﻿M. 
  deSaussure 
  — 
  Graphical 
  Thermodynamics. 
  43 
  

  

  Let 
  us 
  suppose 
  first 
  that 
  the 
  specific 
  heat 
  at 
  constant 
  volume 
  

   of 
  the 
  substance 
  is 
  constant, 
  as 
  is 
  the 
  case 
  for 
  a 
  certain 
  num- 
  

   ber 
  of 
  bodies, 
  and 
  let 
  us 
  find 
  what 
  would 
  be 
  in 
  this 
  hypothesis, 
  

   the 
  general 
  equation 
  of 
  the 
  curves 
  of 
  constant 
  volume. 
  By 
  

   putting 
  V 
  = 
  constant 
  or 
  dV= 
  in 
  equation 
  (12) 
  and 
  replac- 
  

   ing 
  — 
  by 
  : 
  1 
  , 
  we 
  shall 
  obtain 
  the 
  differential 
  equation 
  : 
  

  

  T 
  

  

  . 
  ^.dCp 
  r.TT\dS 
  

  

  (c—K)— 
  + 
  (c— 
  2K)— 
  = 
  

   v 
  ' 
  Cp 
  v 
  ' 
  s 
  

  

  Integrating 
  and 
  denoting 
  the 
  arbitrary 
  constant 
  by 
  JV, 
  the 
  

   general 
  equation 
  to 
  the 
  curves 
  of 
  constant 
  volume 
  is 
  : 
  

  

  On 
  the 
  other 
  hand 
  : 
  <ps 
  = 
  KTE 
  is 
  the 
  general 
  equation 
  of 
  

   the 
  isothermals. 
  The 
  value 
  of 
  the 
  constant 
  JV 
  depends 
  only 
  

   upon 
  the 
  volume 
  V, 
  so 
  that 
  as 
  soon 
  as 
  the 
  experimental 
  data 
  

   V 
  and 
  T 
  are 
  given, 
  these 
  equations 
  will 
  furnish 
  the 
  corre- 
  

   sponding 
  value 
  of 
  <p 
  and 
  s, 
  provided 
  however 
  that 
  the 
  value 
  of 
  

   the 
  constant 
  N 
  be 
  known 
  for 
  any 
  given 
  value 
  of 
  the 
  volume 
  V. 
  

  

  This 
  determination 
  can 
  be 
  made 
  as 
  follows 
  : 
  let 
  V 
  Q 
  and 
  T 
  

   be 
  the 
  experimental 
  data 
  corresponding 
  to 
  the 
  initial 
  state 
  of 
  

   the 
  substance. 
  The 
  point 
  representing 
  7 
  

  

  this 
  state, 
  is 
  on 
  the 
  isothermal 
  : 
  <ps 
  = 
  , 
  

   KT 
  E 
  ; 
  but 
  it 
  can 
  be 
  chosen 
  anywhere 
  

   on 
  this 
  isothermal, 
  because 
  the 
  three 
  

   equations 
  to 
  the 
  thermodynamic 
  surface 
  

   involve 
  always 
  an 
  arbitrary 
  constant, 
  as 
  

   seen 
  in 
  the 
  case 
  of 
  a 
  perfect 
  gas. 
  Let 
  

   A 
  be 
  the 
  chosen 
  point 
  (fig. 
  7) 
  ; 
  ^ 
  and 
  

   s 
  , 
  its 
  coordinates 
  ; 
  then 
  the 
  value 
  of 
  

   the 
  constant 
  JY, 
  corresponding 
  to 
  the 
  

   initial 
  value 
  of 
  the 
  volume, 
  is 
  given 
  by 
  

   the 
  equation 
  : 
  

  

  Let 
  the 
  substance 
  describe 
  any 
  path, 
  such 
  as 
  AB 
  and 
  let 
  V 
  

   and 
  T 
  be 
  the 
  experimental 
  data 
  corresponding 
  to 
  any 
  point, 
  

   such 
  as 
  B 
  ; 
  the 
  coordinates 
  <p 
  and 
  6' 
  of 
  this 
  point 
  will 
  be 
  deter- 
  

   mined 
  by 
  the 
  intersection 
  of 
  the 
  two 
  curves 
  : 
  

  

  DBT: 
  g>s 
  = 
  KT^ 
  ) 
  

  

  and 
  EBN: 
  ^- 
  K 
  s 
  c 
  - 
  2K 
  =N 
  [ 
  

  

  N 
  being 
  given 
  a 
  value 
  corresponding 
  to 
  that 
  of 
  the 
  volume 
  T 
  7 
  / 
  

   to 
  find 
  this 
  value 
  of 
  JY, 
  it 
  must 
  be 
  noticed 
  that 
  the 
  isothermals 
  

   AET 
  , 
  DBT 
  and 
  the 
  curves 
  of 
  constant 
  volume 
  ADN„ 
  EBN, 
  

   form 
  a 
  curved 
  quadrilateral 
  AEBD, 
  whose 
  area 
  is 
  equal 
  to 
  

   the 
  external 
  work 
  done 
  by 
  the 
  substance, 
  if 
  it 
  were 
  made 
  to 
  

  

  