254 PRINCIPLES OF THE MECHANICAL THEORY OF HEAT. 



But if heat can be generated by meclianical power, so inversely must heat he 

 competent to j)roduce mechanical effects, and, in fact, according to the mechanical 

 theory of heat, one heat unit must be regarded as capable of performing the work 

 of 424 metre-kilograms, or, in other words, for each metre-kilogram of work per- 

 formed 0.002358 units of heat must be expended. 



This equivalent results, in the first place, theoretically, if we assume as known 

 the ratio of the specific heat of gases, under constant pressure and in constant 

 volume, as well as the coefficients of the expansion of the gases. One cubic 

 metre of air at 0°, under ordinaiy atmospheric pressure, weighing 1.293 kilogram 

 must be heated to 273° C, if, with unaltered volume, its elasticity be augmented to 

 two atmospheres. But for this are required, 



273 X 1.293 X 0.1686 = 59 units of heat, 



since 0,1686 is the specific heat of air with constant volume. But if one cubic 

 metre of air at 0°, with atmospheric pressure, be raised to the temperature of 

 273° 0., while, with constant pressure, it is free to expand, its volume will be 

 increased to two cubic metres, and the quantity of heat necessary, therefore, is 



273 X 1.293 X 0.2377=83 units of heat, 



since 0.2377 is the specific heat of air with constant pressure. The difference, 

 83 — 59 = 24 units of heat, is thus necessary, over and above the increase of 

 temperature, to expand the gas, under constant pressure, to double the volume. 

 Let us now inquire into the quantity of mechanical work thereby performed. 

 Let us conceive the above-mentioned quantity of air enclosed in a hollow cylin- 

 der, having a transverse section of one square metre, and confined above by a 

 moving piston, which, at its starting point, is elevated one metre above the immov- 

 able floor. On this piston the atmosphere bears with a pressure of 10333 kilo- 

 grams. If the enclosed air, with unaltered pressure, be now expanded to a 

 double volume, it must necessarily push the piston one metre, which corresponds 

 to a mechanical work of 10,333 kilogram-metres. Thus to execute a mechanical 

 work of 10333 metre-kilograms, 24 units of heat are necessary ; hence one unit 



10333 

 of heat coiTesponds to a mechanical work of =430 kilogram-metres, a 



result which so nearly coincides with that obtained in the inverse way, namely, 

 b}'^ conversion of mechanical work into heat, that no doubt of the complete reci- 

 jDrocity between mechanical work and heat can longer exist. 



The experiments and observations above recited have served to establish the 

 proposition that " /« all cases in which ivorh is xjroduced by heat, a quantity of 

 heat proportional to the worlt produced disappears or is consumed, and that inversely 

 the same quantity of heat may he generated by the expenditure of an equal amount 

 of ivorlc;" a proposition which is usually received as the fii'st law of the mechan- 

 ical theory of heat, and which, with this degree of precision and generality, was 

 first enunciated by Clausius. It is the proposition which forms the starting point 

 of the mathematical development of the mechanical theory of heat, and in regard 

 to it the learned have furnished us with a series of articles in PoggendorfF's An- 

 nalen. These articles, accompanied by annotations by Friedrich Vieweg and 

 son, have recently (1865) appeared at Brunswick in a single volume. 



Besides Clausius ; Holzmann, Clapeyron, W. Thomson, Rankine, and others 

 have occupied themselves with the mathematical development of the mechanical 

 theory of heat, while Zeuner may claim the merit of having collected in a clear 

 and comprehensive fonn the leading characteristics of the theory and of having 

 illustrated it by manifold applications, (Grundzilge der mechanischen Wcirme- 

 tJieorie, 1st edition, 1860, 2d, 1866, Leipzig.) Another highly acceptable work 

 on this important subject is the Theoric mecanique de la chaleur, by Hirn, (2d 

 edition, Paris, 1865,) in which, together with the analytic development, the 

 experimental part is very thoroughly treated. 



