were used to eliminate the entropy terms, and that the equations of state P - P(T,V) and V - V(T,P) permit the determination of the state functions E - E(T,V) and H - H(T,P) examples of this procedure are to be furnished in the exercises for this section. 

Caloric Data. Enthalpy and entropy of solid ammonia are given in [32]. Enthalpy and entropy may be calculated by the equations in [31]. Further data are given in [37], [50] and [32]-[37], An enthalpy logp diagram can be found in [37]. 

DSC analysis represents a superior method of thermal analysis, in that the area under a DSC peak is directly proportional to the heat absorbed or evolved by the thermal event, and integration of these peak areas yields the enthalpy of reaction (in units of calor-ies/gram or Joules/gram). Even though conclusions reached on the basis of enthalpies of fusion are possibly compromised by their omission of the entropy contribution, an indication of the thermodynamic trends inherent in the system is often possible. For instance, the same polymorphic form of moricizine hydrochloride was deduced on the basis of thermal analysis and equilibrium solubility measurements. On the other hand, auranofin represents a compound for which one anhydrous polymorphic form is predicted to be the most stable by virtue of its melting point and heat of fusion but for which solubility measurements demonstrate that the other polymorph was in fact the thermodynamically stable form. ... 

Hermann von Helmholtz in the 1840s proposed that energy is conserved during physical and chemical processes, not heat as proposed in caloric theory Rudolf Clausius in the 1860s introduced the concept of entropy. 

The three approaches mentioned in the previous section may also be used to describe caloric properties (enthalpy, entropy, heat capacity) of mixtures. The same considerations mentioned earlier are also true for the application of mixture equations of state and corresponding-states methods for the prediction of caloric properties. 

Other useful sources of historical information are The Early Development of the Concepts of Temperature and Heat The Rise and Decline of the Caloric Theory by D. Roller in Volume 1 of Harvard Case Histories in Experimental Science edited by J.B. Conant and published by Harvard University Press in 1957 articles in Physics Today, such as A Sketch for a History of Early Thermodynamics by E. Mendoza (February, 1961, p.32), Carnot s Contribution to Thermodynamics by M.J. Klein (August, 1974, p. 23) articles in Scientific American and various books on the history of science. Of special interest is the book The Second Law by P.W. Atkins published by Scientific American Books, W.H. Freeman and Company (New York, 1984) which contains a very extensive discussion of the entropy, the second law of thermodynamics, chaos and symmetry. 

The caloric equation does not contain entropy as a variable of state and hence cannot be used for providing information either on thermodynamic equilibria or on chemical potentials, in contrast to the fundamental equation. 

Camot derived these principles from the abstract reversible cycle now called the Camot cycle. He assumed the validity of the caloric theory (heat as an indestmctible substance), which requires that the net heat in the cycle be zero, whereas today we would say that it is the net entropy change that is zero. 

We have seen earlier that after processes have run their course, the various functions of state E,H,A, G, and —S have assumed minimal values consistent with the constraints imposed on the system. To undo the minimization state, work must be executed, or, as a special case, material must be transferred across the boundaries of the system. On this basis, we may reiterate earlier statements by identifying the equilibrium state as that for which the appropriate thermodynamic function of state (depending on the various applicable constraints) is at a minimum, except for entropy, which is at a maximum. Again, any displacement from this state requires a relaxation of the constraints and/or performance of work and/or transfer of matter across boundaries. We later indicate how functions of state may be found via caloric equations. 

It is not our intention to discuss here the application of theorem (ii) as applied to particular cases known from empirical observations of real processes (see, e.g. [202]) but, instead, we proceed further making use of a well established connection between entropy and information [205]. Accordingly, the information has a character of negative entropy (i.e., we can write / = -q) and therefore, in the old-to-new provisional terminology, we can identity the production of caloric with the destruction of information and the flux of caloric with the information flux in an opposite direction. Theorem (ii) can thus be reformulated in terms of information as... 

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