﻿28 
  

  

  R. 
  de 
  Saussure 
  — 
  Graphical 
  Thermodynamics. 
  

  

  and 
  s 
  can 
  always 
  be 
  regarded 
  as 
  two 
  variables 
  defined 
  by 
  the 
  

  

  equations 
  : 
  <p 
  = 
  --• 
  and 
  s 
  = 
  7ra 
  2 
  , 
  whatever 
  be 
  their 
  physical 
  

  

  nature 
  ; 
  moreover, 
  we 
  shall 
  find 
  other 
  reasons 
  for 
  regarding 
  <p 
  

   as 
  a 
  pressure 
  and 
  sasa 
  volume. 
  

  

  Properties 
  of 
  the 
  graphical 
  method. 
  

  

  7. 
  Let 
  M 
  be 
  the 
  point 
  representing 
  any 
  physical 
  state 
  of 
  a 
  

   substance, 
  and 
  <p 
  and 
  s 
  its 
  coordinates, 
  then 
  according 
  to 
  the 
  

   previous 
  definitions 
  : 
  

  

  a 
  = 
  y 
  — 
  and 
  i 
  = 
  y 
  — 
  

  

  9 
  

  

  So 
  that 
  a 
  and 
  i, 
  hence 
  the 
  state 
  of 
  the 
  vibratory 
  motion, 
  are 
  

   readily 
  obtained 
  from 
  the 
  actual 
  value 
  of 
  the 
  coordinates 
  of 
  

   point 
  M. 
  

  

  Denoting 
  by 
  R 
  the 
  total 
  work 
  absorbed 
  during 
  a 
  transforma- 
  

   tion, 
  we 
  have 
  found 
  that 
  : 
  

  

  dK 
  = 
  2fda 
  = 
  cpds 
  

  

  Whence 
  by 
  integration 
  : 
  

  

  R 
  — 
  / 
  cpds 
  

  

  a 
  

  

  i. 
  e., 
  if 
  AB 
  be 
  the 
  curve 
  (fig. 
  1) 
  representing 
  the 
  path 
  of 
  the 
  

   substance 
  referred 
  to 
  the 
  coordinates 
  <p 
  and 
  s, 
  the 
  total 
  work 
  

   (external 
  and 
  internal) 
  absorbed 
  during 
  

   the 
  transformation 
  is 
  equal 
  to 
  the 
  area 
  

   AabB 
  limited 
  by 
  the 
  path, 
  the 
  axis 
  of 
  s 
  

   and 
  the 
  two 
  extreme 
  ordinates. 
  

  

  Comparing 
  this 
  result 
  with 
  the 
  prop- 
  

   erty 
  of 
  Clapeyron's 
  graphical 
  method, 
  we 
  

   see 
  that 
  the 
  symbolical 
  pressure 
  and 
  the 
  

   symbolical 
  volume 
  are 
  in 
  the 
  same 
  rela- 
  

   tion 
  with 
  the 
  total 
  work, 
  as 
  the 
  ordinary 
  

   pressure 
  and 
  volume 
  are 
  with 
  the 
  external 
  

   work. 
  

   8. 
  The 
  last 
  of 
  equations 
  (8) 
  : 
  

  

  ^5 
  = 
  KTE 
  

   holding 
  true 
  for 
  all 
  substances, 
  shows 
  that 
  the 
  area 
  of 
  the 
  rec- 
  

   tangle 
  MmOn 
  formed 
  by 
  the 
  coordinates 
  <p 
  and 
  s, 
  is 
  equal 
  to 
  

   the 
  actual 
  amount 
  of 
  energy 
  contained 
  in 
  the 
  substance 
  at 
  the 
  

   physical 
  state 
  M. 
  Thus, 
  if 
  AB 
  represents 
  the 
  path 
  of 
  the 
  

   substance 
  the 
  area 
  of 
  the 
  rectangles 
  AaOa 
  and 
  BbOfi 
  is 
  equal 
  

   to 
  the 
  energy 
  of 
  the 
  heat 
  contained 
  in 
  the 
  substance 
  at 
  its 
  

   initial 
  and 
  final 
  states. 
  

  

  