﻿172 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  equal 
  to 
  that 
  consumed 
  during 
  the 
  evaporation 
  ; 
  for 
  as 
  the 
  sum 
  of 
  the 
  expansive 
  

   and 
  compressive 
  powers, 
  and 
  of 
  those 
  dependent 
  on 
  molecular 
  arrangement 
  during 
  

   the 
  whole 
  process, 
  is 
  equal 
  to 
  zero, 
  so 
  must 
  the 
  sum 
  of 
  the 
  quantities 
  of 
  heat 
  

   absorbed 
  and 
  evolved. 
  

  

  The 
  heat 
  of 
  liquefaction, 
  at 
  a 
  given 
  temperature, 
  is 
  therefore 
  equal 
  to 
  that 
  

   of 
  evaporation, 
  with 
  the 
  sign 
  reversed. 
  

  

  (18.) 
  If 
  to 
  the 
  latent 
  heat 
  of 
  evaporation 
  at 
  a 
  given 
  temperature, 
  is 
  added 
  the 
  

   quantity 
  of 
  heat 
  necessary 
  to 
  raise 
  unity 
  of 
  weight 
  of 
  the 
  liquid 
  from 
  a 
  certain 
  

   fixed 
  temperature 
  (usually 
  that 
  of 
  melting 
  ice) 
  to 
  the 
  temperature 
  at 
  which 
  the 
  

   evaporation 
  takes 
  place, 
  the 
  result 
  is 
  called 
  the 
  total 
  heat 
  of 
  evaporation 
  from 
  the 
  

   fixed 
  temperature 
  chosen. 
  

  

  According 
  to 
  the 
  theory 
  of 
  Carnot, 
  this 
  quantity 
  is 
  called 
  the 
  constituent 
  

   heat 
  of 
  vapour 
  ; 
  and 
  it 
  is 
  conceived, 
  that 
  if 
  liquid 
  at 
  the 
  temperature 
  of 
  melting 
  

   ice 
  be 
  raised 
  to 
  any 
  temperature 
  and 
  evaporated, 
  and 
  finally 
  brought 
  in 
  the 
  state 
  

   of 
  vapour 
  to 
  a 
  certain 
  given 
  temperature, 
  the 
  whole 
  heat 
  expended 
  will 
  be 
  equal 
  

   to 
  the 
  constituent 
  heat 
  corresponding 
  to 
  that 
  given 
  temperature, 
  and 
  will 
  be 
  the 
  

   same, 
  whatsoever 
  may 
  have 
  been 
  the 
  intermediate 
  changes 
  of 
  volume, 
  or 
  the 
  tem- 
  

   perature 
  of 
  actual 
  evaporation. 
  

  

  According 
  to 
  the 
  mechanical 
  theory 
  of 
  heat, 
  on 
  the 
  other 
  hand, 
  the 
  quantity 
  

   of 
  heat 
  expended 
  must 
  vary 
  with 
  the 
  intermediate 
  circumstances 
  ; 
  for 
  otherwise 
  

   no 
  power 
  could 
  be 
  gained 
  by 
  the 
  alternate 
  evaporation 
  and 
  liquefaction 
  of 
  a 
  fluid 
  

   at 
  different 
  temperatures. 
  

  

  (19.) 
  The 
  law 
  of 
  the 
  latent 
  and 
  total 
  heat 
  of 
  evaporation 
  is 
  immediately 
  

   deducible 
  from 
  the 
  principle 
  of 
  the 
  constancy 
  of 
  the 
  total 
  vis 
  viva 
  in 
  the 
  two 
  forms 
  

   of 
  heat 
  and 
  expansive 
  power, 
  when 
  the 
  body 
  has 
  returned 
  to 
  its 
  primitive 
  density 
  

   and 
  temperature, 
  as 
  already 
  laid 
  down 
  in 
  Article 
  7. 
  

  

  That 
  principle, 
  when 
  applied 
  to 
  evaporation 
  and 
  liquefaction, 
  may 
  be 
  stated 
  

   as 
  follows 
  : 
  — 
  

  

  Let 
  a 
  portion 
  of 
  fluid 
  in 
  the 
  liquid 
  state 
  be 
  raised 
  from 
  a 
  certain 
  temperature 
  

   to 
  a 
  higher 
  temperature 
  : 
  let 
  it 
  be 
  evaporated 
  at 
  the 
  higher 
  temperature 
  : 
  let 
  the 
  

   vapour 
  then 
  be 
  allowed 
  to 
  expand, 
  being 
  maintained 
  always 
  at 
  the 
  temperature 
  

   of 
  saturation 
  for 
  its 
  density, 
  until 
  it 
  is 
  restored 
  to 
  the 
  original 
  temperature, 
  at 
  

   which 
  temperature 
  let 
  it 
  be 
  liquefied 
  : 
  — 
  then 
  the 
  excess 
  of 
  the 
  heat 
  absorbed 
  by 
  the 
  

   fluid 
  above 
  the 
  heat 
  given 
  out, 
  mill 
  be 
  equal 
  to 
  the 
  expansive 
  power 
  generated. 
  

  

  To 
  represent 
  those 
  operations 
  algebraically, 
  — 
  let 
  the 
  lower 
  absolute 
  tempe- 
  

   rature 
  be 
  t 
  : 
  — 
  the 
  volume 
  of 
  unity 
  of 
  weight 
  of 
  liquid 
  at 
  that 
  temperature, 
  v 
  , 
  and 
  

   that 
  of 
  vapour 
  at 
  saturation, 
  V 
  : 
  let 
  the 
  pressure 
  of 
  that 
  vapour 
  be 
  P 
  : 
  the 
  latent 
  

   heat 
  of 
  evaporation 
  of 
  unity 
  of 
  weight, 
  L 
  ; 
  and 
  let 
  the 
  corresponding 
  quantities 
  

   for 
  the 
  higher 
  absolute 
  temperature 
  t 
  v 
  be 
  v 
  v 
  V 
  l5 
  P 
  x 
  , 
  L 
  x 
  . 
  Let 
  K 
  L 
  represent 
  the 
  

   mean 
  apparent 
  specific 
  heat 
  of 
  the 
  substance 
  in 
  the 
  liquid 
  form 
  between 
  the 
  tem- 
  

   peratures 
  t 
  and 
  Tj. 
  Then, 
  — 
  

  

  