656 



SCIENCE. 



[N. S. Vol. XVIII. No. 4G4. 



The entropy of a substance in a given 

 state is proportional to the mass of the 

 substance, for doubling the mass will 

 double the value of clH for each step of any 

 reversible process. Entropy is, of course, 

 expressed in imits of heat per degree of 

 temperature. 



jBemarfc.— Equation (5), due to Clausius, 

 was further generalized by Clausius so as 

 to apply in his opinion to cyclic processes 

 which are not reversible, in which ease, 

 according to Clausius, equation (5) be- 

 comes 



- y 



'>o. 



This extension of the integral -dE/T 

 to include sweeping processes is incorrect 

 except in so far as steady sweeps are con- 

 cerned as explained above. 



18. SUMMARY. 



The precise idea of temperature is asso- 

 ciated with the notion of thermal equilib- 

 rium, and the precise idea of temperature 

 has nothing to do with the sensations of 

 hot and cold. The electric arc, for ex- 

 ample, is very hot, but it has no tempera- 

 ture. 



The error of Clausius in extending his 

 summation to irreversible processes lies in 

 the fact that in general the idea of tem- 

 perature xitterly fails in such cases, and 

 the summation -dH/T has no meaning 

 whatever. Of course, this summation may 

 always be applied to the reversible changes 

 (when they exist) which take place in the 

 external substances which envelop the 

 substance which is undergoing the irre- 

 versible process. 



Not only is the precise idea of tempera- 

 ture limited to substances in thermal 

 equilibrium, but it applies only to a finite 

 portion of a substance. It is meaningless 

 to speak of the temperature of a molecule. 



There are many cases of steady sweeps, 



such as thermal conduction in a gas, steady 

 electric discharge through a gas, steady 

 radiation from a hot to a cold region, in 

 which the sweeping substance, be it ma- 

 terial or ether, is far from being in thermal 

 equilibrium, although in a permanent or 

 unvarying state. The precise idea of tem- 

 perature is not applicable to such states. 

 Thus radiation in space has no definite 

 temperature unless the space is enclosed in 

 an envelope which is in thermal equilib- 

 rium, in which case the radiation is the 

 normal radiation for the given tempera- 

 tiire, and the space occupied by the radia- 

 tion has, in fact, the same temperature as 

 the adjacent material. 



Wlien normal radiation issues from an 

 aperture in an enclosure it becomes atten- 

 uated as it travels farther and fartlier 

 from the apertiire, and this attenuated 

 radiation (absorption of medium supposed 

 to be nil), although conforming to a sim- 

 ple law of distribution of energy among 

 its various phases, has not a definite tem- 

 perature. Neither does a monochromatic 

 beam of light have a definite, temperature. 



In general, all cases of molecular motion 

 and of ether motion (radiant heat) in 

 which some definite and unvarjdng func- 

 tion exists expressing the distribution of 

 energy among the various phases of the 

 motion, are to be classed as steady sweeps. 

 In all such cases the precise idea of tem- 

 perature is inapplicable to the sweeping 

 substance or space. Still, all such pro- 

 cesses are amenable to precise and sys- 

 tematic treatment. This systematic treat- 

 ment always depends upon a knowledge of 

 the function of distribution of energy 

 among the phases, and the characteristics 

 of the sweeping substance or space are 

 properly described in terms of this func- 

 tion, not in terms of temperature and 

 entropy. 



It is true, however, that a generalized 

 idea of entropy, for example, can be ap- 



