﻿R. 
  de 
  Saussure 
  — 
  Graphical 
  Thermodynamics. 
  35 
  

  

  The 
  demonstration 
  is 
  based 
  upon 
  the 
  fact 
  that 
  the 
  internal 
  

   work 
  depends 
  only 
  upon 
  the 
  initial 
  and 
  final 
  states 
  of 
  the 
  

   body 
  and 
  not 
  upon 
  the 
  path 
  described, 
  so 
  that 
  the 
  internal 
  

   work 
  along 
  AB 
  is 
  equal 
  to 
  the 
  internal 
  work 
  along 
  A 
  CB 
  ; 
  

   but, 
  by 
  hypothesis, 
  the 
  internal 
  work 
  along 
  CB 
  equals 
  zero 
  ; 
  

   hence, 
  the 
  internal 
  work 
  from 
  A 
  to 
  B 
  is 
  equal 
  to 
  the 
  internal 
  

   work 
  from 
  A 
  to 
  C. 
  On 
  the 
  other 
  hand, 
  the 
  total 
  work 
  from 
  

   A 
  to 
  C 
  is 
  given 
  by 
  the 
  area 
  AacC 
  ; 
  but 
  the 
  external 
  work 
  

   from 
  A 
  to 
  C 
  is 
  equal 
  to 
  zero, 
  since 
  the 
  volume 
  remains 
  con- 
  

   stant 
  along 
  the 
  path 
  AC 
  ; 
  hence 
  the 
  area 
  AacC 
  is 
  also 
  equal 
  to 
  

   the 
  internal 
  work 
  from 
  A 
  to 
  C, 
  which 
  is 
  the 
  same 
  as 
  the 
  inter- 
  

   nal 
  work 
  from 
  A 
  to 
  B, 
  as 
  just 
  seen. 
  

  

  The 
  area 
  AacC 
  giving 
  the 
  internal 
  work 
  / 
  along 
  the 
  path 
  

   AB, 
  the 
  remaining 
  area 
  ACcbB 
  must 
  be 
  equal 
  to 
  the 
  external 
  

   work 
  T 
  along 
  the 
  same 
  path. 
  Since 
  the 
  external 
  work 
  can 
  be 
  

   easily 
  computed 
  in 
  most 
  cases, 
  this 
  demonstration 
  gives 
  us 
  also 
  

   a 
  graphical 
  method 
  for 
  tracing, 
  through 
  any 
  point 
  B, 
  the 
  

   curve 
  defined 
  by 
  the 
  condition 
  d\ 
  = 
  : 
  trace 
  any 
  path 
  BA 
  

   through 
  B, 
  compute 
  the 
  external 
  work 
  from 
  B 
  to 
  A 
  and 
  sub- 
  

   tract 
  it 
  from 
  area 
  AabB 
  ; 
  the 
  result 
  is 
  the 
  internal 
  work 
  from 
  

   B 
  to 
  A 
  ; 
  trace 
  through 
  A 
  the 
  curve 
  of 
  constant 
  volume 
  AC 
  

   and 
  an 
  ordinate 
  cC 
  cutting 
  off 
  an 
  area 
  AacC 
  equal 
  to 
  the 
  in- 
  

   ternal 
  work 
  previously 
  computed. 
  The 
  point 
  C 
  thus 
  obtained 
  

   is 
  a 
  point 
  of 
  the 
  required 
  curve. 
  Other 
  points 
  can 
  be 
  found 
  

   in 
  the 
  same 
  way, 
  by 
  moving 
  point 
  A 
  on 
  the 
  curve 
  BA. 
  Since 
  

   the 
  path 
  BA 
  is 
  arbitrary, 
  it 
  must 
  be 
  chosen 
  so 
  that 
  the 
  ex- 
  

   ternal 
  work 
  can 
  be 
  easily 
  computed 
  ; 
  for 
  instance, 
  if 
  BA 
  be 
  

   the 
  curve 
  of 
  constant 
  pressure 
  passing 
  through 
  B, 
  then 
  the 
  

   external 
  work 
  : 
  

  

  fPdV 
  = 
  pfdV 
  = 
  P(V 
  A 
  - 
  V.) 
  

  

  Remark: 
  When 
  the 
  path 
  described 
  by 
  point 
  M 
  is 
  a 
  closed 
  

   cycle, 
  the 
  area 
  enclosed 
  by 
  it 
  is 
  equal 
  to 
  the 
  total 
  work 
  ab- 
  

   sorbed 
  by 
  the 
  substance 
  ; 
  but, 
  since 
  the 
  final 
  state 
  is 
  the 
  same 
  

   as 
  the 
  initial 
  state, 
  the 
  internal 
  work 
  is 
  equal 
  to 
  zero 
  ; 
  hence 
  

   said 
  area 
  is 
  also 
  equal 
  to 
  the 
  external 
  work 
  done 
  by 
  the 
  sub- 
  

   stance, 
  as 
  this 
  is 
  the 
  case 
  in 
  Clapeyron's 
  graphical 
  representa- 
  

   tion 
  where 
  P 
  and 
  T^are 
  taken 
  as 
  coordinates 
  ; 
  this 
  result 
  can 
  

   be 
  expressed 
  by 
  the 
  equation 
  : 
  

  

  Ccpds 
  =/] 
  

  

  FdV 
  

  

  which 
  applies 
  only 
  to 
  a 
  closed 
  cycle. 
  We 
  shall 
  soon 
  express 
  

   the 
  same 
  equation 
  under 
  a 
  different 
  form. 
  

  

  