﻿908 
  On 
  some 
  Relations 
  in 
  Capillarity. 
  

  

  liquid 
  and 
  vapour 
  respectively. 
  AVhen 
  a 
  gram 
  of 
  the 
  liquid 
  

   in 
  contact 
  with 
  its 
  saturated 
  vapour 
  is 
  raised 
  ^T 
  in 
  tempe- 
  

   rature, 
  the 
  internal 
  energy 
  absorbed 
  is 
  S^t^T. 
  Let 
  one 
  gram 
  

   of 
  the 
  liquid 
  evaporate. 
  The 
  energy 
  absorbed 
  is 
  L 
  + 
  f?L, 
  

   where 
  L 
  denotes 
  the 
  internal 
  latent 
  heat 
  at 
  the 
  temperature 
  T. 
  

   Let 
  the 
  temperature 
  be 
  now 
  lowered 
  by 
  (iT, 
  adjusting 
  the 
  

   pressure 
  so 
  that 
  the 
  vapour 
  remains 
  saturated. 
  The 
  internal 
  

   energy 
  given 
  out 
  by 
  the 
  vapour 
  is 
  S"^T. 
  Let 
  one 
  gram 
  of 
  

   the 
  vapour 
  be 
  now 
  condensed, 
  the 
  heat 
  given 
  out 
  is 
  L. 
  The 
  

   substance 
  has 
  been 
  taken 
  through 
  a 
  complete 
  cycle 
  and 
  the 
  

   algebraic 
  sum 
  of 
  the 
  internal 
  energy 
  absorbed 
  is 
  therefore 
  

   zero. 
  Hence 
  

  

  S'^T4-L 
  + 
  £/L 
  = 
  S'OT 
  + 
  L, 
  

  

  or 
  ^,, 
  ^, 
  dh 
  

  

  Integrating, 
  

  

  \ 
  S'OT-l 
  S^<iT=LT,-LT 
  

  

  Jt, 
  Jt, 
  

  

  which 
  may 
  be 
  written 
  

  

  S''t,T2~S^t,T2=Ltj 
  — 
  Lt^, 
  (6) 
  

  

  where 
  S'tjT 
  and 
  S''t,T2 
  denote 
  the 
  change 
  in 
  the 
  internal 
  

   energy 
  of 
  a 
  gram 
  of 
  liquid 
  and 
  of 
  its 
  saturated 
  vapour 
  

   respectively 
  when 
  the 
  temperature 
  is 
  raised 
  from 
  Tj 
  to 
  Tg, 
  

   Lt. 
  and 
  Ltj 
  denote 
  the 
  latent 
  heats 
  at 
  those 
  temperatures. 
  

  

  W 
  hen 
  T2 
  is 
  the 
  critical 
  temperature, 
  Lt^ 
  is 
  zero, 
  and 
  the 
  

   equation 
  becomes 
  

  

  Lt, 
  = 
  S"t,t2~ 
  S 
  T,T2» 
  

  

  The 
  values 
  of 
  Lt, 
  and 
  Lig 
  can 
  be 
  obtained 
  from 
  equation 
  (1). 
  

   Combining 
  this 
  with 
  equation 
  (6) 
  we 
  get 
  the 
  difference 
  of 
  

   the 
  energies 
  in 
  terms 
  of 
  the 
  quantities 
  involved 
  in 
  equation 
  (1). 
  

   B 
  can 
  be 
  found 
  for 
  any 
  liquid, 
  and 
  is 
  the 
  same 
  for 
  all 
  liquids 
  

   at 
  corresponding 
  states, 
  while 
  the 
  values 
  of 
  Ca 
  for 
  eight 
  

   common 
  elements 
  are 
  given 
  at 
  the 
  head 
  of 
  Table 
  I. 
  This 
  

   illustrates 
  the 
  application 
  of 
  equation 
  (1). 
  

  

  The 
  value 
  of 
  L 
  may 
  of 
  course 
  be 
  deduced 
  from 
  the 
  common 
  

   thermodynamic 
  equation 
  given 
  at 
  the 
  beginning 
  of 
  this 
  paper 
  

  

  when 
  p, 
  Vi, 
  ^2, 
  T, 
  and 
  -^ 
  are 
  know^n. 
  Cases 
  may 
  arise 
  when 
  

  

  the 
  values 
  of 
  these 
  quantities 
  are 
  not 
  all 
  known, 
  but 
  the 
  

   values 
  of 
  m 
  and 
  p 
  maybe 
  obtainable; 
  in 
  such 
  cases 
  L 
  may 
  be 
  

   found 
  from 
  equation 
  (1). 
  

  

  Cambridge, 
  October 
  30, 
  1909. 
  

  

  