Equivalence of heat and work

The first law is closely related to the conservation of energy (Section A) and is a consequence of it. The first law implies the equivalence of heat and work as means of transferring energy, but heat is a concept that occurs only when we are considering the properties of systems composed of large numbers of particles. The concept of heat does not occur in the description of single particles. 

The work of Carnot, published in 1824, and later the work of Clausius (1850) and Kelvin (1851), advanced the formulation of the properties of entropy and temperature and the second law. Clausius introduced the word entropy in 1865. The first law expresses the qualitative equivalence of heat and work as well as the conservation of energy. The second law is a qualitative statement on the accessibility of energy and the direction of progress of real processes. For example, the efficiency of a reversible engine is a function of temperature only, and efficiency cannot exceed unity. These statements are the results of the first and second laws, and can be used to define an absolute scale of temperature that is independent of ary material properties used to measure it. A quantitative description of the second law emerges by determining entropy and entropy production in irreversible processes. 

Principle of the equivalence of heat and work.—The usefulness of the preceding principle becomes greatly limited from... 

Extendon of the principle of the equivalence of heat and work to an unclosed cycle.— The principle of the equivalence between heat and work, such as we have stated it in Art. 19, requires that the modification to which it is desired to apply it is a closed cycle this restriction is sometimes embarrassing we shall obviate this by modifying the statement of the principle. 

This proposition bears the name of the principle of the con-servation of energy. It is quite uimecessary to assign to it a vague metaph3rsic sense or a mysterious origin it is simply a special case of a physical law, the law of the equivalence of heat and work. 

Gases which obey Mariotte s Law. Absolute temperature.— Before applying the principle of the equivalence of heat and work to the various problems of chemical calorimetry, we shall make an application which we shall employ in what follows. 

But if we denote by W the kinetic energy of the system in a given state, by U the internal energy in this same state, by the work done by the external forces during the modification considered, the principle of the equivalence of heat and work gives [Chap. II, eq. (4)]... 

These experiments show no more than that the mechanical equivalent of heat, determined in various ways by converting work into heat or vice versa, is roughly constant. There are considerable differences in the values found by the various methods, so that these experiments cannot be regarded as proving the law of the exact equivalence of heat and work. It might still be possible that the amount of work done in producing the unit of heat should vary slightly with the method by which... 

Entrojiy and probability. The recognition of the universal applicability of the law of the conservation of energy is partly based on the mechanical conception of heat as motion of the ultimate particles of matter. If heat, energy, and kinetic energy of the molecules are essentially of the same nature, and are differentiated from one another only by the units in which we measure them, the validity of the law of the equivalence of heat and work is explained. At first sight, however, it is not easy to understand why heat cannot be converted completely into work, or, in other words, why the conversion of heat into work is an irreversible process (second law of thermodynamics). In pure mechanics we deal only with perfectly reversible processes. By the principles of mechanics the complete conversion of heat into work should be just as possible as the conversion... 

From experience, we know that work can be changed to heat (e.g. heating of the liquid at mixing). There is thus an equivalence of work W and heat Q W = J Q, where / is a physical quantity called the mechanical equivalent of heat and its value and the dimensions are J = 4.184 J/cal (J is the unit of heat and work called Joule). This is the principle of equivalency of heat and work. 

Tnble 1.5-1 E.%periniems Designed to Prove the Energy Equivalence of Heat and Work... 

Beginning in 1844, Clapeyron taught the course on steam engines at the Ecole Nationale des Fonts et Chaussees near Paris, the oldest French engineering school. In this course, surprisingly, he seldom mentioned his theory of heat engines based on Carnot s work." He eventually embraced the equivalence of heat and work established by Joule s experiments." ... 

Clausius Rudolf Julius Emmanuel (1822-1888) Ger. math., reconciled Carnot s theory of heat to equivalence of heat and work (2nd Law of thermodynamics), changes of state (Clausius-Clapeyron equation), contributed theory of electrolysis... 

Mayer (von) Julius Robert (1814—1878) Ger. phys., determined quantitatively equivalence of heat and work, studied principle of conservation laws even extended to living and cosmic phenomena Mayow John (1641-1679) Brit, chem., studied similarity between chem. process of combustion and physiological function... 

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