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  423 
  ] 
  

  

  XLVII. 
  On 
  a 
  Law 
  of 
  Molecular 
  Attraction. 
  

   By 
  J. 
  W- 
  Mbllob, 
  D.Sc. 
  {JST.Z.)*. 
  

  

  'HE 
  term 
  — 
  which 
  occurs 
  in 
  the 
  well-known 
  van 
  der 
  

  

  Waals-Budde 
  equation 
  of 
  state, 
  

  

  (p+$* 
  

  

  was 
  added 
  by 
  van 
  der 
  Waals 
  in 
  order 
  to 
  provide 
  for 
  the 
  

   diminished 
  outward 
  pressure 
  p 
  of 
  the 
  gas 
  caused 
  by 
  mole- 
  

   cular 
  attractions, 
  a 
  is 
  a 
  constant. 
  

  

  Let 
  us 
  assume 
  van 
  der 
  Waals' 
  correction 
  to 
  be 
  an 
  approxi- 
  

   mate 
  representation 
  o£ 
  the 
  magnitude 
  of 
  the 
  molecular 
  

   attraction. 
  

  

  The 
  total 
  work 
  of 
  expansion 
  W 
  is, 
  therefore, 
  

  

  W' 
  = 
  j 
  (p+ 
  C 
  ^)dv= 
  \p 
  . 
  dv 
  + 
  j| 
  dv. 
  

  

  The 
  first 
  term 
  \p.dv 
  represents 
  the 
  external 
  work 
  of 
  ex- 
  

   pansion, 
  while 
  the 
  second 
  term 
  gives 
  the 
  internal 
  work 
  of 
  

   expansion. 
  That 
  is, 
  the 
  work 
  W 
  done 
  against 
  molecular 
  

   force 
  when 
  a 
  gas 
  expands 
  from 
  a 
  volume 
  i\ 
  to 
  a 
  volume 
  v 
  2 
  , 
  

   is 
  

  

  W=|J>=«(J--I) 
  (1) 
  

  

  It 
  is 
  apparent 
  that 
  this 
  expression 
  represents 
  the 
  internal 
  

   work 
  done 
  when 
  a 
  liquid 
  expands 
  into 
  a 
  very 
  great 
  volume 
  

   of 
  its 
  vapour, 
  and 
  it 
  is 
  a 
  simple 
  matter 
  to 
  evaluate 
  the 
  con- 
  

   stant 
  a 
  when 
  the 
  latent 
  heat 
  of 
  vaporization 
  f 
  of 
  the 
  given 
  

   substance 
  is 
  known. 
  v 
  x 
  then 
  represents 
  the 
  volume 
  of 
  the 
  

   liquid, 
  v 
  2 
  the 
  volume 
  of 
  the 
  vapour. 
  

  

  For 
  the 
  sake 
  of 
  fixing 
  our 
  ideas, 
  consider 
  a 
  volume 
  of 
  gas 
  

   containing 
  two 
  molecules 
  at 
  a 
  distance 
  r 
  apart. 
  Since 
  r 
  is 
  

   linear, 
  the 
  volume 
  of 
  the 
  gas 
  will 
  vary 
  as 
  r 
  3 
  . 
  Let 
  

  

  where 
  c 
  is 
  the 
  constant 
  of 
  variation. 
  From 
  (1), 
  therefore, 
  

  

  c 
  V'V 
  >Y7 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  ~\ 
  See 
  van 
  't 
  Hoff's 
  Vorlesungen, 
  iii. 
  p. 
  55 
  (1900). 
  

  

  