﻿i?. 
  cle 
  Saitssure 
  — 
  Graphical 
  Thermodynamics. 
  41 
  

  

  two 
  equations, 
  the 
  result 
  will 
  be 
  the 
  thermodynamic 
  function 
  

   under 
  the 
  usual 
  form 
  : 
  so 
  that 
  we 
  might 
  say 
  that 
  the 
  thermo- 
  

   dynamic 
  function 
  of 
  any 
  substance 
  expresses 
  the 
  fact 
  that 
  the 
  

   product 
  of 
  the 
  symbolical 
  pressure 
  by 
  the 
  symbolical 
  volume 
  

   is 
  proportional 
  to 
  the 
  absolute 
  temperature. 
  

  

  But 
  the 
  thermodynamic 
  function 
  of 
  perfect 
  gases 
  expresses 
  

   also 
  that 
  the 
  product 
  of 
  the 
  pressure 
  by 
  the 
  volume 
  is 
  propor- 
  

   tional 
  to 
  the 
  absolute 
  temperature. 
  Hence, 
  for 
  perfect 
  gases, 
  

   the 
  symbolical 
  pressures 
  and 
  volumes 
  can 
  be 
  respectively 
  re- 
  

   placed 
  by 
  the 
  ordinary 
  pressures 
  and 
  volumes 
  ; 
  and 
  since 
  there 
  

   is 
  the 
  same 
  relation 
  between 
  the 
  total 
  work 
  and 
  the 
  symbolical 
  

   pressure 
  and 
  volume, 
  as 
  there 
  is 
  between 
  the 
  external 
  work 
  

   and 
  the 
  ordinary 
  pressure. 
  and 
  volume, 
  it 
  follows 
  that 
  for 
  per- 
  

   fect 
  gases 
  the 
  total 
  work 
  is 
  equivalent 
  to 
  the 
  external 
  work, 
  in 
  

   other 
  words 
  there 
  is 
  no 
  internal 
  work 
  in 
  perfect 
  gases. 
  So 
  

   that, 
  for 
  these 
  gases 
  : 
  

  

  fa-/ 
  1 
  

  

  PdY 
  

  

  even 
  when 
  the 
  cycle 
  is 
  not 
  closed. 
  

  

  For 
  the 
  same 
  reason, 
  the 
  curves 
  of 
  constant 
  volume 
  must 
  be 
  

   the 
  same 
  as 
  the 
  curves 
  of 
  constant 
  symbolical 
  volume, 
  i. 
  e., 
  

   they 
  must 
  be 
  straight 
  lines 
  parallel 
  to 
  the 
  axis 
  of 
  <p, 
  for 
  if 
  s 
  be 
  

   constant, 
  els 
  = 
  or 
  : 
  (pels 
  = 
  YdV 
  = 
  0, 
  hence 
  dY 
  = 
  or 
  Y 
  = 
  

   constant. 
  And 
  according 
  to 
  what 
  has 
  been 
  said 
  in 
  the 
  graph- 
  

   ical 
  determination 
  of 
  specific 
  heats, 
  it 
  follows 
  also 
  that 
  the 
  

   specific 
  heat 
  at 
  constant 
  volume 
  of 
  a 
  perfect 
  gas 
  is 
  equal 
  to 
  its 
  

   absolute 
  specific 
  heat 
  : 
  c 
  = 
  K. 
  All 
  these 
  results 
  are 
  well 
  

   known, 
  but 
  as 
  they 
  have 
  been 
  established 
  only 
  by 
  experiment, 
  

   we 
  have 
  tried 
  to 
  show 
  how 
  they 
  are 
  direct 
  consequences 
  of 
  the 
  

   laws 
  of 
  thermodynamics. 
  

  

  Xow 
  that 
  c 
  = 
  K 
  for 
  perfect 
  gases, 
  equation 
  (12) 
  reduces 
  to 
  : 
  

  

  I 
  ds 
  

  

  On 
  the 
  other 
  hand 
  : 
  

   Hence, 
  by 
  substitution 
  : 
  

   and 
  by 
  integration 
  : 
  

  

  1— 
  i 
  f7 
  Z- 
  R 
  

   T~Ef/T"EV 
  

  

  E 
  \~ 
  s 
  

  

  KE 
  

  

  M 
  being 
  an 
  arbitrary 
  constant. 
  We 
  have 
  also, 
  for 
  any 
  sub- 
  

   stance 
  : 
  

  

  