94 Prof. Clausius on the Internal Work 



If we now apply this equation to a perfect gas, the specific 

 heat under constant volume is in this case to be regarded as the 

 true specific heat, and this gives the increase in the quantity of 

 heat actually present in the gas ; for here no heat is consumed 

 in work, since external work is only performed when increase of 

 volume occurs, and internal work has no existence in the case of 

 perfect gases. We may therefore regard cdT as identical with 

 dH. We have further, for the perfect gases, the equation 



where R is a constant, and thence we get 



-£Ldc= — dv = Hd .log v. 

 di v 



Equation (6) is thus transformed into 



rfQ=rfH + ARTrf.logt; (7) 



This equation agrees, disregarding the difference in the sign of 

 dQ, (which is caused only by the different way in which we have 

 chosen to employ the signs + and — in this case), with equa- 

 tion (4), and the function there represented by the general sym- 

 bol Z has, in this particular case, the form AR log v. 



Rankine, who has written several interesting memoirs on the 



transformation of heat into work*, has in like manner proposed 



to transform equation (6), which in its original form applies to 



perfect gases only f, so as to render it applicable to other bodies, 



, and writes (only with slightly different letters) 



dQ=kdT + ATdY, (8) 



where k denotes the true specific heat of the body, and F is a 



magnitude in the determination of which Rankine appears to 



have been led chiefly by the circumstance mentioned above, that 



dp 

 the quantity -~ dv which occurs in equation (6) represents the 



increase of external work which accompanies an infinitely small 

 alteration of state under increased temperature. Rankine defines 

 the magnitude F as " the rate of variation of effective work with 

 temperature;" and denoting the external work which the body 

 can do in passing, at a given temperature, from a given former 

 state into its present condition, by U, he puts 



F= ZT ( 9 ) 



In the discussion which immediately follows, of the casein which 



* Philosophical Magazine, S. 4. vol. v. p. 106; Edinburgh New Philo- 

 sophical Journal, vol. ii. p. 120; Manual of the Steam-engine, 

 t Manual of the Steam-engine, p. 310. 



