﻿( 
  441 
  ) 
  

  

  XXVIII. 
  — 
  On 
  the 
  Computation 
  of 
  the 
  Specific 
  Heat 
  of 
  Liquid 
  Water 
  at 
  various 
  

   Temperatures, 
  from 
  the 
  Experiments 
  of 
  M. 
  Regnault. 
  By 
  William 
  John 
  

   Macquorn 
  Rankine, 
  Civil 
  Engineer, 
  F.R.S.E., 
  F.R.S.S.A., 
  &c. 
  

  

  (Read 
  December 
  15, 
  1851.) 
  

  

  Correction 
  of 
  M. 
  Regnault 
  's 
  Experiments 
  for 
  the 
  Effect 
  of 
  Agitation. 
  

  

  The 
  discovery 
  by 
  Mr 
  Joule 
  of 
  the 
  fact, 
  that 
  mechanical 
  power 
  expended 
  in 
  

   the 
  agitation 
  of 
  liquids 
  is 
  converted 
  into 
  heat 
  as 
  the 
  visible 
  agitation 
  subsides, 
  

   renders 
  a 
  certain 
  correction 
  necessary 
  in 
  calculating 
  the 
  results 
  of 
  experiments 
  

   on 
  specific 
  heat 
  in 
  which 
  such 
  agitation 
  has 
  occurred. 
  

  

  Of 
  this 
  kind 
  are 
  the 
  experiments 
  of 
  M. 
  Regnault 
  on 
  the 
  apparent 
  specific 
  

   heat 
  of 
  liquid 
  water 
  at 
  different 
  temperatures. 
  Water 
  at 
  a 
  high 
  temperature, 
  T 
  3 
  , 
  

   was 
  emitted 
  from 
  a 
  boiler 
  into 
  a 
  calorimeter 
  containing 
  water 
  at 
  a 
  low 
  tempera- 
  

   ture, 
  T 
  p 
  and 
  the 
  resulting 
  intermediate 
  temperature 
  of 
  the 
  whole 
  mass, 
  T 
  2 
  , 
  was 
  

   used 
  as 
  the 
  means 
  of 
  calculating 
  the 
  ratio 
  of 
  the 
  mean 
  specific 
  heat 
  of 
  water 
  be- 
  

   tween 
  T 
  3 
  and 
  T 
  2 
  , 
  to 
  its 
  mean 
  specific 
  heat 
  between 
  T 
  2 
  and 
  T 
  x 
  . 
  Now, 
  the 
  upper 
  

   part 
  of 
  the 
  boiler 
  contained 
  steam 
  at 
  a 
  high 
  pressure, 
  so 
  that 
  the 
  hot 
  water 
  was 
  

   expelled 
  with 
  great 
  force. 
  The 
  vis-viva 
  thus 
  communicated 
  to 
  the 
  water, 
  having 
  

   been 
  converted 
  by 
  fluid 
  friction 
  into 
  heat, 
  ought 
  to 
  be 
  allowed 
  for 
  in 
  computing 
  

   the 
  results 
  of 
  the 
  experiments, 
  

  

  Let 
  W 
  x 
  be 
  the 
  weight 
  of 
  water 
  originally 
  contained 
  in 
  the 
  calorimeter, 
  at 
  the 
  

   temperature 
  T 
  x 
  : 
  

  

  W 
  3 
  , 
  The 
  weight 
  of 
  water 
  introduced 
  into 
  the 
  calorimeter 
  from 
  the 
  boiler, 
  at 
  

   the 
  temperature 
  T 
  3 
  ; 
  

  

  T 
  2 
  , 
  the 
  resulting 
  temperature, 
  corrected, 
  as 
  has 
  been 
  done 
  by 
  M. 
  Regnault, 
  

   for 
  the 
  effect 
  of 
  conduction. 
  

  

  Let 
  K 
  1? 
  2 
  be 
  the 
  mean 
  dynamical 
  specific 
  heat 
  of 
  water 
  between 
  the 
  tempera- 
  

   tures 
  T 
  x 
  and 
  T 
  2 
  , 
  — 
  

  

  K 
  2 
  , 
  3 
  , 
  its 
  mean 
  dynamical 
  specific 
  heat 
  between 
  T 
  2 
  and 
  T 
  3 
  . 
  

  

  Let 
  P 
  be 
  the 
  pressure 
  of 
  steam 
  of 
  saturation 
  at 
  the 
  temperature 
  T 
  3 
  , 
  — 
  

  

  ■us, 
  the 
  pressure 
  of 
  the 
  atmosphere, 
  — 
  

  

  And 
  v, 
  the 
  volume 
  of 
  unity 
  of 
  weight 
  of 
  water 
  at 
  the 
  temperature 
  T 
  3 
  . 
  

  

  Then 
  the 
  following 
  equation 
  must 
  be 
  fulfilled 
  ; 
  — 
  

  

  W 
  x 
  K 
  19 
  2 
  (T 
  2 
  -T 
  1 
  )-W 
  3 
  K 
  2 
  , 
  3 
  (T 
  3 
  -T 
  2 
  )- 
  W 
  3 
  (P-w)t, 
  = 
  : 
  

  

  Consequently, 
  

  

  K 
  2 
  , 
  3 
  _ 
  W 
  1 
  (T 
  2 
  -T 
  1 
  ) 
  (P-m)v 
  

  

  K 
  1 
  , 
  2 
  ~W 
  3 
  (T 
  3 
  -T 
  2 
  ) 
  K 
  152 
  (T 
  3 
  -T 
  2 
  ) 
  ' 
  * 
  • 
  ^ 
  

  

  VOL. 
  XX. 
  PART 
  III. 
  6 
  C 
  

  

  