﻿Equilibrium 
  of 
  Heterogeneous 
  Substances. 
  821 
  

  

  given 
  homogeneous 
  mass 
  is 
  a 
  new 
  one, 
  and 
  likely 
  to 
  become 
  

   very 
  important 
  in 
  the 
  theory 
  of 
  chemistry, 
  I 
  shall 
  give 
  

   Professor 
  Gibbs's 
  definition 
  of 
  it. 
  

  

  " 
  If 
  to 
  any 
  homogeneous 
  mass 
  we 
  suppose 
  an 
  infinitesimal 
  

   quantity 
  of 
  any 
  substance 
  added, 
  the 
  mass 
  remaining 
  homo- 
  

   geneous 
  and 
  its 
  entropy 
  and 
  volume 
  remaining 
  unchanged, 
  

   the 
  increase 
  of 
  the 
  energy 
  of 
  the 
  mass, 
  divided 
  by 
  the 
  mass 
  

   of 
  the 
  substance 
  added, 
  is 
  the 
  potential 
  of 
  that 
  substance 
  in 
  

   the 
  mass 
  considered." 
  

  

  These 
  n 
  + 
  2 
  new 
  quantities, 
  the 
  pressure, 
  the 
  temperature, 
  

   and 
  the 
  n 
  potentials 
  of 
  the 
  component 
  substances, 
  form 
  a 
  

   class 
  differing 
  in 
  kind 
  from 
  the 
  first 
  set 
  of 
  variables. 
  They 
  

   are 
  not 
  quantities 
  capable 
  of 
  combination 
  by 
  addition, 
  but 
  

   denote 
  the 
  intensity 
  of 
  certain 
  physical 
  properties 
  of 
  the 
  

   substance. 
  Thus 
  the 
  pressure 
  is 
  the 
  intensity 
  of 
  the 
  ten- 
  

   dency 
  of 
  the 
  body 
  to 
  expand, 
  the 
  temperature 
  is 
  the 
  intensity 
  

   of 
  its 
  tendency 
  to 
  part 
  with 
  heat 
  ; 
  and 
  the 
  potential 
  of 
  any 
  

   component 
  substance 
  is 
  the 
  intensity 
  with 
  which 
  it 
  tends 
  to 
  

   expel 
  that 
  substance 
  from 
  its 
  mass. 
  

  

  We 
  may 
  therefore 
  distinguish 
  between 
  these 
  two 
  classes 
  

   of 
  variables 
  by 
  calling 
  the 
  volume, 
  the 
  entropy, 
  and 
  the 
  

   component 
  masses 
  the 
  magnitudes, 
  and 
  the 
  pressure, 
  the 
  

   temperature, 
  and 
  the 
  potentials 
  the 
  intensities 
  of 
  the 
  system. 
  

  

  The 
  problem 
  before 
  us 
  may 
  be 
  stated 
  thus 
  : 
  — 
  Given 
  a 
  

   homogeneous 
  mass 
  in 
  a 
  certain 
  phase, 
  will 
  it 
  remain 
  in 
  that 
  

   phase, 
  or 
  will 
  the 
  whole 
  or 
  part 
  of 
  it 
  pass 
  into 
  some 
  other 
  

   phase 
  ? 
  

  

  The 
  criterion 
  of 
  stability 
  may 
  be 
  expressed 
  thus 
  in 
  Pro- 
  

   fessor 
  Gibbs's 
  words 
  : 
  — 
  " 
  For 
  the 
  equilibrium 
  of 
  any 
  isolated 
  

   system 
  it 
  is 
  necessary 
  and 
  sufficient 
  that 
  in 
  all 
  possible 
  

   variations 
  of 
  the 
  state 
  of 
  the 
  system 
  which 
  do 
  not 
  alter 
  its 
  

   energy, 
  the 
  variation 
  of 
  its 
  entropy 
  shall 
  either 
  vanish 
  or 
  

   be 
  negative. 
  

  

  " 
  The 
  condition 
  may 
  also 
  be 
  expressed 
  by 
  saying 
  that 
  for 
  

   all 
  possible 
  variations 
  of 
  the 
  state 
  of 
  the 
  system 
  which 
  do 
  not 
  

   alter 
  its 
  entropy, 
  the 
  variation 
  of 
  its 
  energy 
  shall 
  either 
  

   vanish 
  or 
  be 
  negative." 
  

  

  Professor 
  Gibbs 
  has 
  made 
  a 
  most 
  important 
  contribution 
  

   to 
  science 
  by 
  giving 
  us 
  a 
  mathematical 
  expression 
  for 
  the 
  

   stability 
  of 
  any 
  given 
  phase 
  (A) 
  of 
  matter 
  with 
  respect 
  to 
  

   any 
  other 
  phase 
  (B). 
  

  

  If 
  this 
  expression 
  for 
  the 
  stability 
  (which 
  we 
  may 
  denote 
  

   by 
  the 
  letter 
  K) 
  is 
  positive, 
  the 
  phase 
  A 
  will 
  not 
  of 
  itself 
  

   pass 
  into 
  the 
  phase 
  B, 
  but 
  if 
  it 
  is 
  negative 
  the 
  phase 
  A 
  will 
  

   of 
  itself 
  pass 
  into 
  the 
  phase 
  B, 
  unless 
  prevented 
  by 
  passive 
  

   resistances. 
  

  

  