478 TEE POPULAR SCIENCE MONTHLY 



Helmholtz-Kelvin statement of the first and second laws as conservation 

 and dissipation of energy enables us to apply these principles in the 

 broadest and most philosophical way. Lord Kelvin extended the 

 application of the second law to cosmic physics and, with Boltz- 

 mann, to predictions as to the ultimate thermal death of the earth. 

 Meanwhile Clausius, Maxwell and Boltzmann began to apply the 

 second law to the kinetic theory of gases, a phase of the subject 

 which belongs essentially to the last stage of its development. Maxwell 

 in particular emphasized the important point that since the heat 

 of a body is the kinetic energy of its molecular motions, the 

 second law is in reality not a mathematical but a statistical truth. 

 It can not, says Maxwell, be reduced to a form as axiomatic as that of 

 the first law, but stands upon a lower plane of probability, because it 

 depends upon the motions of millions of molecules of which we can 

 not get hold of a single one.^"* Could we reduce ourselves to molecular 

 dimensions, and with the gift of molecular vision trace the movements 

 of individual molecules, the distinction between work and heat would 



Thomson's " available energy," with the statement that Clausius meant by it 

 that part of the energy which can not be converted into work. As Gibbs pointed 

 out, this is entirely incorrect. The entropy of a body is a definite physical 

 property of the body itself, and can not be measured by the same unit as energy. 

 If dQ represent the amount of heat imparted to a body at any point and T its 

 absolute temperature at that point, Clausius has shown that dQ/T represents the 

 infinitesimal change of entropy at that point for any given moment. The total 

 (fliange of entropy of any reversible chemical system in passing from an initial 

 state a to a final state 6 would then be 



. C^dQ 



and for a reversible (Carnot) cycle the mathematical statement of the second 

 law is the " Carnot-Clausius equation " : 



/(f) 



0. 



This means that the positive and negative entropies of the system in passing 

 from a to 6 and in reversing backwards from 6 to a must balance each other. 

 Or as Gibbs has expressed it, " The second law requires ( for a reversible cycle ) 

 that the algebraic sum of all the heat received from external bodies, divided, 

 each portion thereof, by the absolute temperature at which it is received shall 

 be zero." The criterion of irreversible processes is the " inequality of Clausius " 



sm 



<o 



which implies that the phenomenon will proceed irrevocably or irreversibly in a 

 definite direction, entropy increasing or available energy dissipating to a maxi- 

 mum until a final state of rest or equilibrium (uniformly distributed tempera- 

 ture) is attained. Reversible thermodynamics deals, then, with equations; irre- 

 versible thermodynamics with inequalities, because in reversible processes the 

 total entropy of a system remains unchanged while in irreversible processes it 

 continually increases. 



^'^ Maxwell, Nature, London, 1877-8, XVII., 279. 



