﻿R. 
  de 
  Saussure 
  — 
  Graphical 
  Thermodynamics. 
  

  

  29 
  

  

  Since 
  the 
  energy 
  of 
  the 
  heat 
  : 
  KTE 
  is 
  proportional 
  to 
  the 
  

   temperature 
  T, 
  we 
  can 
  also 
  say 
  that 
  the 
  area 
  of 
  the 
  rectangle 
  

   MO 
  is 
  proportional 
  to 
  the 
  temperature 
  of 
  the 
  substance 
  at 
  the 
  

   state 
  M. 
  

  

  When 
  a 
  substance 
  undergoes 
  a 
  transformation, 
  its 
  tempera- 
  

   ture 
  being 
  maintained 
  constant, 
  the 
  second 
  member 
  of 
  the 
  

   equation 
  <ps 
  = 
  KTE 
  remains 
  constant. 
  Hence, 
  the 
  general 
  

   equation 
  of 
  the 
  isothermal 
  lines 
  is 
  : 
  

  

  <p 
  = 
  constant 
  

  

  which 
  is 
  the 
  equation 
  of 
  equilateral 
  hyperbolas, 
  whose 
  asymp- 
  

   totes 
  coincide 
  with 
  the 
  axes 
  of 
  coordinates. 
  The 
  isothermal 
  

   lines 
  are 
  the 
  same 
  for 
  all 
  substances, 
  since 
  the 
  equation 
  : 
  <ps 
  = 
  

   KTE 
  applies 
  to 
  any 
  substance. 
  

  

  a 
  2 
  

   Remark 
  : 
  As 
  cps 
  = 
  tt 
  2 
  — 
  = 
  KTE, 
  we 
  see 
  that 
  the 
  ratio 
  of 
  the 
  

  

  square 
  of 
  the 
  amplitude 
  to 
  the 
  square 
  of 
  the 
  period 
  of 
  the 
  

   vibratory 
  motion 
  of 
  the 
  heat, 
  is 
  proportional 
  to 
  the 
  tempera- 
  

   ture 
  ; 
  so 
  that 
  this 
  ratio 
  remains 
  constant 
  as 
  long 
  as 
  the 
  tempera- 
  

   ture 
  of 
  the 
  body 
  is 
  maintained 
  constant. 
  

  

  9. 
  The 
  amount 
  of 
  heat, 
  dH, 
  absorbed 
  during 
  an 
  elementary 
  

   transformation, 
  is 
  composed 
  of 
  two 
  parts 
  : 
  1st, 
  the 
  variation 
  of 
  

   the 
  actual 
  amount 
  of 
  heat 
  contained 
  in 
  the 
  substance, 
  which 
  

  

  amount 
  equals--^/ 
  2d, 
  the 
  heat 
  absorbed 
  by 
  the 
  total 
  work 
  

  

  done 
  during 
  the 
  elementary 
  transformation, 
  which 
  is 
  dR 
  = 
  

  

  Hence 
  : 
  E<^H 
  = 
  d(cps) 
  + 
  cpds 
  

  

  Or 
  : 
  EdR 
  = 
  sdcp 
  + 
  2 
  cpds 
  ( 
  9) 
  

  

  Whence, 
  for 
  a 
  finite 
  transformation 
  : 
  

  

  EH 
  = 
  / 
  sdcp 
  + 
  2 
  / 
  cpds 
  

  

  We 
  see 
  from 
  this 
  equation, 
  that 
  the 
  amount 
  of 
  

   sary 
  to 
  let 
  the 
  substance 
  describe 
  a 
  certain 
  

   path 
  AB 
  (fig. 
  2) 
  is 
  proportional 
  to 
  the 
  area 
  

   Aa^B 
  plus 
  twice 
  the 
  area 
  AabB 
  (both 
  of 
  

   these 
  areas 
  being 
  determined 
  by 
  the 
  path 
  

   AB). 
  

  

  When 
  a 
  substance 
  undergoes 
  a 
  'transfor- 
  

   mation 
  without 
  transmission 
  of 
  heat, 
  the 
  

   path 
  described 
  is 
  called 
  an 
  " 
  adidbatic 
  " 
  or 
  

   " 
  isentropic 
  line." 
  This 
  path 
  is 
  determined 
  

   by 
  the 
  condition 
  : 
  

  

  dn= 
  

  

  neces- 
  

  

  Or 
  

  

  sdcp 
  + 
  2 
  cpds 
  = 
  

  

  6 
  S 
  

  

  