November 20, 1903.] 



SCIENCE. 



655 



Examples. — A gas is allowed to sweep 

 throujrh an orifice and increase in volume 

 from f to F with imperceptible change of 

 temperature. The same gas is then ex- 

 panded slowly in a cylinder from volume 

 V to volume V without change of tempera- 

 ture. To prevent change of temperature 

 heat must be given to the gas at each step 

 of the expansion (dH positive), and there- 

 fore the sum (I'dH/T) is positive. 



A gas is heated at constant volume by 

 the degeneration of work into heat. The 

 same result may be accomplished reversibly 

 by heating the gas slowly on a stove. In 

 this latter process dH is positive at each 

 step and the sum (I'dH/T) extended over 

 the slow heating process is positive. 



The creation of an external compensating 

 degeneration (decrease of entropy) when 

 the effect of a sweeping process is repaired 

 by a reversible process may be expressed 

 by the entropj-^ change of external sub- 

 stances. Thus in each of the above ex- 

 amples the reversible process involves the 

 taking of heat from external substances so 

 that the sum (idH/T) is negative as ap- 

 plied to the external changes which are 

 involved in the reversible processes men- 

 tioned, or in other words, external sub- 

 stances suffer an increase of entropy when 

 a given substance has its entropy decreased 

 by a reversible process. 



In general the thermodynamic degener- 

 ation associated with a sweeping process 

 can be represented as an increase of entropy 

 (summation of dE/T as above explained) 

 only by devising a reversible process which 

 produces the same change as the given 

 sweep so far as the substance under con- 

 sideration is concerned. In the case of 

 steady sweeps, however, it is not necessary 

 to devise a reversible process for producing 

 the same result in order to represent the 

 result of a steady sweep as an increase of 

 entropy. The entropy increase which is 

 associated with a steady sweep may be de- 



rived from a consideration of the reversible 

 processes which always accompany a steady 

 sweep, using Clausius's summation IdR/T, 

 as follows : 



Consider the slow flow of heat from a 

 body A at temperature T^ to a body B at 

 temperature T^. The transfer of heat be- 

 ing slow, the cooling of A and the heating 

 of B are reversible processes, and A and B 

 are at each instant in thermal equilibrium. 



While an amount of heat 2? is trans- 

 ferred the decrease of entropy of body A 

 is }:dH/T =-E/Ti and the increase of 

 entropy of body B is ldn/T = E/T^, so 

 that the net increase of entropy due to the 

 steady sweep is {E/T„ — E/T^). 



Consider a fine wire submerged in a 

 large vessel of water at temperature T, 

 heat being slowly generated in the wire by 

 an electric current. Then the water will 

 be at each instant in thermal equilibrium, 

 that is, the heating of the water will be a 

 reversible process to which Clausius's sum- 

 mation may be applied. Thus, while the 

 water receives an amount of heat W (meas- 

 ured in terms of the work lost in the wire), 

 the value of ^dW/T will be W/T, which 

 is the increase of entropy of the water. In 

 this case there is no decrease of entropy 

 anywhere ; so that W/T measures the ther- 

 modjaiamic degeneration involved in the 

 conversion of the work TF into heat at tem- 

 perature T. 



Absolute Values of Eniropr/. — 'Entropy 

 changes or entropy differences only have 

 real physical significance. However, a 

 certain state of a sub.stance may be arbi- 

 trarily chosen as a zero state or reference 

 state and the absolute value of the entropy 

 of the substance in any other given state 

 may be defined as the value of Clausius's 

 summation extended over any reversible 

 process leading from the zero state to the 

 given state. This is equivalent to assign- 

 ing arbitrarily the value zero to the en- 

 tropy of the substance in the zero state. 



