THERMOCHEMISTRY. 213 THERMODYNAMICS. of a more economic use of coal the question must naturally arise. How much mechanical work could possibly be obtained altogether by burn- ing a certain amount of coal, supposing that an ideally perfect device were employed for the purpose? The direct measurement of the maxi- mum work, although theoretically possible, could not be actually carried out. But the maximum work of a reaction can be readily calculated, with the aid of thermodynamics, if the concentra- tions of the reacting substances and their prod- ucts, when in the state of chemical equilibrium, are known. In the case of the combustion of coal the equilibrium-concentrations have been determined by indirect measurement, and on the basis of this Nernst has calculated approxi- matelj' the ma.ximum work of the combustion for three different temperatures: If 12 grams of carbon were burned at the absolute zero ( — 273° C. ), the equivalent of 97,650 calories might be obtained; at 18° C. the maximum work would be equivalent to 01.470 calories; at 1000° C. the equivalent of only 70.625 calories can be ob- tained ; this in spite of the fact that the heat given off bv the combustion is practically the same at all temperatures, viz. 07,650 calories. Only at the absolute zero of temperature could the heat produced by the combustion of coal be entirely transformed into mechanical work. In conclusion, a few words must be said with reference to an erroneous principle that has gained somewhat wide acceptance among chem- ists — viz. Berthelot's principle, according to which it is the heat produced by a reaction, and not the maximum possible mechanical work, that measures the cause of the reaction ; and of two re- actions that might take place in a given system, the one accompanied by the greatest evolution of heat must necessarily take place. This principle holds good often, but not always, and so cannot be looked upon as a law of nature. The most important argument against it is that, were it unlimited in its application, as Berthelot claims it to be, reversible reactions would be'impossible ; for one of a pair of reversible reactions not only does not develop heat, but necessarily absorbs heat ; and hence, if Berthelot's principle were correct, that reaction could not take place at all, and its opposite reaction would be complete. See Reaction, Chemical. The principal names connected with experi- mental thermochemistry are those of Hess, Julius Thomsen, Berthelot, and Stohmann. The first to apply the principles of thermodynamics to chemical phenomena was Horstmann. The problem was next taken up by Dr. Gibbs, of Yale University, whose thorough and original treatment of the subject remained unkno«Ti for a number of years. The importance of Van 't Hoff's thermo-chemical work may be readily seen from the present sketch. Finally, Le Chatelier, Planck. Riecke. and Duheni have made note- worthy contributions to the mathematical treat- ment of the subject. Bibliography. Thomson, Thermochemische TJntersuchtinffen (Leipzig. 1882-86) ; Berthelot, Thei-mochimie (Paris, 1897) ; id., Trnite pra- tique de calorimftrie chimique (ib., 189.3) ; Muir and Wilson, The Elements of Thermal Chemistry (London. 1885) : .Jahn, Die (IrundsHtze der Thermochemie (Vienna, 1892) ; Planck. Grund- riss der allgemeinen Thermochemie (Breslau, 189.3) ; Naumann, Thermochemie (Brunswick, 1892). Consult also the literature of theoretical and physical chemistry recommended in the article Che.mistrv. THERMO-COUPLE, THERMOPILE. See THKRMO-KLKCTRIcnY. THERMODYNAMICS (from Cik. eip^tj, therme, heat + Sifa/ui, dyiimnisi, power). The application of the principles of mechanics to heat-phenomena. It is shown in the article Heat that all heat-effects can be traced for their cause to work having been done against the molec- ular forces of the body — e.g. friction, compression, etc. — or to the reception of energy by the minute portions of the body — e.g. radiation, conduction, etc. In short, it may be regarded as proved ex- perimentally that heat-effects always accom- pany changes in the intrinsic energy of a body; and the idea that the numerical value of the heat-effects depends on the energy added to the minute portions of the body and on that alone is now accepted by every one. If a small amount of energy AQ is added to a body, its intrinsic energy is changed (dU) and as a rule a certain amount of external work is done by the expan- sion of the body {pdv, where p is the external pressure on the body and dr is the change in volume). By the conservation of energy, then, if no other work is done, &Q—dU+pdv. This is sometimes called the 'first principle of thermodynamics.' In any form of heat engine — e.g. a steam en- gine — the 'working substance,' water, starts at ordinary temperature ; heat-energy is added to it by the boiler; it reaches a high temperature, that of the boiler, and a high pressure ; it ex- pands, doing work in pushing out the piston; its temperature and its pressure therefore fall ; the 'cylinder' is now joined to the 'condenser.' and the steam passes out and is condensed to water, giving up heat-energy ; the piston is drawn back and the process is repeated. So far as the heat-energy and work are concerned, heat-en- fii'gy (Qi) at a high temperature has been given to the working substance, heat-energy (Q.) at a low temperature is taken away from it, external work (W) is done. By the first principle of thermodynamics W = Q, — Q,, if we assume that the water at the end of its cycle of changes has the same energy that it had at the beginning. The 'efficiency' of the process is defined as the W Qi— Q, ratio ^ or — ^ — =. In considering the efficiencies of various processes Carnot in 1824 was led to imagine one which bears his name and which can be discus.sed theoretically. This process is one which consists of a working substance in- closed in a cylinder with a movable piston pass- ing around a cycle so as to return to its initial condition. There are supposed to be two large reservoirs of a liquid, at different temperatures. The cylinder containing the working substance at a high pressure and small volume is imagined placed in the high-temperature tank ; the sub- stance is allowed to expand, so slowly that its temperature remains practically unchanged at that of the surrounding liquid in the tank; in doing this. heat-energ;s' must flow into the work- ing substance, otherwise its temperature would
