Temperature, Heat and Quantitative Laws of Gases

Similarly an entropy density, s T,nk), can be defined. The total energy U, the total entropy S and the tot number of moles of the system then are  

In texts on classical thermodynamics, when it is sometimes stated that the entropy of a nonequilibrium system is not defined, it is meant that S is not a function of the variables U, V and N. If the temperature of the system is locally well defined, then indeed the entropy of a nonequilibrium system can be defined in terms of an entropy density, as in (1.2.3). 

The most insightful use of the thermometer was made by Joseph Black (1728-1799), a professor of medicine and chemistry at Glasgow. Black drew a clear distinction between temperature or degree of hotness, and the quantity of heat. His experiments using the newly developed thermometers established the fundamental fact that, in thermal equilibrium, the temperatures of all the 

Joseph Black (1728-1799) (Courtesy the E. F. Smith Collection, Van Pelt-Dietrich Library, University of Pennsylvania) 

Though the work of Joseph Black and others established clearly the distinction between heat and temperature, the nature of heat remained an enigma for a long time. Whether heat was an indestructible substance, called the caloric, that moved from one substance to another or whether it was a form of microscopic motion, continued to be debated as late as the nineteenth century. Finally it became clear that heat was a form of energy that could be transformed to other forms, and the caloric theory was laid to rest — though we still measure the amount of heat in calories. 

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The quantitative laws of chemical combination provide clear pointers to the molecular theory of matter, which increases progressively in vividness and realism with the application of Newton s laws to the motions of the particles. The interpretation of phenomena such as the pressure and viscosity of gases and the Brownian motion, and the assignment of definite magnitudes to molecular speeds, masses, and diameters render it clear that a continual interchange of energies must occur between the molecules of a material system, a circumstance which lies at the basis of temperature equilibrium and determines what in ordinary experience is called the flow of heat. It is responsible indeed for far more than this, and a large part of physical chemistry follows from the conception of the chaotic motion of the molecules. This matter must now be examined more deeply. 

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