﻿R. 
  deSaiissure 
  — 
  Graphical 
  Thermodynamics. 
  45 
  

  

  This 
  form 
  of 
  the 
  thermodynamic 
  function 
  applies 
  only 
  to 
  the 
  

   case 
  in 
  which 
  the 
  specific 
  heats 
  are 
  constant. 
  

  

  In 
  the 
  general 
  case, 
  the 
  specific 
  heats 
  vary 
  with 
  the 
  physical 
  

   state 
  of 
  the 
  substance 
  ; 
  but 
  as 
  this 
  variation 
  is 
  always 
  compara- 
  

   tively 
  small, 
  the 
  sheet 
  of 
  paper 
  can 
  be 
  divided 
  into 
  a 
  sufficient 
  

   number 
  of 
  regions, 
  so 
  that 
  either 
  one 
  of 
  the 
  specific 
  heats 
  of 
  

   the 
  substance 
  may 
  be 
  regarded 
  as 
  constant 
  inside 
  of 
  any 
  one 
  of 
  

   these 
  regions. 
  Then 
  the 
  equations 
  given 
  above 
  will 
  hold 
  true, 
  

   provided 
  that 
  the 
  specific 
  heat 
  be 
  given 
  a 
  special 
  value 
  for 
  

   each 
  region. 
  

  

  Another 
  method 
  consists 
  in 
  finding 
  first 
  the 
  value 
  of 
  the 
  

   specific 
  heat 
  in 
  terms 
  of 
  the 
  volume 
  and 
  the 
  temperature 
  ; 
  

   since 
  the 
  variation 
  of 
  c 
  is 
  slow, 
  it 
  will 
  be 
  sufficient 
  to 
  take 
  only 
  

   in 
  consideration 
  the 
  first 
  and 
  second 
  powers 
  of 
  F~and 
  T, 
  so 
  

   that 
  it 
  can 
  always 
  be 
  assumed 
  that 
  : 
  

  

  c 
  = 
  a 
  + 
  bV 
  + 
  kT+dT 
  + 
  eVT+fV 
  2 
  

  

  a, 
  b, 
  k, 
  etc., 
  being 
  constant 
  coefficients 
  determined 
  empirically. 
  

   The 
  differential 
  equation 
  to 
  the 
  curves 
  of 
  constant 
  volume 
  

   being 
  still 
  : 
  

  

  ( 
  C 
  _K)^ 
  = 
  K^ 
  

  

  or, 
  by 
  replacing 
  c 
  by 
  its 
  value 
  : 
  

  

  p»y 
  + 
  /y.-K 
  +k+er+dy 
  y 
  T 
  = 
  K 
  J 
  

  

  We 
  shall 
  obtain 
  by 
  integration, 
  V 
  being 
  constant 
  : 
  

  

  ( 
  a 
  +bV+fV 
  2 
  -K) 
  log 
  T+(&+eV)T-|-4dT 
  2 
  — 
  Klogs-|- 
  constant. 
  

  

  ws 
  

   Replacing 
  T 
  by 
  its 
  value 
  ^=, 
  the 
  result 
  will 
  be 
  the 
  equation 
  

  

  of 
  the 
  curves 
  of 
  constant 
  volume, 
  involving 
  only 
  one 
  unknown 
  

   constant, 
  which 
  can 
  be 
  determined 
  by 
  the 
  method 
  given 
  above. 
  

  

  Conclusion. 
  

  

  15. 
  The 
  object 
  we 
  have 
  been 
  trying 
  to 
  fulfill 
  in 
  this 
  short 
  

   study, 
  was 
  to 
  determine 
  which 
  is 
  the 
  best 
  system 
  of 
  coordi- 
  

   nates 
  to 
  adopt 
  in 
  graphical 
  representations 
  of 
  thermodynamical 
  

   phenomena. 
  Evidently, 
  the 
  best 
  system 
  is 
  the 
  one 
  in 
  which 
  

   the 
  value 
  of 
  each 
  variable 
  depending 
  upon 
  the 
  phenomenon 
  

   can 
  be 
  obtained 
  graphically 
  ; 
  hence', 
  each 
  one 
  of 
  these 
  variables 
  

   must 
  be 
  represented 
  by 
  a 
  geometrical 
  magnitude 
  depending 
  

   only 
  upon 
  the 
  form 
  and 
  position 
  of 
  the 
  path 
  described 
  by 
  the 
  

   substance 
  with 
  respect 
  to 
  said 
  system 
  of 
  coordinates. 
  

  

  The 
  system 
  of 
  coordinates 
  <p, 
  s 
  seems 
  to 
  possess 
  this 
  property 
  

   to 
  a 
  higher 
  degree 
  than 
  the 
  system 
  P, 
  V, 
  which 
  is 
  usually 
  

   adopted 
  and 
  known 
  as 
  Clapeyron's 
  system. 
  

  

  