carnot's theory of the motive power of heat. 567 



From this result we draw the following conclusion : — 



47. Equal volumes of all elastic fluids, when rMmpressed to smaller equal 

 volumes, disengage equal quantities of heat. 



This extremely remarkable theorem of Carnot's was independently laid down 

 as a probable experimental law by Dulong, in his " Recherches sur la Chaleur 

 Specifique des Fluides Elastiques," and it therefore affords a most powerful con- 

 firmation of the theory.* 



48. In some very remarkable researches made by Mr Joule upon the heat 

 developed by the compression of air, the quantity of heat produced in different 

 experiments has been ascertained with reference to the amount of work spent in 

 the operation. To compare the results which he has obtained with the indi- 

 cations of theory, let us determine the amount of work necessary actually to pro- 

 duce the compression considered above. 



49. In the first place, to compress the gas from the volume v+dvtov, the 

 work required is, pdv, or, since p v =p^ «„ (1 + E <), 



„ -_ . rf e 



Hence, if we denote by W the total amount of work necessary to produce the 

 compression from V to V, we obtain, by integration, 



W=jB„«„(l + E01ogy,, 



Comparing this with the expression above, we find 



^=^i(^> (11) 



50. Hence we infer that 



(1.) The amount of work necessary to produce a unit of heat by the compres- 

 sion of a gas, is the same for all gases at the same temperature. 



(2.) And that the quantity of heat evolved in all circumstances, when the 

 temperature of the gas is given, is proportional to the amount of work spent in 

 the compression. 



* Caenot varies the statement of his theorem, and illustrates it in a passage, pp. 52, 53, of 

 which the following is a translation : — 



" When a gas varies in volume without any change of temperature, the quantities of heat absorbed 

 or evolved by this gas are in arithmetical progression, if the augmentation or diminutions of volume 

 are in geometrical progression. ^ j ■ i, if 



" When we compress a litre of air maintained at the temperature 10 , and reduce it to halt 

 a litre, it disengages a certain quantity of heat. If, again, the volume he reduced from half a litre 

 to a quarter of a litre, from a quarter to an eighth, and so on, the quantities of heat successively 

 evolved will he the same. 



" If, in place of compressing the air, we allow it to expand to two litres, four litres, eight litres, 

 &c., it will be necessary to supply equal quantities of heat to maintain the temperature always at the 

 same degree." 



