﻿46 
  P. 
  deSaussure 
  — 
  Graphical 
  Thermodynamics. 
  

  

  It 
  is 
  true 
  that 
  in 
  the 
  latter 
  system, 
  the 
  location 
  of 
  the 
  point 
  

   representing 
  any 
  state 
  of 
  the 
  substance, 
  is 
  obtained 
  directly 
  

   from 
  the 
  experimental 
  data 
  P 
  and 
  V, 
  while 
  in 
  the 
  system 
  <p, 
  s 
  

   the 
  point 
  has 
  to 
  be 
  located 
  by 
  a 
  more 
  or 
  less 
  indirect 
  way 
  ; 
  but 
  

   when 
  the 
  path 
  of 
  the 
  substance 
  has 
  been 
  traced 
  in 
  Clapeyron's 
  

   system, 
  it 
  does 
  not 
  give 
  any 
  information 
  relating 
  to 
  the 
  phe- 
  

   nomena 
  (except 
  the 
  value 
  of 
  the 
  external 
  work, 
  but 
  this 
  work 
  

   can 
  usually 
  be 
  computed 
  without 
  difficulty) 
  ; 
  if 
  it 
  is 
  desired 
  to 
  

   know 
  more 
  about 
  the 
  transformation, 
  it 
  is 
  necessary 
  to 
  trace 
  

   first 
  all 
  the 
  isothermals 
  and 
  adiabatics 
  ; 
  this 
  is 
  a 
  long 
  work, 
  

   these 
  curves 
  being 
  irregular 
  curves 
  in 
  the 
  system 
  P, 
  V. 
  On 
  

   the 
  contrary, 
  when 
  <p 
  and 
  s 
  are 
  chosen 
  as 
  coordinates, 
  the 
  path 
  

   itself 
  is 
  sufficient 
  to 
  give 
  any 
  information 
  concerning 
  the 
  phe- 
  

   nomenon, 
  because 
  the 
  various 
  physical 
  variables 
  depending 
  

   upon 
  the 
  transformation 
  are 
  given 
  by 
  geometrical 
  magnitudes 
  

   determined 
  by 
  the 
  path 
  itself, 
  and 
  also 
  because 
  the 
  isothermals 
  

   R 
  and 
  adiabatics, 
  instead 
  of 
  being 
  irregu- 
  

  

  lar, 
  are 
  geometrical 
  curves 
  whose 
  equa- 
  

   tions 
  are 
  known, 
  being 
  the 
  same 
  for 
  any 
  

   substance 
  ; 
  so 
  that 
  the 
  curves 
  : 
  cps 
  = 
  

   constant, 
  and 
  : 
  <ps*=- 
  constant, 
  need 
  to 
  

   be 
  traced 
  but 
  once 
  for 
  all 
  ; 
  they 
  can 
  be 
  

   reproduced 
  as 
  many 
  times 
  as 
  necessary 
  

   by 
  the 
  blue-print 
  process 
  or 
  by 
  any 
  

   other 
  printing 
  process. 
  

  

  The 
  use 
  of 
  the 
  coordinates 
  <p 
  and 
  s 
  

   ~~ 
  s 
  simplifies 
  also 
  the 
  demonstration 
  of 
  

   most 
  of 
  the 
  theorems 
  of 
  thermody- 
  

   namics 
  ; 
  let 
  us 
  take, 
  as 
  an 
  example, 
  Carnot's 
  theorem. 
  

  

  If 
  a 
  substance 
  describes 
  a 
  closed 
  path 
  formed 
  by 
  two 
  adia- 
  

   batics 
  AD, 
  GB 
  (fig. 
  8) 
  and 
  by 
  two 
  isothermals 
  DG, 
  PA, 
  and 
  

   if 
  the 
  amount 
  of 
  heat 
  absorbed 
  and 
  abandoned 
  by 
  the 
  sub- 
  

   stance 
  be 
  denoted 
  respectively 
  by 
  H 
  x 
  and 
  PT 
  , 
  the 
  expression 
  

  

  XT 
  TT 
  

  

  —~ 
  — 
  °, 
  which 
  is 
  called 
  the 
  economical 
  coefficient 
  of 
  the 
  cycle, 
  

  

  is 
  independent 
  of 
  the 
  nature 
  of 
  the 
  substance, 
  and 
  is 
  equal 
  to 
  

  

  T 
  — 
  T 
  

  

  — 
  l 
  — 
  — 
  -, 
  T 
  and 
  T^ 
  being 
  the 
  temperatures 
  corresponding 
  to 
  

  

  the 
  isothermals. 
  

  

  Since 
  there 
  is 
  no 
  transmission 
  of 
  heat 
  along 
  the 
  adiabatics 
  

   AD 
  and 
  GB, 
  the 
  amounts 
  of 
  heat 
  H 
  x 
  and 
  P 
  Q 
  correspond 
  re- 
  

   spectively 
  to 
  the 
  isothermals 
  DG 
  and 
  BA. 
  We 
  have 
  seen 
  

   that 
  : 
  

  

  = 
  / 
  sdcp 
  + 
  2 
  / 
  q 
  

  

  EU=f 
  sdcp 
  + 
  2/ 
  yds 
  

  

  