﻿42 
  R. 
  deSaussure 
  — 
  Graphical 
  Thermodyna 
  

  

  mics. 
  

  

  T— 
  **~ 
  

   ~"KE 
  

  

  Substituting 
  these 
  values 
  of 
  Fand 
  Tin 
  the 
  thermodynamic 
  

   function 
  : 
  PV 
  = 
  RT, 
  it 
  

  

  R 
  

  

  cps 
  

  

  MKE 
  

  

  TCF 
  

  

  Finally, 
  if 
  we 
  put 
  — 
  - 
  = 
  a 
  for 
  abreviation, 
  the 
  thermodynamic 
  

  

  function 
  of 
  perfect 
  gases, 
  expressed 
  in 
  terms 
  of 
  <p 
  and 
  s, 
  is 
  : 
  

  

  P= 
  ^~ 
  a 
  

  

  { 
  Y=Ms 
  a 
  

   T— 
  *!L 
  

  

  Remarks 
  : 
  By 
  differentiating 
  the 
  second 
  of 
  these 
  equations 
  

   and 
  multiplying 
  the 
  result 
  by 
  the 
  first 
  one, 
  we 
  see 
  that 
  T 
  > 
  dY= 
  

   (pds 
  as 
  stated 
  above. 
  The 
  equation 
  Y= 
  Ms 
  a 
  shows 
  that 
  the 
  

   volume 
  of 
  a 
  perfect 
  gas 
  happens 
  to 
  be 
  independent 
  of 
  cp, 
  i. 
  e., 
  

   of 
  the 
  period 
  of 
  the 
  vibratory 
  motion. 
  In 
  other 
  words, 
  the 
  

   amplitude 
  a 
  keeps 
  the 
  same 
  value 
  as 
  long 
  as 
  the 
  volume 
  

   remains 
  the 
  same 
  (V 
  being 
  constant 
  when 
  s 
  or 
  a 
  is 
  constant). 
  

   This 
  is 
  not 
  true 
  of 
  other 
  substances, 
  as 
  in 
  the 
  general 
  case, 
  the 
  

   expression 
  of 
  V 
  involves 
  <p 
  as 
  well 
  as 
  s(Y 
  = 
  g(<p 
  y 
  s) 
  ). 
  This 
  

   example 
  shows 
  how 
  the 
  thermodynamic 
  function 
  can 
  be 
  ex- 
  

   pressed 
  in 
  terms 
  of 
  cp 
  and 
  s, 
  when 
  it 
  is 
  already 
  known 
  under 
  

   the 
  usual 
  form 
  : 
  F(P, 
  Y, 
  T) 
  = 
  0. 
  » 
  In 
  general, 
  this 
  problem 
  

   consists 
  in 
  transforming 
  the 
  given 
  equation 
  F(P, 
  V, 
  T) 
  = 
  

   into 
  three 
  others 
  giving 
  the 
  value 
  of 
  _P, 
  V 
  and 
  T 
  in 
  terms 
  of 
  

   two 
  auxiliary 
  variables 
  <p 
  and 
  <?, 
  which 
  must 
  satisfy 
  the 
  condi- 
  

   tions 
  found 
  above 
  : 
  

  

  vs 
  = 
  KTE 
  

   cWdY_dYdP__ 
  

   dcp 
  ds 
  dcp 
  ds 
  

  

  Let 
  us 
  examine 
  now 
  the 
  case 
  in 
  which 
  the 
  thermodynamic 
  

   function 
  is 
  entirely 
  unknown. 
  In 
  Clapeyron's 
  graphical 
  pro- 
  

   cess, 
  the 
  path 
  described 
  by 
  a 
  substance 
  can 
  always 
  be 
  traced 
  on 
  

   the 
  paper 
  by 
  measuring 
  directly 
  the 
  volume 
  and 
  the 
  pressure 
  

   for 
  a 
  sufficient 
  number 
  of 
  points 
  along 
  the 
  path, 
  whether 
  the 
  

   thermodynamic 
  function 
  be 
  known 
  or 
  not. 
  When 
  <p 
  and 
  s 
  are 
  

   chosen 
  as 
  coordinates 
  the 
  position 
  of 
  the 
  point 
  corresponding 
  

   to 
  any 
  physical 
  state 
  of 
  the 
  substance 
  can 
  also 
  be 
  determined 
  

   directly 
  from 
  experimental 
  data. 
  

  

  